sample_id,family_id,paper,citation_key,classification,assessment,raw_bibliography,original_records,original_evidence_urls,secondary_locator_evidence,coverage_note,citing_source_url,bibliography_line,claim_verdict,nearby_claim,claim_assessment,claim_source_abstracts
R001,015,Equidistribution-of-Prime-Degree-Torus-Packets-with-Arbitrary-Local-Type-September-24-2026,EKL2006,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{EKL2006,
  author = {Einsiedler, Manfred and Katok, Anatole and Lindenstrauss, Elon},
  title = {Invariant measures and the set of exceptions to {Littlewood}'s conjecture},
  journal = {Annals of Mathematics},
  volume = {164}, number = {2}, year = {2006}, pages = {513--560},
  doi = {10.4007/annals.2006.164.513}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.4007/annals.2006.164.513"", ""title"": [""Invariant measures and the set of exceptions to Littlewood’s conjecture""], ""authors"": [{""given"": ""Manfred"", ""family"": ""Einsiedler"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}, {""given"": ""Anatole"", ""family"": ""Katok"", ""sequence"": ""additional"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}, {""given"": ""Elon"", ""family"": ""Lindenstrauss"", ""sequence"": ""additional"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""Annals of Mathematics"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2006, 9, 1]]}, ""container_title"": [""Annals of Mathematics""], ""url"": ""https://doi.org/10.4007/annals.2006.164.513"", ""license"": [], ""source_url"": ""https://api.crossref.org/works/10.4007%2Fannals.2006.164.513""}}]",https://api.crossref.org/works/10.4007%2Fannals.2006.164.513,"[{""doi"": ""10.4007/annals.2006.164.513"", ""title"": ""Invariant measures and the set of exceptions to Littlewood’s conjecture"", ""biblio"": {""volume"": ""164"", ""issue"": ""2"", ""first_page"": ""513"", ""last_page"": ""560""}, ""publication_year"": 2006, ""openalex_id"": ""W2102029381""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Equidistribution-of-Prime-Degree-Torus-Packets-with-Arbitrary-Local-Type-September-24-2026/build/references.bib#L34,34,,,,[]
R002,015,Equidistribution-of-Prime-Degree-Torus-Packets-with-Arbitrary-Local-Type-September-24-2026,ELMV2011,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{ELMV2011,
  author = {Einsiedler, Manfred and Lindenstrauss, Elon and Michel, Philippe and Venkatesh, Akshay},
  title = {Distribution of periodic torus orbits and {Duke}'s theorem for cubic fields},
  journal = {Annals of Mathematics},
  volume = {173}, number = {2}, year = {2011}, pages = {815--885},
  doi = {10.4007/annals.2011.173.2.5}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.4007/annals.2011.173.2.5"", ""title"": [""Distribution of periodic torus orbits and Duke's theorem for cubic fields""], ""authors"": [{""given"": ""Manfred"", ""family"": ""Einsiedler"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}, {""given"": ""Elon"", ""family"": ""Lindenstrauss"", ""sequence"": ""additional"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}, {""given"": ""Philippe"", ""family"": ""Michel"", ""sequence"": ""additional"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}, {""given"": ""Akshay"", ""family"": ""Venkatesh"", ""sequence"": ""additional"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""Annals of Mathematics"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2011, 3, 1]]}, ""container_title"": [""Annals of Mathematics""], ""url"": ""https://doi.org/10.4007/annals.2011.173.2.5"", ""license"": [], ""source_url"": ""https://api.crossref.org/works/10.4007%2Fannals.2011.173.2.5""}}]",https://api.crossref.org/works/10.4007%2Fannals.2011.173.2.5,"[{""doi"": ""10.4007/annals.2011.173.2.5"", ""title"": ""Distribution of periodic torus orbits and Duke's theorem for cubic fields"", ""biblio"": {""volume"": ""173"", ""issue"": ""2"", ""first_page"": null, ""last_page"": null}, ""publication_year"": 2011, ""openalex_id"": ""W2115929736""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Equidistribution-of-Prime-Degree-Torus-Packets-with-Arbitrary-Local-Type-September-24-2026/build/references.bib#L18,18,,,,[]
R003,015,Equidistribution-of-Prime-Degree-Torus-Packets-with-Arbitrary-Local-Type-September-24-2026,Khayutin2019,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{Khayutin2019,
  author = {Khayutin, Ilya},
  title = {Arithmetic of double torus quotients and the distribution of periodic torus orbits},
  journal = {Duke Mathematical Journal},
  volume = {168}, number = {12}, year = {2019}, pages = {2365--2432},
  doi = {10.1215/00127094-2019-0016},
  eprint = {1510.08481}, archivePrefix = {arXiv}, primaryClass = {math.NT}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1215/00127094-2019-0016"", ""title"": [""Arithmetic of double torus quotients and the distribution of periodic torus orbits""], ""authors"": [{""given"": ""Ilya"", ""family"": ""Khayutin"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""role"": ""author"", ""vocabulary"": ""crossref""}]}], ""publisher"": ""Duke University Press"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2019, 9, 1]]}, ""container_title"": [""Duke Mathematical Journal""], ""url"": ""https://doi.org/10.1215/00127094-2019-0016"", ""license"": [], ""source_url"": ""https://api.crossref.org/works/10.1215%2F00127094-2019-0016""}}, {""provider"": ""arXiv original repository"", ""record"": {""arxiv_id"": ""1510.08481"", ""version"": 2, ""id_versioned"": ""1510.08481v2"", ""title"": ""Arithmetic of Double Torus Quotients and the Distribution of Periodic Torus Orbits"", ""abstract"": ""We describe new arithmetic invariants for pairs of torus orbits on groups isogenous to an inner form of $\\mathbf{PGL}_n$ over a number field. These invariants are constructed by studying the double quotient of a linear algebraic group by a maximal torus. Using the new invariants we significantly strengthen results towards the equidistribution of packets of periodic torus orbits on higher rank $S$-arithmetic quotients. Packets of periodic torus orbits are natural collections of torus orbits coming from a single adelic torus and are closely related to class groups of number fields. The distribution of these orbits is akin to the distribution of integral points on homogeneous algebraic varieties with a torus stabilizer. The proof combines geometric invariant theory, Galois actions, local arithmetic estimates and homogeneous dynamics."", ""authors"": [""Ilya Khayutin""], ""published"": ""2015-10-28T20:45:09Z"", ""updated"": ""2019-02-25T21:25:42Z"", ""primary_category"": ""math.NT"", ""categories"": [""math.NT"", ""math.DS""], ""doi"": ""10.1215/00127094-2019-0016"", ""journal_ref"": ""Duke Math. J. 168, no. 12 (2019), 2365-2432"", ""comment"": ""To appear in Duke Math. J. Updated according to referee comments. 61 pages"", ""abs_url"": ""http://arxiv.org/abs/1510.08481v2"", ""pdf_url"": ""https://arxiv.org/pdf/1510.08481v2""}}]",https://api.crossref.org/works/10.1215%2F00127094-2019-0016 | http://arxiv.org/abs/1510.08481v2,"[{""doi"": ""10.1215/00127094-2019-0016"", ""title"": ""Arithmetic of double torus quotients and the distribution of periodic torus orbits"", ""biblio"": {""volume"": ""168"", ""issue"": ""12"", ""first_page"": null, ""last_page"": null}, ""publication_year"": 2019, ""openalex_id"": ""W2214473080""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Equidistribution-of-Prime-Degree-Torus-Packets-with-Arbitrary-Local-Type-September-24-2026/build/references.bib#L51,51,,,,[]
R004,015,Equidistribution-of-Prime-Degree-Torus-Packets-with-Arbitrary-Local-Type-September-24-2026,Stark1974,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{Stark1974,
  author = {Stark, H. M.},
  title = {Some effective cases of the {Brauer--Siegel} theorem},
  journal = {Inventiones Mathematicae},
  volume = {23}, number = {2}, year = {1974}, pages = {135--152},
  doi = {10.1007/BF01405166}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1007/bf01405166"", ""title"": [""Some effective cases of the Brauer-Siegel Theorem""], ""authors"": [{""given"": ""H. M."", ""family"": ""Stark"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""Springer Science and Business Media LLC"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[1974, 6]]}, ""container_title"": [""Inventiones Mathematicae""], ""url"": ""https://doi.org/10.1007/bf01405166"", ""license"": [{""start"": {""date-parts"": [[1974, 6, 1]], ""date-time"": ""1974-06-01T00:00:00Z"", ""timestamp"": 139276800000}, ""content-version"": ""tdm"", ""delay-in-days"": 0, ""URL"": ""http://www.springer.com/tdm""}], ""source_url"": ""https://api.crossref.org/works/10.1007%2Fbf01405166""}}]",https://api.crossref.org/works/10.1007%2Fbf01405166,"[{""doi"": ""10.1007/bf01405166"", ""title"": ""Some effective cases of the Brauer-Siegel Theorem"", ""biblio"": {""volume"": ""23"", ""issue"": ""2"", ""first_page"": ""135"", ""last_page"": ""152""}, ""publication_year"": 1974, ""openalex_id"": ""W1992416585""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Equidistribution-of-Prime-Degree-Torus-Packets-with-Arbitrary-Local-Type-September-24-2026/build/references.bib#L60,60,unverifiable,"Stark Lemmas 3 and 8 supply a zero-free-region exception and force a quadratic subfield for a sufficiently close real zero, including nonnormal fields.","The exact lemmas were not retrieved, so constants, hypotheses, and applicability to nonnormal fields could not be checked.",[]
R005,015,Equidistribution-of-Prime-Degree-Torus-Packets-with-Arbitrary-Local-Type-September-24-2026,Milne2020,unverified,Milne course notes: original author site access denied; discovery did not establish the cited version 3.08 (2020).,"@misc{Milne2020,
  author = {Milne, James S.},
  title = {Algebraic Number Theory},
  year = {2020}, note = {Version 3.08},
  url = {https://www.jmilne.org/math/CourseNotes/ANT.pdf}
}",[],,[],Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Equidistribution-of-Prime-Degree-Torus-Packets-with-Arbitrary-Local-Type-September-24-2026/build/references.bib#L86,86,,,,[]
R006,024,An-asymptotic-formula-for-the-number-of-totients-September-25-2026,Pomerance1986,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{Pomerance1986,
  author = {Pomerance, Carl},
  title = {On the distribution of the values of {Euler}'s function},
  journal = {Acta Arithmetica},
  volume = {47},
  number = {1},
  year = {1986},
  pages = {63--70},
  doi = {10.4064/aa-47-1-63-70},
  note = {\url{https://math.dartmouth.edu/~carlp/PDF/57.pdf}}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.4064/aa-47-1-63-70"", ""title"": [""On the distribution of the values of Euler's function""], ""authors"": [{""given"": ""Carl"", ""family"": ""Pomerance"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""role"": ""author"", ""vocabulary"": ""crossref""}]}], ""publisher"": ""Institute of Mathematics, Polish Academy of Sciences"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[1986]]}, ""container_title"": [""Acta Arithmetica""], ""url"": ""https://doi.org/10.4064/aa-47-1-63-70"", ""license"": [], ""source_url"": ""https://api.crossref.org/works/10.4064%2Faa-47-1-63-70""}}]",https://api.crossref.org/works/10.4064%2Faa-47-1-63-70,"[{""doi"": ""10.4064/aa-47-1-63-70"", ""title"": ""On the distribution of the values of Euler's function"", ""biblio"": {""volume"": ""47"", ""issue"": ""1"", ""first_page"": ""63"", ""last_page"": ""70""}, ""publication_year"": 1986, ""openalex_id"": ""W922556180""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-asymptotic-formula-for-the-number-of-totients-September-25-2026/build/source/references.bib#L129,129,,,,[]
R007,024,An-asymptotic-formula-for-the-number-of-totients-September-25-2026,Erdos1958,unverified,Erdos 1958: author-hosted original access denied; bounded discovery searches did not retrieve an original record.,"@article{Erdos1958,
  author = {Erd{\H{o}}s, Paul},
  title = {Some remarks on {Euler}'s {$\phi$} function},
  journal = {Acta Arithmetica},
  volume = {4},
  year = {1958},
  pages = {10--19},
  note = {\url{https://users.renyi.hu/~p_erdos/1958-18.pdf}}
}",[],,[],Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-asymptotic-formula-for-the-number-of-totients-September-25-2026/build/source/references.bib#L94,94,,,,[]
R008,024,An-asymptotic-formula-for-the-number-of-totients-September-25-2026,ErdosHall1976,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{ErdosHall1976,
  author = {Erd{\H{o}}s, Paul and Hall, R. R.},
  title = {Distinct values of {Euler}'s {$\phi$}-function},
  journal = {Mathematika},
  volume = {23},
  number = {1},
  year = {1976},
  pages = {1--3},
  doi = {10.1112/S0025579300006100},
  note = {\url{https://users.renyi.hu/~p_erdos/1976-11.pdf}}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1112/s0025579300006100"", ""title"": [""Distinct values of Euler's ø‐function""], ""authors"": [{""given"": ""P."", ""family"": ""Erdős"", ""sequence"": ""first"", ""affiliation"": [{""name"": ""Department of MathematicsUniversity of YorkEngland""}], ""role"": [{""role"": ""author"", ""vocabulary"": ""crossref""}]}, {""given"": ""R. R."", ""family"": ""Hall"", ""sequence"": ""additional"", ""affiliation"": [{""name"": ""Department of MathematicsUniversity of YorkEngland""}], ""role"": [{""role"": ""author"", ""vocabulary"": ""crossref""}]}], ""publisher"": ""Wiley"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[1976, 6]]}, ""container_title"": [""Mathematika""], ""url"": ""https://doi.org/10.1112/s0025579300006100"", ""license"": [{""start"": {""date-parts"": [[1976, 6, 1]], ""date-time"": ""1976-06-01T00:00:00Z"", ""timestamp"": 202435200000}, ""content-version"": ""vor"", ""delay-in-days"": 0, ""URL"": ""http://onlinelibrary.wiley.com/termsAndConditions#vor""}, {""start"": {""date-parts"": [[1976, 6, 1]], ""date-time"": ""1976-06-01T00:00:00Z"", ""timestamp"": 202435200000}, ""content-version"": ""tdm"", ""delay-in-days"": 0, ""URL"": ""http://doi.wiley.com/10.1002/tdm_license_1.1""}], ""source_url"": ""https://api.crossref.org/works/10.1112%2Fs0025579300006100""}}]",https://api.crossref.org/works/10.1112%2Fs0025579300006100,"[{""doi"": ""10.1112/s0025579300006100"", ""title"": ""Distinct values of Euler's ø‐function"", ""biblio"": {""volume"": ""23"", ""issue"": ""1"", ""first_page"": ""1"", ""last_page"": ""3""}, ""publication_year"": 1976, ""openalex_id"": ""W2138353546""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-asymptotic-formula-for-the-number-of-totients-September-25-2026/build/source/references.bib#L116,116,,,,[]
R009,024,An-asymptotic-formula-for-the-number-of-totients-September-25-2026,Erdos1945,unverified,Erdos 1945: author-hosted original access denied; bounded discovery searches did not retrieve an original record.,"@article{Erdos1945,
  author = {Erd{\H{o}}s, Paul},
  title = {Some remarks on {Euler}'s {$\phi$} function and some related problems},
  journal = {Bulletin of the American Mathematical Society},
  volume = {51},
  year = {1945},
  pages = {540--544},
  note = {\url{https://users.renyi.hu/~p_erdos/1945-08.pdf}}
}",[],,[],Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-asymptotic-formula-for-the-number-of-totients-September-25-2026/build/source/references.bib#L105,105,,,,[]
R010,024,An-asymptotic-formula-for-the-number-of-totients-September-25-2026,Pillai1929,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{Pillai1929,
  author = {Pillai, S. S.},
  title = {On some functions connected with {$\phi(n)$}},
  journal = {Bulletin of the American Mathematical Society},
  volume = {35},
  number = {6},
  year = {1929},
  pages = {832--836},
  note = {\url{https://www.ams.org/journals/bull/1929-35-06/S0002-9904-1929-04799-2/S0002-9904-1929-04799-2.pdf}}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1090/s0002-9904-1929-04799-2"", ""title"": [""On some functions connected with 𝜙(𝑛)""], ""authors"": [{""given"": ""S. Sivasankaranarayana"", ""family"": ""Pillai"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""role"": ""author"", ""vocabulary"": ""crossref""}]}], ""publisher"": ""American Mathematical Society (AMS)"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[1929]]}, ""container_title"": [""Bulletin of the American Mathematical Society""], ""url"": ""https://doi.org/10.1090/s0002-9904-1929-04799-2"", ""license"": [], ""source_url"": ""https://api.crossref.org/works/10.1090%2Fs0002-9904-1929-04799-2""}}]",https://api.crossref.org/works/10.1090%2Fs0002-9904-1929-04799-2,[],Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-asymptotic-formula-for-the-number-of-totients-September-25-2026/build/source/references.bib#L70,70,,,,[]
R011,046,A-projective-fourfold-with-large-fundamental-group-and-non-Stein-universal-cover-October-5-2026,KatzarkovRamachandran1998,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{KatzarkovRamachandran1998,
  author = {Katzarkov, Ludmil and Ramachandran, Mohan},
  title = {On the universal coverings of algebraic surfaces},
  journal = {Annales scientifiques de l'{\'E}cole Normale Sup{\'e}rieure},
  series = {4},
  volume = {31},
  number = {4},
  pages = {525--535},
  year = {1998},
  doi = {10.1016/S0012-9593(98)80105-5}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1016/s0012-9593(98)80105-5"", ""title"": [""On the universal coverings of algebraic surfaces""], ""authors"": [{""given"": ""L"", ""family"": ""KATZARKOV"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}, {""given"": ""M"", ""family"": ""RAMACHANDRAN"", ""sequence"": ""additional"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""Societe Mathematique de France"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[1998, 7]]}, ""container_title"": [""Annales Scientifiques de l’École Normale Supérieure""], ""url"": ""https://doi.org/10.1016/s0012-9593(98)80105-5"", ""license"": [{""start"": {""date-parts"": [[1998, 7, 1]], ""date-time"": ""1998-07-01T00:00:00Z"", ""timestamp"": 899251200000}, ""content-version"": ""tdm"", ""delay-in-days"": 0, ""URL"": ""http://www.elsevier.com/tdm/userlicense/1.0/""}], ""source_url"": ""https://api.crossref.org/works/10.1016%2Fs0012-9593(98)80105-5""}}]",https://api.crossref.org/works/10.1016%2Fs0012-9593(98)80105-5,"[{""doi"": ""10.1016/s0012-9593(98)80105-5"", ""title"": ""On the universal coverings of algebraic surfaces"", ""biblio"": {""volume"": ""31"", ""issue"": ""4"", ""first_page"": ""525"", ""last_page"": ""535""}, ""publication_year"": 1998, ""openalex_id"": ""W2074896987""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-projective-fourfold-with-large-fundamental-group-and-non-Stein-universal-cover-October-5-2026/build/references.bib#L223,223,,,,[]
R012,046,A-projective-fourfold-with-large-fundamental-group-and-non-Stein-universal-cover-October-5-2026,MilnorSingular,minor_difference,"Same Milnor book, author, publisher and AM-61 identity. Citation says 1968; publisher-deposited record for the discovered edition says 1969-12-31. Edition/date discrepancy unresolved, not evidence of a different book.","@book{MilnorSingular,
  author = {Milnor, John},
  title = {Singular Points of Complex Hypersurfaces},
  series = {Annals of Mathematics Studies},
  volume = {61},
  publisher = {Princeton University Press},
  address = {Princeton, NJ},
  year = {1968}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1515/9781400881819"", ""title"": [""Singular Points of Complex Hypersurfaces. (AM-61)""], ""authors"": [{""given"": ""John"", ""family"": ""Milnor"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""Princeton University Press"", ""type"": ""edited-book"", ""published"": {""date-parts"": [[1969, 12, 31]]}, ""container_title"": [], ""url"": ""https://doi.org/10.1515/9781400881819"", ""license"": [], ""source_url"": ""https://api.crossref.org/works/10.1515%2F9781400881819""}}]",https://api.crossref.org/works/10.1515%2F9781400881819,[],Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-projective-fourfold-with-large-fundamental-group-and-non-Stein-universal-cover-October-5-2026/build/references.bib#L276,276,,,,[]
R013,046,A-projective-fourfold-with-large-fundamental-group-and-non-Stein-universal-cover-October-5-2026,BailyBorel1966,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{BailyBorel1966,
  author = {Baily, Jr., Walter L. and Borel, Armand},
  title = {Compactification of arithmetic quotients of bounded symmetric domains},
  journal = {Annals of Mathematics},
  series = {2},
  volume = {84},
  number = {3},
  pages = {442--528},
  year = {1966},
  doi = {10.2307/1970457}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.2307/1970457"", ""title"": [""Compactification of Arithmetic Quotients of Bounded Symmetric Domains""], ""authors"": [{""suffix"": ""join(' '"", ""given"": ""W. L."", ""family"": ""Baily"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}, {""given"": ""A."", ""family"": ""Borel"", ""sequence"": ""additional"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""JSTOR"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[1966, 11]]}, ""container_title"": [""The Annals of Mathematics""], ""url"": ""https://doi.org/10.2307/1970457"", ""license"": [], ""source_url"": ""https://api.crossref.org/works/10.2307%2F1970457""}}]",https://api.crossref.org/works/10.2307%2F1970457,"[{""doi"": ""10.2307/1970457"", ""title"": ""Compactification of Arithmetic Quotients of Bounded Symmetric Domains"", ""biblio"": {""volume"": ""84"", ""issue"": ""3"", ""first_page"": ""442"", ""last_page"": ""442""}, ""publication_year"": 1966, ""openalex_id"": ""W2319666400""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-projective-fourfold-with-large-fundamental-group-and-non-Stein-universal-cover-October-5-2026/build/references.bib#L49,49,,,,[]
R014,046,A-projective-fourfold-with-large-fundamental-group-and-non-Stein-universal-cover-October-5-2026,Gromov1987,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@incollection{Gromov1987,
  author = {Gromov, Mikhail},
  title = {Hyperbolic groups},
  booktitle = {Essays in Group Theory},
  editor = {Gersten, S. M.},
  series = {Mathematical Sciences Research Institute Publications},
  volume = {8},
  pages = {75--263},
  publisher = {Springer-Verlag},
  address = {New York},
  year = {1987},
  doi = {10.1007/978-1-4613-9586-7_3}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1007/978-1-4613-9586-7_3"", ""title"": [""Hyperbolic Groups""], ""authors"": [{""given"": ""M."", ""family"": ""Gromov"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""Springer New York"", ""type"": ""book-chapter"", ""published"": {""date-parts"": [[1987]]}, ""container_title"": [""Mathematical Sciences Research Institute Publications"", ""Essays in Group Theory""], ""url"": ""https://doi.org/10.1007/978-1-4613-9586-7_3"", ""license"": [], ""source_url"": ""https://api.crossref.org/works/10.1007%2F978-1-4613-9586-7_3""}}]",https://api.crossref.org/works/10.1007%2F978-1-4613-9586-7_3,"[{""doi"": ""10.1007/978-1-4613-9586-7_3"", ""title"": ""Hyperbolic Groups"", ""biblio"": {""volume"": null, ""issue"": null, ""first_page"": ""75"", ""last_page"": ""263""}, ""publication_year"": 1987, ""openalex_id"": ""W4235484205""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-projective-fourfold-with-large-fundamental-group-and-non-Stein-universal-cover-October-5-2026/build/references.bib#L12,12,,,,[]
R015,046,A-projective-fourfold-with-large-fundamental-group-and-non-Stein-universal-cover-October-5-2026,Hartshorne,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@book{Hartshorne,
  author = {Hartshorne, Robin},
  title = {Algebraic Geometry},
  series = {Graduate Texts in Mathematics},
  volume = {52},
  publisher = {Springer-Verlag},
  address = {New York},
  year = {1977},
  doi = {10.1007/978-1-4757-3849-0}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1007/978-1-4757-3849-0"", ""title"": [""Algebraic Geometry""], ""authors"": [{""given"": ""Robin"", ""family"": ""Hartshorne"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""Springer New York"", ""type"": ""book"", ""published"": {""date-parts"": [[1977]]}, ""container_title"": [""Graduate Texts in Mathematics""], ""url"": ""https://doi.org/10.1007/978-1-4757-3849-0"", ""license"": [{""start"": {""date-parts"": [[1977, 1, 1]], ""date-time"": ""1977-01-01T00:00:00Z"", ""timestamp"": 220924800000}, ""content-version"": ""tdm"", ""delay-in-days"": 0, ""URL"": ""http://www.springer.com/tdm""}], ""source_url"": ""https://api.crossref.org/works/10.1007%2F978-1-4757-3849-0""}}]",https://api.crossref.org/works/10.1007%2F978-1-4757-3849-0,"[{""doi"": ""10.1007/978-1-4757-3849-0"", ""title"": ""Algebraic Geometry"", ""biblio"": {""volume"": null, ""issue"": null, ""first_page"": null, ""last_page"": null}, ""publication_year"": 1977, ""openalex_id"": ""W4248269519""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-projective-fourfold-with-large-fundamental-group-and-non-Stein-universal-cover-October-5-2026/build/references.bib#L286,286,,,,[]
R016,065,Virasoro-Constraints-under-Projectivization-October-5-2026,Fan,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"\bibitem{Fan}
H.~Fan,
\emph{Chern classes and Gromov--Witten theory of projective bundles},
Amer. J. Math. \textbf{143} (2021), no.~3, 811--832.
\href{https://doi.org/10.1353/ajm.2021.0020}{doi:10.1353/ajm.2021.0020}.","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1353/ajm.2021.0020"", ""title"": [""Chern classes and Gromov-Witten theory of projective bundles""], ""authors"": [{""given"": ""Honglu"", ""family"": ""Fan"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""role"": ""author"", ""vocabulary"": ""crossref""}]}], ""publisher"": ""Project MUSE"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2021]]}, ""container_title"": [""American Journal of Mathematics""], ""url"": ""https://doi.org/10.1353/ajm.2021.0020"", ""license"": [], ""source_url"": ""https://api.crossref.org/works/10.1353%2Fajm.2021.0020""}}]",https://api.crossref.org/works/10.1353%2Fajm.2021.0020,"[{""doi"": ""10.1353/ajm.2021.0020"", ""title"": ""Chern classes and Gromov-Witten theory of projective bundles"", ""biblio"": {""volume"": ""143"", ""issue"": ""3"", ""first_page"": ""811"", ""last_page"": ""832""}, ""publication_year"": 2021, ""openalex_id"": ""W3168070877""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Virasoro-Constraints-under-Projectivization-October-5-2026/build/references.tex#L33,33,,,,[]
R017,065,Virasoro-Constraints-under-Projectivization-October-5-2026,Teleman,minor_difference,"Same Teleman work and DOI. Citation uses 2012; Crossref published date is 2011-09-24, compatible with online-first versus print dating. Retrieved schema does not expose both date types.","\bibitem{Teleman}
C.~Teleman,
\emph{The structure of 2D semi-simple field theories},
Invent. Math. \textbf{188} (2012), no.~3, 525--588.
\href{https://doi.org/10.1007/s00222-011-0352-5}{doi:10.1007/s00222-011-0352-5}.","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1007/s00222-011-0352-5"", ""title"": [""The structure of 2D semi-simple field theories""], ""authors"": [{""given"": ""Constantin"", ""family"": ""Teleman"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""Springer Science and Business Media LLC"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2011, 9, 24]]}, ""container_title"": [""Inventiones mathematicae""], ""url"": ""https://doi.org/10.1007/s00222-011-0352-5"", ""license"": [{""start"": {""date-parts"": [[2011, 9, 24]], ""date-time"": ""2011-09-24T00:00:00Z"", ""timestamp"": 1316822400000}, ""content-version"": ""tdm"", ""delay-in-days"": 0, ""URL"": ""http://www.springer.com/tdm""}], ""source_url"": ""https://api.crossref.org/works/10.1007%2Fs00222-011-0352-5""}}]",https://api.crossref.org/works/10.1007%2Fs00222-011-0352-5,"[{""doi"": ""10.1007/s00222-011-0352-5"", ""title"": ""The structure of 2D semi-simple field theories"", ""biblio"": {""volume"": ""188"", ""issue"": ""3"", ""first_page"": ""525"", ""last_page"": ""588""}, ""publication_year"": 2011, ""openalex_id"": ""W2123872555""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Virasoro-Constraints-under-Projectivization-October-5-2026/build/references.tex#L124,124,,,,[]
R018,065,Virasoro-Constraints-under-Projectivization-October-5-2026,QRR,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"\bibitem{QRR}
T.~Coates and A.~Givental,
\emph{Quantum Riemann--Roch, Lefschetz and Serre},
Ann. of Math. (2) \textbf{165} (2007), no.~1, 15--53.
\href{https://doi.org/10.4007/annals.2007.165.15}{doi:10.4007/annals.2007.165.15}.","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.4007/annals.2007.165.15"", ""title"": [""Quantum Riemann–Roch, Lefschetz and Serre""], ""authors"": [{""given"": ""Thomas"", ""family"": ""Coates"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}, {""given"": ""Alexander"", ""family"": ""Givental"", ""sequence"": ""additional"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""Annals of Mathematics"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2007, 1, 1]]}, ""container_title"": [""Annals of Mathematics""], ""url"": ""https://doi.org/10.4007/annals.2007.165.15"", ""license"": [], ""source_url"": ""https://api.crossref.org/works/10.4007%2Fannals.2007.165.15""}}]",https://api.crossref.org/works/10.4007%2Fannals.2007.165.15,"[{""doi"": ""10.4007/annals.2007.165.15"", ""title"": ""Quantum Riemann–Roch, Lefschetz and Serre"", ""biblio"": {""volume"": ""165"", ""issue"": ""1"", ""first_page"": ""15"", ""last_page"": ""53""}, ""publication_year"": 2007, ""openalex_id"": ""W2121326231""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Virasoro-Constraints-under-Projectivization-October-5-2026/build/references.tex#L9,9,,,,[]
R019,065,Virasoro-Constraints-under-Projectivization-October-5-2026,GetzlerVirasoro,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization. Identity verified at preprint level; claimed journal/chapter publication details are not independently certified by that record.,"\bibitem{GetzlerVirasoro}
E.~Getzler,
\emph{The Virasoro conjecture for Gromov--Witten invariants},
in \emph{Algebraic Geometry: Hirzebruch 70} (Warsaw, 1998),
Contemp. Math., vol.~241, Amer. Math. Soc., Providence, RI, 1999,
147--176.
\href{https://arxiv.org/abs/math/9812026}{arXiv:math/9812026}.","[{""provider"": ""arXiv original repository"", ""record"": {""arxiv_id"": ""math/9812026"", ""version"": 4, ""id_versioned"": ""math/9812026v4"", ""title"": ""The Virasoro conjecture for Gromov-Witten invariants"", ""abstract"": ""The Virasoro conjecture is a conjectured sequence of relations among the descendent Gromov-Witten invariants of a smooth projective variety in all genera; the only varieties for which it is known to hold are a point (Kontsevich) and Calabi-Yau threefolds (S. Katz). We review the statement of the conjecture and its proof in genus 0, following Eguchi, Hori and Xiong. This version incorporates many changes and improvements compared with the first, and a small number of misprints from the second. It will appear in the AMS volume \""Hirzebruch 70\"", edited by P. Pragacz et al."", ""authors"": [""Ezra Getzler""], ""published"": ""1998-12-03T19:57:13Z"", ""updated"": ""1999-04-06T20:31:42Z"", ""primary_category"": ""math.AG"", ""categories"": [""math.AG"", ""hep-th""], ""doi"": null, ""journal_ref"": null, ""comment"": ""amslatex 1.2, 30 pages"", ""abs_url"": ""http://arxiv.org/abs/math/9812026v4"", ""pdf_url"": ""https://arxiv.org/pdf/math/9812026v4""}}]",http://arxiv.org/abs/math/9812026v4,[],Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Virasoro-Constraints-under-Projectivization-October-5-2026/build/references.tex#L39,39,,,,[]
R020,065,Virasoro-Constraints-under-Projectivization-October-5-2026,IritaniKoto,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization. Identity verified at preprint level; claimed journal/chapter publication details are not independently certified by that record.,"\bibitem{IritaniKoto}
H.~Iritani and Y.~Koto,
\emph{Quantum cohomology of projective bundles},
preprint, 2023, revised January 31, 2026.
\href{https://arxiv.org/abs/2307.03696v4}{arXiv:2307.03696v4}.","[{""provider"": ""arXiv original repository"", ""record"": {""arxiv_id"": ""2307.03696"", ""version"": 4, ""id_versioned"": ""2307.03696v4"", ""title"": ""Quantum cohomology of projective bundles"", ""abstract"": ""We construct an I-function of the projective bundle P(V) associated with a not necessarily split vector bundle V\\to B as a Fourier transform of the S^1-equivariant J-function of the total space of V and show that it lies on the Givental Lagrangian cone of P(V). Using this result, we show that the quantum cohomology D-module of P(V) splits into the direct sum of the quantum cohomology D-modules of the base space B. This has applications to the semisimplicity of big quantum cohomology."", ""authors"": [""Hiroshi Iritani"", ""Yuki Koto""], ""published"": ""2023-07-07T16:13:20Z"", ""updated"": ""2026-01-31T00:49:40Z"", ""primary_category"": ""math.AG"", ""categories"": [""math.AG"", ""math.SG""], ""doi"": null, ""journal_ref"": null, ""comment"": ""40 pages, 2 figures; v2: Figure 2 added, v3: Introducion improved, v4: proof of Theorem 1.1 streamlined, log q term in the change of coordinates for Theorem 1.7 removed, error in Theorem 5.1(5) corrected, a reconstruction algorithm added in Section 5.8"", ""abs_url"": ""http://arxiv.org/abs/2307.03696v4"", ""pdf_url"": ""https://arxiv.org/pdf/2307.03696v4""}}]",http://arxiv.org/abs/2307.03696v4,[],Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Virasoro-Constraints-under-Projectivization-October-5-2026/build/references.tex#L86,86,partial_support_abstract_only,"For arbitrary projective bundles, Iritani–Koto construct a mirror theorem and split the quantum D-module into base-space pieces; nearby text also asserts a generic-semisimplicity equivalence and a Virasoro consequence.","The original arXiv abstract explicitly describes the I-function construction for a not necessarily split vector bundle and the direct-sum D-module decomposition. It mentions applications to semisimplicity, but does not establish the precise equivalence or the downstream Virasoro implication in the nearby text.","[{""url"": ""http://arxiv.org/abs/2307.03696v4"", ""id_versioned"": ""2307.03696v4"", ""abstract"": ""We construct an I-function of the projective bundle P(V) associated with a not necessarily split vector bundle V\\to B as a Fourier transform of the S^1-equivariant J-function of the total space of V and show that it lies on the Givental Lagrangian cone of P(V). Using this result, we show that the quantum cohomology D-module of P(V) splits into the direct sum of the quantum cohomology D-modules of the base space B. This has applications to the semisimplicity of big quantum cohomology.""}]"
R021,082,Annular-variation-of-the-triangular-Hilbert-transform-at-the-symmetric-point-October-5-2026,OberlinSeegerTaoThieleWright2012,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{OberlinSeegerTaoThieleWright2012,
  author = {Oberlin, Richard and Seeger, Andreas and Tao, Terence and Thiele, Christoph and Wright, James},
  title = {A variation norm {Carleson} theorem},
  journal = {Journal of the European Mathematical Society},
  volume = {14},
  number = {2},
  pages = {421--464},
  year = {2012},
  doi = {10.4171/JEMS/307},
  url = {https://arxiv.org/abs/0910.1555}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.4171/jems/307"", ""title"": [""A variation norm Carleson theorem""], ""authors"": [{""given"": ""Richard"", ""family"": ""Oberlin"", ""sequence"": ""first"", ""affiliation"": [{""name"": ""Louisiana State University, Baton Rouge, USA""}], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}, {""given"": ""Andreas"", ""family"": ""Seeger"", ""sequence"": ""additional"", ""affiliation"": [{""name"": ""University of Wisconsin, Madison, USA""}], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}, {""ORCID"": ""https://orcid.org/0000-0002-0140-7641"", ""authenticated-orcid"": false, ""given"": ""Terence"", ""family"": ""Tao"", ""sequence"": ""additional"", ""affiliation"": [{""name"": ""University of California Los Angeles, United States""}], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}, {""given"": ""Christoph"", ""family"": ""Thiele"", ""sequence"": ""additional"", ""affiliation"": [{""name"": ""Universität Bonn, Germany""}], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}, {""given"": ""James"", ""family"": ""Wright"", ""sequence"": ""additional"", ""affiliation"": [{""name"": ""University of Edinburgh, UK""}], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""European Mathematical Society - EMS - Publishing House GmbH"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2012, 2, 4]]}, ""container_title"": [""Journal of the European Mathematical Society""], ""url"": ""https://doi.org/10.4171/jems/307"", ""license"": [], ""source_url"": ""https://api.crossref.org/works/10.4171%2Fjems%2F307""}}, {""provider"": ""arXiv original repository"", ""record"": {""arxiv_id"": ""0910.1555"", ""version"": 2, ""id_versioned"": ""0910.1555v2"", ""title"": ""A variation norm Carleson theorem"", ""abstract"": ""We strengthen the Carleson-Hunt theorem by proving $L^p$ estimates for the $r$-variation of the partial sum operators for Fourier series and integrals, for $p>\\max\\{r',2\\}$. Four appendices are concerned with transference, a variation norm Menshov-Paley-Zygmund theorem, and applications to nonlinear Fourier transforms and ergodic theory."", ""authors"": [""Richard Oberlin"", ""Andreas Seeger"", ""Terence Tao"", ""Christoph Thiele"", ""James Wright""], ""published"": ""2009-10-08T17:11:17Z"", ""updated"": ""2010-08-25T15:03:37Z"", ""primary_category"": ""math.CA"", ""categories"": [""math.CA""], ""doi"": null, ""journal_ref"": null, ""comment"": ""41 pages"", ""abs_url"": ""http://arxiv.org/abs/0910.1555v2"", ""pdf_url"": ""https://arxiv.org/pdf/0910.1555v2""}}]",https://api.crossref.org/works/10.4171%2Fjems%2F307 | http://arxiv.org/abs/0910.1555v2,"[{""doi"": ""10.4171/jems/307"", ""title"": ""A variation norm Carleson theorem"", ""biblio"": {""volume"": ""14"", ""issue"": ""2"", ""first_page"": ""421"", ""last_page"": ""464""}, ""publication_year"": 2012, ""openalex_id"": ""W1984895635""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Annular-variation-of-the-triangular-Hilbert-transform-at-the-symmetric-point-October-5-2026/build/references.bib#L150,150,,,,[]
R022,082,Annular-variation-of-the-triangular-Hilbert-transform-at-the-symmetric-point-October-5-2026,Lepingle1976,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{Lepingle1976,
  author = {L\'epingle, Dominique},
  title = {La variation d'ordre {$p$} des semi-martingales},
  journal = {Zeitschrift f\""ur Wahrscheinlichkeitstheorie und Verwandte Gebiete},
  volume = {36},
  number = {4},
  pages = {295--316},
  year = {1976},
  doi = {10.1007/BF00532696}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1007/bf00532696"", ""title"": [""La variation d'ordre p des semi-martingales""], ""authors"": [{""given"": ""D."", ""family"": ""Lepingle"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""Springer Science and Business Media LLC"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[1976]]}, ""container_title"": [""Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete""], ""url"": ""https://doi.org/10.1007/bf00532696"", ""license"": [{""start"": {""date-parts"": [[1976, 1, 1]], ""date-time"": ""1976-01-01T00:00:00Z"", ""timestamp"": 189302400000}, ""content-version"": ""tdm"", ""delay-in-days"": 0, ""URL"": ""http://www.springer.com/tdm""}], ""source_url"": ""https://api.crossref.org/works/10.1007%2Fbf00532696""}}]",https://api.crossref.org/works/10.1007%2Fbf00532696,"[{""doi"": ""10.1007/bf00532696"", ""title"": ""La variation d'ordre p des semi-martingales"", ""biblio"": {""volume"": ""36"", ""issue"": ""4"", ""first_page"": ""295"", ""last_page"": ""316""}, ""publication_year"": 1976, ""openalex_id"": ""W2078012491""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Annular-variation-of-the-triangular-Hilbert-transform-at-the-symmetric-point-October-5-2026/build/references.bib#L127,127,,,,[]
R023,082,Annular-variation-of-the-triangular-Hilbert-transform-at-the-symmetric-point-October-5-2026,GrafakosEtAl2017,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization. Identity verified at preprint level; claimed journal/chapter publication details are not independently certified by that record.,"@misc{GrafakosEtAl2017,
  author = {Grafakos, Loukas and Oliveira e Silva, Diogo and Pramanik, Malabika and Seeger, Andreas and Stovall, Betsy},
  title = {Some problems in harmonic analysis},
  year = {2017},
  howpublished = {arXiv:1701.06637},
  url = {https://arxiv.org/abs/1701.06637},
  note = {Section 9, contributed by Christoph Thiele, Problem 13}
}","[{""provider"": ""arXiv original repository"", ""record"": {""arxiv_id"": ""1701.06637"", ""version"": 1, ""id_versioned"": ""1701.06637v1"", ""title"": ""Some Problems in Harmonic Analysis"", ""abstract"": ""In May 2016, we organized a conference in harmonic analysis in honor of Professor Michael Christ, on the campus of the University of Wisconsin in Madison. We are happy to present sixteen open problems, almost all of which were contributed by participants of a problem session held in the afternoon of May 19, 2016."", ""authors"": [""Loukas Grafakos"", ""Diogo Oliveira e Silva"", ""Malabika Pramanik"", ""Andreas Seeger"", ""Betsy Stovall""], ""published"": ""2017-01-23T21:19:09Z"", ""updated"": ""2017-01-23T21:19:09Z"", ""primary_category"": ""math.CA"", ""categories"": [""math.CA"", ""math.AP""], ""doi"": null, ""journal_ref"": null, ""comment"": ""19 pages"", ""abs_url"": ""http://arxiv.org/abs/1701.06637v1"", ""pdf_url"": ""https://arxiv.org/pdf/1701.06637v1""}}]",http://arxiv.org/abs/1701.06637v1,[],Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Annular-variation-of-the-triangular-Hilbert-transform-at-the-symmetric-point-October-5-2026/build/references.bib#L1,1,,,,[]
R024,082,Annular-variation-of-the-triangular-Hilbert-transform-at-the-symmetric-point-October-5-2026,LinSlavikova2026,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization. Identity verified at preprint level; claimed journal/chapter publication details are not independently certified by that record.,"@misc{LinSlavikova2026,
  author = {Lin, Fred Yu-Hsiang and Slav\'ikov\'a, Lenka},
  title = {Rough averages of triangular {Hilbert} transforms},
  year = {2026},
  howpublished = {arXiv:2607.20206},
  url = {https://arxiv.org/abs/2607.20206},
  note = {July 22, 2026}
}","[{""provider"": ""arXiv original repository"", ""record"": {""arxiv_id"": ""2607.20206"", ""version"": 1, ""id_versioned"": ""2607.20206v1"", ""title"": ""Rough averages of triangular Hilbert transforms"", ""abstract"": ""We study a bilinear singular integral operator obtained by taking rough averages of certain directional variants of the triangular Hilbert transform. This operator can be interpreted as the twisted paraproduct with a rough homogeneous kernel. Under a balance condition on the $L^q$ integrability of the kernel on the unit sphere, we establish a range of $L^{p_1} \\times L^{p_2} \\rightarrow L^p$ bounds for this operator. Our results are optimal within the known boundedness range for the twisted paraproduct with a smooth kernel."", ""authors"": [""Fred Yu-Hsiang Lin"", ""Lenka Slavíková""], ""published"": ""2026-07-22T14:26:36Z"", ""updated"": ""2026-07-22T14:26:36Z"", ""primary_category"": ""math.CA"", ""categories"": [""math.CA""], ""doi"": null, ""journal_ref"": null, ""comment"": null, ""abs_url"": ""http://arxiv.org/abs/2607.20206v1"", ""pdf_url"": ""https://arxiv.org/pdf/2607.20206v1""}}]",http://arxiv.org/abs/2607.20206v1,[],Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Annular-variation-of-the-triangular-Hilbert-transform-at-the-symmetric-point-October-5-2026/build/references.bib#L227,227,,,,[]
R025,082,Annular-variation-of-the-triangular-Hilbert-transform-at-the-symmetric-point-October-5-2026,ZorinKranich2017,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{ZorinKranich2017,
  author = {Zorin-Kranich, Pavel},
  title = {Cancellation for the simplex {Hilbert} transform},
  journal = {Mathematical Research Letters},
  volume = {24},
  number = {2},
  pages = {581--592},
  year = {2017},
  doi = {10.4310/MRL.2017.v24.n2.a16},
  url = {https://arxiv.org/abs/1507.02436}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.4310/mrl.2017.v24.n2.a16"", ""title"": [""Cancellation for the simplex Hilbert transform""], ""authors"": [{""given"": ""Pavel"", ""family"": ""Zorin-Kranich"", ""sequence"": ""first"", ""affiliation"": [{""name"": ""Mathematisches Institut, Universität Bonn, Germany""}], ""role"": [{""role"": ""author"", ""vocabulary"": ""crossref""}]}], ""publisher"": ""International Press of Boston"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2017]]}, ""container_title"": [""Mathematical Research Letters""], ""url"": ""https://doi.org/10.4310/mrl.2017.v24.n2.a16"", ""license"": [], ""source_url"": ""https://api.crossref.org/works/10.4310%2Fmrl.2017.v24.n2.a16""}}, {""provider"": ""arXiv original repository"", ""record"": {""arxiv_id"": ""1507.02436"", ""version"": 1, ""id_versioned"": ""1507.02436v1"", ""title"": ""Cancellation for the simplex Hilbert transform"", ""abstract"": ""We show that the truncated simplex Hilbert transform enjoys some cancellation in the sense that its norm grows sublinearly in the number of scales retained in the truncation. This extends the recent result by Tao on cancellation for the multilinear Hilbert transform. Our main tool is the Hilbert space regularity lemma due to Gowers, which enables a very short proof."", ""authors"": [""Pavel Zorin-Kranich""], ""published"": ""2015-07-09T09:53:17Z"", ""updated"": ""2015-07-09T09:53:17Z"", ""primary_category"": ""math.CA"", ""categories"": [""math.CA""], ""doi"": ""10.4310/MRL.2017.v24.n2.a16"", ""journal_ref"": ""Math. Res. Lett. 24.2 (2017), pp. 581-592"", ""comment"": ""8 pages"", ""abs_url"": ""http://arxiv.org/abs/1507.02436v1"", ""pdf_url"": ""https://arxiv.org/pdf/1507.02436v1""}}]",https://api.crossref.org/works/10.4310%2Fmrl.2017.v24.n2.a16 | http://arxiv.org/abs/1507.02436v1,"[{""doi"": ""10.4310/mrl.2017.v24.n2.a16"", ""title"": ""Cancellation for the simplex Hilbert transform"", ""biblio"": {""volume"": ""24"", ""issue"": ""2"", ""first_page"": ""581"", ""last_page"": ""592""}, ""publication_year"": 2017, ""openalex_id"": ""W1676190354""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Annular-variation-of-the-triangular-Hilbert-transform-at-the-symmetric-point-October-5-2026/build/references.bib#L45,45,,,,[]
R026,113,A-Fully-Polynomial-Randomized-Approximation-Scheme-for-Perfect-Matchings-in-General-Graphs-September-23-2026,EfronStein1981,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"\bibitem[Efron and Stein(1981)]{EfronStein1981}
Bradley Efron and Charles Stein.
\newblock The jackknife estimate of variance.
\newblock \emph{The Annals of Statistics}, 9\penalty0
  (3):\penalty0 586--596, 1981.
\newblock \doi{10.1214/aos/1176345462}.","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1214/aos/1176345462"", ""title"": [""The Jackknife Estimate of Variance""], ""authors"": [{""given"": ""B."", ""family"": ""Efron"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}, {""given"": ""C."", ""family"": ""Stein"", ""sequence"": ""additional"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""Institute of Mathematical Statistics"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[1981, 5, 1]]}, ""container_title"": [""The Annals of Statistics""], ""url"": ""https://doi.org/10.1214/aos/1176345462"", ""license"": [], ""source_url"": ""https://api.crossref.org/works/10.1214%2Faos%2F1176345462""}}]",https://api.crossref.org/works/10.1214%2Faos%2F1176345462,"[{""doi"": ""10.1214/aos/1176345462"", ""title"": ""The Jackknife Estimate of Variance"", ""biblio"": {""volume"": ""9"", ""issue"": ""3"", ""first_page"": null, ""last_page"": null}, ""publication_year"": 1981, ""openalex_id"": ""W1992068214""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Fully-Polynomial-Randomized-Approximation-Scheme-for-Perfect-Matchings-in-General-Graphs-September-23-2026/build/main.tex#L3354,3354,,,,[]
R027,113,A-Fully-Polynomial-Randomized-Approximation-Scheme-for-Perfect-Matchings-in-General-Graphs-September-23-2026,CaiLiu2020,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"\bibitem[Cai and Liu(2020)]{CaiLiu2020}
Jin-Yi Cai and Tianyu Liu.
\newblock Counting perfect matchings and the eight-vertex model.
\newblock In Artur Czumaj, Anuj Dawar, and Emanuela Merelli, editors,
  \emph{47th International Colloquium on Automata, Languages, and Programming
  (ICALP 2020)}, volume 168 of \emph{Leibniz International Proceedings in
  Informatics}, pages 23:1--23:18. Schloss Dagstuhl--Leibniz-Zentrum f{\""u}r
  Informatik, 2020.
\newblock \doi{10.4230/LIPIcs.ICALP.2020.23}.
\newblock URL
  \url{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.23}.","[{""provider"": ""DataCite original deposit"", ""record"": {""record"": {""doi"": ""10.4230/lipics.icalp.2020.23"", ""titles"": [{""title"": ""Counting Perfect Matchings and the Eight-Vertex Model"", ""lang"": ""en""}], ""creators"": [{""name"": ""Cai, Jin-Yi"", ""nameType"": ""Personal"", ""givenName"": ""Jin-Yi"", ""familyName"": ""Cai"", ""affiliation"": [""University of Wisconsin-Madison, Madison, WI, USA""], ""nameIdentifiers"": []}, {""name"": ""Liu, Tianyu"", ""nameType"": ""Personal"", ""givenName"": ""Tianyu"", ""familyName"": ""Liu"", ""affiliation"": [""University of Wisconsin-Madison, Madison, WI, USA""], ""nameIdentifiers"": []}], ""publisher"": ""Schloss Dagstuhl – Leibniz-Zentrum für Informatik"", ""publication_year"": 2020, ""resource_type"": {""resourceTypeGeneral"": ""ConferencePaper"", ""ris"": ""CPAPER"", ""bibtex"": ""inproceedings"", ""citeproc"": """", ""schemaOrg"": ""Article"", ""resourceType"": ""Track A: Algorithms, Complexity and Games""}, ""url"": ""https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.23"", ""rights"": [{""lang"": ""en"", ""rights"": ""Creative Commons Attribution 3.0 Unported license"", ""rightsUri"": ""https://creativecommons.org/licenses/by/3.0/legalcode"", ""rightsIdentifier"": ""cc by 3.0""}, {""rights"": ""info:eu-repo/semantics/openAccess""}], ""related_identifiers"": [{""relationType"": ""IsVersionOf"", ""relatedIdentifier"": ""arXiv:1904.10493"", ""resourceTypeGeneral"": ""Text"", ""relatedIdentifierType"": ""arXiv""}, {""relationType"": ""IsPartOf"", ""relatedIdentifier"": ""10.4230/LIPIcs.ICALP.2020"", ""relatedIdentifierType"": ""DOI""}, {""relationType"": ""IsPartOf"", ""relatedIdentifier"": ""978-3-95977-138-2"", ""relatedIdentifierType"": ""ISBN""}, {""relationType"": ""IsPartOf"", ""relatedIdentifier"": ""1868-8969"", ""relatedIdentifierType"": ""ISSN""}, {""relationType"": ""Cites"", ""relatedIdentifier"": ""10.1103/PhysRevLett.26.832"", ""relatedIdentifierType"": ""DOI""}, {""relationType"": ""Cites"", ""relatedIdentifier"": ""10.1016/0003-4916(72)90335-1"", ""relatedIdentifierType"": ""DOI""}, {""relationType"": ""Cites"", ""relatedIdentifier"": ""10.1016/j.tcs.2017.05.001"", ""relatedIdentifierType"": ""DOI""}, {""relationType"": ""Cites"", ""relatedIdentifier"": ""10.1017/9781107477063"", ""relatedIdentifierType"": ""DOI""}, {""relationType"": ""Cites"", ""relatedIdentifier"": ""arXiv:1702.07938"", ""relatedIdentifierType"": ""arXiv""}, {""relationType"": ""Cites"", ""relatedIdentifier"": ""10.1137/1.9781611975482.136"", ""relatedIdentifierType"": ""DOI""}, {""relationType"": ""Cites"", ""relatedIdentifier"": ""arXiv:1811.03126"", ""relatedIdentifierType"": ""arXiv""}, {""relationType"": ""Cites"", ""relatedIdentifier"": ""10.1103/PhysRevB.2.723"", ""relatedIdentifierType"": ""DOI""}, {""relationType"": ""Cites"", ""relatedIdentifier"": ""10.1145/2785964"", ""relatedIdentifierType"": ""DOI""}, {""relationType"": ""Cites"", ""relatedIdentifier"": ""10.1016/j.ic.2008.04.003"", ""relatedIdentifierType"": ""DOI""}, {""relationType"": ""Cites"", ""relatedIdentifier"": ""10.1007/s00453-008-9246-3"", ""relatedIdentifierType"": ""DOI""}, {""relationType"": ""Cites"", ""relatedIdentifier"": ""10.1002/rsa.20560"", ""relatedIdentifierType"": ""DOI""}, {""relationType"": ""Cites"", ""relatedIdentifier"": ""10.1109/SFCS.1983.35"", ""relatedIdentifierType"": ""DOI""}, {""relationType"": ""Cites"", ""relatedIdentifier"": ""10.1016/0031-8914(61)90063-5"", ""relatedIdentifierType"": ""DOI""}, {""relationType"": ""Cites"", ""relatedIdentifier"": ""10.4230/LIPIcs.APPROX-RANDOM.2018.52"", ""relatedIdentifierType"": ""DOI""}, {""relationType"": ""Cites"", ""relatedIdentifier"": ""arXiv:1301.2880"", ""relatedIdentifierType"": ""arXiv""}, {""relationType"": ""Cites"", ""relatedIdentifier"": ""10.1063/1.1665111"", ""relatedIdentifierType"": ""DOI""}, {""relationType"": ""Cites"", ""relatedIdentifier"": ""10.1080/14786436108243366"", ""relatedIdentifierType"": ""DOI""}, {""relationType"": ""Cites"", ""relatedIdentifier"": ""10.1137/S0097539700377025"", ""relatedIdentifierType"": ""DOI""}, {""relationType"": ""Cites"", ""relatedIdentifier"": ""10.1137/070682575"", ""relatedIdentifierType"": ""DOI""}], ""version"": null}, ""source_url"": ""https://api.datacite.org/dois/10.4230%2Flipics.icalp.2020.23""}}]",https://api.datacite.org/dois/10.4230%2Flipics.icalp.2020.23,[],Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Fully-Polynomial-Randomized-Approximation-Scheme-for-Perfect-Matchings-in-General-Graphs-September-23-2026/build/main.tex#L3323,3323,,,,[]
R028,113,A-Fully-Polynomial-Randomized-Approximation-Scheme-for-Perfect-Matchings-in-General-Graphs-September-23-2026,Hastings1970,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"\bibitem[Hastings(1970)]{Hastings1970}
W.~K. Hastings.
\newblock Monte Carlo sampling methods using Markov chains and their applications.
\newblock \emph{Biometrika}, 57\penalty0 (1):\penalty0 97--109, 1970.
\newblock \doi{10.1093/biomet/57.1.97}.","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1093/biomet/57.1.97"", ""title"": [""Monte Carlo sampling methods using Markov chains and their applications""], ""authors"": [{""given"": ""W. K."", ""family"": ""Hastings"", ""sequence"": ""first"", ""affiliation"": [{""name"": ""University of Toronto""}], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""Oxford University Press (OUP)"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[1970, 4, 1]]}, ""container_title"": [""Biometrika""], ""url"": ""https://doi.org/10.1093/biomet/57.1.97"", ""license"": [], ""source_url"": ""https://api.crossref.org/works/10.1093%2Fbiomet%2F57.1.97""}}]",https://api.crossref.org/works/10.1093%2Fbiomet%2F57.1.97,"[{""doi"": ""10.1093/biomet/57.1.97"", ""title"": ""Monte Carlo sampling methods using Markov chains and their applications"", ""biblio"": {""volume"": ""57"", ""issue"": ""1"", ""first_page"": ""97"", ""last_page"": ""109""}, ""publication_year"": 1970, ""openalex_id"": ""W2138309709""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Fully-Polynomial-Randomized-Approximation-Scheme-for-Perfect-Matchings-in-General-Graphs-September-23-2026/build/main.tex#L3367,3367,,,,[]
R029,113,A-Fully-Polynomial-Randomized-Approximation-Scheme-for-Perfect-Matchings-in-General-Graphs-September-23-2026,MetropolisEtAl1953,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"\bibitem[Metropolis et~al.(1953)Metropolis, Rosenbluth, Rosenbluth, Teller, and Teller]{MetropolisEtAl1953}
Nicholas Metropolis, Arianna~W. Rosenbluth, Marshall~N. Rosenbluth,
Augusta~H. Teller, and Edward Teller.
\newblock Equation of state calculations by fast computing machines.
\newblock \emph{The Journal of Chemical Physics}, 21\penalty0
  (6):\penalty0 1087--1092, 1953.
\newblock \doi{10.1063/1.1699114}.","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1063/1.1699114"", ""title"": [""Equation of State Calculations by Fast Computing Machines""], ""authors"": [{""given"": ""Nicholas"", ""family"": ""Metropolis"", ""sequence"": ""first"", ""affiliation"": [{""name"": ""Los Alamos Scientific Laboratory, Los Alamos, New Mexico""}], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}, {""given"": ""Arianna W."", ""family"": ""Rosenbluth"", ""sequence"": ""additional"", ""affiliation"": [{""name"": ""Los Alamos Scientific Laboratory, Los Alamos, New Mexico""}], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}, {""given"": ""Marshall N."", ""family"": ""Rosenbluth"", ""sequence"": ""additional"", ""affiliation"": [{""name"": ""Los Alamos Scientific Laboratory, Los Alamos, New Mexico""}], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}, {""given"": ""Augusta H."", ""family"": ""Teller"", ""sequence"": ""additional"", ""affiliation"": [{""name"": ""Los Alamos Scientific Laboratory, Los Alamos, New Mexico""}], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}, {""given"": ""Edward"", ""family"": ""Teller"", ""sequence"": ""additional"", ""affiliation"": [{""name"": ""Department of Physics, University of Chicago, Chicago, Illinois""}], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""AIP Publishing"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[1953, 6, 1]]}, ""container_title"": [""The Journal of Chemical Physics""], ""url"": ""https://doi.org/10.1063/1.1699114"", ""license"": [], ""source_url"": ""https://api.crossref.org/works/10.1063%2F1.1699114""}}]",https://api.crossref.org/works/10.1063%2F1.1699114,"[{""doi"": ""10.1063/1.1699114"", ""title"": ""Equation of State Calculations by Fast Computing Machines"", ""biblio"": {""volume"": ""21"", ""issue"": ""6"", ""first_page"": ""1087"", ""last_page"": ""1092""}, ""publication_year"": 1953, ""openalex_id"": ""W2056760934""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Fully-Polynomial-Randomized-Approximation-Scheme-for-Perfect-Matchings-in-General-Graphs-September-23-2026/build/main.tex#L3409,3409,,,,[]
R030,113,A-Fully-Polynomial-Randomized-Approximation-Scheme-for-Perfect-Matchings-in-General-Graphs-September-23-2026,Kasteleyn1963,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"\bibitem[Kasteleyn(1963)]{Kasteleyn1963}
P.~W. Kasteleyn.
\newblock Dimer statistics and phase transitions.
\newblock \emph{Journal of Mathematical Physics}, 4\penalty0 (2):\penalty0
  287--293, 1963.
\newblock \doi{10.1063/1.1703953}.","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1063/1.1703953"", ""title"": [""Dimer Statistics and Phase Transitions""], ""authors"": [{""given"": ""P. W."", ""family"": ""Kasteleyn"", ""sequence"": ""first"", ""affiliation"": [{""name"": ""Koninklijke/Shell-Laboratorium, Amsterdam, Netherlands, (Shell Internationale Research Maatschappij N.V.)""}], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""AIP Publishing"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[1963, 2, 1]]}, ""container_title"": [""Journal of Mathematical Physics""], ""url"": ""https://doi.org/10.1063/1.1703953"", ""license"": [], ""source_url"": ""https://api.crossref.org/works/10.1063%2F1.1703953""}}]",https://api.crossref.org/works/10.1063%2F1.1703953,"[{""doi"": ""10.1063/1.1703953"", ""title"": ""Dimer Statistics and Phase Transitions"", ""biblio"": {""volume"": ""4"", ""issue"": ""2"", ""first_page"": ""287"", ""last_page"": ""293""}, ""publication_year"": 1963, ""openalex_id"": ""W1982250981""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Fully-Polynomial-Randomized-Approximation-Scheme-for-Perfect-Matchings-in-General-Graphs-September-23-2026/build/main.tex#L3402,3402,unverifiable,Pfaffian methods give polynomial-time exact counting of perfect matchings in planar graphs.,"The source record matches, but no inspectable abstract or full-text passage was returned; the claim was not verified from this source.",[]
R031,115,Exact-Uniform-Sampling-of-Contingency-Tables-with-Arbitrary-Margins-September-24-2026,CDGJM2006,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{CDGJM2006,
  author = {Cryan, Mary and Dyer, Martin and Goldberg, Leslie Ann
            and Jerrum, Mark and Martin, Russell},
  title = {Rapidly Mixing {Markov} Chains for Sampling Contingency Tables
           with a Constant Number of Rows},
  journal = {SIAM Journal on Computing},
  volume = {36},
  number = {1},
  pages = {247--278},
  year = {2006},
  doi = {10.1137/S0097539703434243},
  note = {\href{https://doi.org/10.1137/S0097539703434243}{doi:10.1137/S0097539703434243}}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1137/s0097539703434243"", ""title"": [""Rapidly Mixing Markov Chains for Sampling Contingency Tables with a Constant Number of Rows""], ""authors"": [{""given"": ""Mary"", ""family"": ""Cryan"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}, {""given"": ""Martin"", ""family"": ""Dyer"", ""sequence"": ""additional"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}, {""given"": ""Leslie Ann"", ""family"": ""Goldberg"", ""sequence"": ""additional"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}, {""given"": ""Mark"", ""family"": ""Jerrum"", ""sequence"": ""additional"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}, {""given"": ""Russell"", ""family"": ""Martin"", ""sequence"": ""additional"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""Society for Industrial & Applied Mathematics (SIAM)"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2006, 1]]}, ""container_title"": [""SIAM Journal on Computing""], ""url"": ""https://doi.org/10.1137/s0097539703434243"", ""license"": [], ""source_url"": ""https://api.crossref.org/works/10.1137%2Fs0097539703434243""}}]",https://api.crossref.org/works/10.1137%2Fs0097539703434243,"[{""doi"": ""10.1137/s0097539703434243"", ""title"": ""Rapidly Mixing Markov Chains for Sampling Contingency Tables with a Constant Number of Rows"", ""biblio"": {""volume"": ""36"", ""issue"": ""1"", ""first_page"": ""247"", ""last_page"": ""278""}, ""publication_year"": 2006, ""openalex_id"": ""W2162508244""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Exact-Uniform-Sampling-of-Contingency-Tables-with-Arbitrary-Margins-September-24-2026/build/refs/sources.bib#L173,173,,,,[]
R032,115,Exact-Uniform-Sampling-of-Contingency-Tables-with-Arbitrary-Margins-September-24-2026,AGW2021,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization. Identity verified at preprint level; claimed journal/chapter publication details are not independently certified by that record.,"@misc{AGW2021,
  author        = {Arman, Andrii and Gao, Pu and Wormald, Nicholas},
  title         = {Linear-time uniform generation of random sparse
                   contingency tables with specified marginals},
  howpublished  = {\href{https://arxiv.org/abs/2104.09413v2}{arXiv:2104.09413v2}},
  year          = {2021},
  eprint        = {2104.09413},
  archivePrefix = {arXiv},
  primaryClass  = {math.CO},
  note          = {Version 2, 15 June 2021},
  url           = {https://arxiv.org/abs/2104.09413v2}
}","[{""provider"": ""arXiv original repository"", ""record"": {""arxiv_id"": ""2104.09413"", ""version"": 2, ""id_versioned"": ""2104.09413v2"", ""title"": ""Linear-time uniform generation of random sparse contingency tables with specified marginals"", ""abstract"": ""We give an algorithm that generates a uniformly random contingency table with specified marginals, i.e. a matrix with non-negative integer values and specified row and column sums. Such algorithms are useful in statistics and combinatorics. When $Δ^4< M/5$, where $Δ$ is the maximum of the row and column sums and $M$ is the sum of all entries of the matrix, our algorithm runs in time linear in $M$ in expectation. Most previously published algorithms for this problem are approximate samplers based on Markov chain Monte Carlo, whose provable bounds on the mixing time are typically polynomials with rather large degrees."", ""authors"": [""Andrii Arman"", ""Pu Gao"", ""Nicholas Wormald""], ""published"": ""2021-04-19T16:03:24Z"", ""updated"": ""2021-06-15T20:02:34Z"", ""primary_category"": ""math.CO"", ""categories"": [""math.CO"", ""cs.DS"", ""math.PR""], ""doi"": null, ""journal_ref"": null, ""comment"": ""27 pages, 1 figure"", ""abs_url"": ""http://arxiv.org/abs/2104.09413v2"", ""pdf_url"": ""https://arxiv.org/pdf/2104.09413v2""}}]",http://arxiv.org/abs/2104.09413v2,[],Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Exact-Uniform-Sampling-of-Contingency-Tables-with-Arbitrary-Margins-September-24-2026/build/refs/sources.bib#L1,1,,,,[]
R033,115,Exact-Uniform-Sampling-of-Contingency-Tables-with-Arbitrary-Margins-September-24-2026,DZ2016,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization. Identity verified at preprint level; claimed journal/chapter publication details are not independently certified by that record.,"@misc{DZ2016,
  author = {DeSalvo, Stephen and Zhao, James Y.},
  title = {Random Sampling of Contingency Tables via Probabilistic Divide-and-Conquer},
  year = {2016},
  howpublished = {\href{https://arxiv.org/abs/1507.00070v4}{arXiv:1507.00070v4}},
  eprint = {1507.00070},
  archivePrefix = {arXiv},
  primaryClass = {math.ST},
  note = {Version 4, 29 February 2016},
  url = {https://arxiv.org/abs/1507.00070v4}
}","[{""provider"": ""arXiv original repository"", ""record"": {""arxiv_id"": ""1507.00070"", ""version"": 4, ""id_versioned"": ""1507.00070v4"", ""title"": ""Random Sampling of Contingency Tables via Probabilistic Divide-and-Conquer"", ""abstract"": ""We present a new approach for random sampling of contingency tables of any size and constraints based on a recently introduced $\\textit{probabilistic divide-and-conquer}$ technique. A simple exact sampling algorithm is presented for $2\\times n$ tables, as well as a generalization where each entry of the table has a specified marginal distribution."", ""authors"": [""Stephen DeSalvo"", ""James Y. Zhao""], ""published"": ""2015-07-01T00:06:21Z"", ""updated"": ""2016-02-29T19:14:46Z"", ""primary_category"": ""math.ST"", ""categories"": [""math.ST"", ""math.PR""], ""doi"": null, ""journal_ref"": null, ""comment"": ""32 Pages, rewritten"", ""abs_url"": ""http://arxiv.org/abs/1507.00070v4"", ""pdf_url"": ""https://arxiv.org/pdf/1507.00070v4""}}]",http://arxiv.org/abs/1507.00070v4,[],Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Exact-Uniform-Sampling-of-Contingency-Tables-with-Arbitrary-Margins-September-24-2026/build/refs/sources.bib#L136,136,,,,[]
R034,115,Exact-Uniform-Sampling-of-Contingency-Tables-with-Arbitrary-Margins-September-24-2026,DKM1997,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{DKM1997,
  author = {Dyer, Martin and Kannan, Ravi and Mount, John},
  title = {Sampling contingency tables},
  journal = {Random Structures \& Algorithms},
  volume = {10},
  number = {4},
  pages = {487--506},
  year = {1997},
  note = {\href{https://www.math.cmu.edu/~af1p/Teaching/MCC17/Papers/contingency.pdf}{Published article}},
  url = {https://www.math.cmu.edu/~af1p/Teaching/MCC17/Papers/contingency.pdf}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1002/(sici)1098-2418(199707)10:4<487::aid-rsa4>3.0.co;2-q"", ""title"": [""Sampling contingency tables""], ""authors"": [{""given"": ""Martin"", ""family"": ""Dyer"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}, {""given"": ""Ravi"", ""family"": ""Kannan"", ""sequence"": ""additional"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}, {""given"": ""John"", ""family"": ""Mount"", ""sequence"": ""additional"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""Wiley"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[1997, 7]]}, ""container_title"": [""Random Structures and Algorithms""], ""url"": ""https://doi.org/10.1002/(sici)1098-2418(199707)10:4<487::aid-rsa4>3.0.co;2-q"", ""license"": [{""start"": {""date-parts"": [[2015, 9, 1]], ""date-time"": ""2015-09-01T00:00:00Z"", ""timestamp"": 1441065600000}, ""content-version"": ""tdm"", ""delay-in-days"": 6636, ""URL"": ""http://doi.wiley.com/10.1002/tdm_license_1.1""}], ""source_url"": ""https://api.crossref.org/works/10.1002%2F(sici)1098-2418(199707)10%3A4%3C487%3A%3Aaid-rsa4%3E3.0.co%3B2-q""}}]",https://api.crossref.org/works/10.1002%2F(sici)1098-2418(199707)10%3A4%3C487%3A%3Aaid-rsa4%3E3.0.co%3B2-q,[],Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Exact-Uniform-Sampling-of-Contingency-Tables-with-Arbitrary-Margins-September-24-2026/build/refs/sources.bib#L55,55,,,,[]
R035,115,Exact-Uniform-Sampling-of-Contingency-Tables-with-Arbitrary-Margins-September-24-2026,Dyer2003,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@inproceedings{Dyer2003,
  author = {Dyer, Martin},
  title = {Approximate counting by dynamic programming},
  booktitle = {Proceedings of the Thirty-Fifth Annual ACM Symposium on
               Theory of Computing},
  pages = {693--699},
  publisher = {ACM},
  year = {2003},
  note = {\href{https://www.math.cmu.edu/~af1p/Teaching/MCC17/Papers/knapsack.pdf}{Published article}},
  url = {https://www.math.cmu.edu/~af1p/Teaching/MCC17/Papers/knapsack.pdf}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1145/780542.780643"", ""title"": [""Approximate counting by dynamic programming""], ""authors"": [{""given"": ""Martin"", ""family"": ""Dyer"", ""sequence"": ""first"", ""affiliation"": [{""name"": ""University of Leeds, Leeds, UK""}], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""ACM"", ""type"": ""proceedings-article"", ""published"": {""date-parts"": [[2003, 6, 9]]}, ""container_title"": [""Proceedings of the thirty-fifth annual ACM symposium on Theory of computing""], ""url"": ""https://doi.org/10.1145/780542.780643"", ""license"": [{""start"": {""date-parts"": [[2003, 6, 9]], ""date-time"": ""2003-06-09T00:00:00Z"", ""timestamp"": 1055116800000}, ""content-version"": ""vor"", ""delay-in-days"": 0, ""URL"": ""https://www.acm.org/publications/policies/copyright_policy#Background""}], ""source_url"": ""https://api.crossref.org/works/10.1145%2F780542.780643""}}]",https://api.crossref.org/works/10.1145%2F780542.780643,[],Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Exact-Uniform-Sampling-of-Contingency-Tables-with-Arbitrary-Margins-September-24-2026/build/refs/sources.bib#L161,161,,,,[]
R036,127,Average-Sensitivity-of-Polynomial-Threshold-Functions-September-25-2026,Xu2004,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"\bibitem{Xu2004}
Yuan Xu,
\emph{On discrete orthogonal polynomials of several variables},
Advances in Applied Mathematics \textbf{33} (2004), 615--632.
\href{https://doi.org/10.1016/j.aam.2004.03.002}{\nolinkurl{doi:10.1016/j.aam.2004.03.002}}.
Preprint: \href{https://arxiv.org/abs/math/0401418v2}{arXiv:math/0401418v2}.","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1016/j.aam.2004.03.002"", ""title"": [""On discrete orthogonal polynomials of several variables""], ""authors"": [{""given"": ""Yuan"", ""family"": ""Xu"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""role"": ""author"", ""vocabulary"": ""crossref""}]}], ""publisher"": ""Elsevier BV"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2004, 10]]}, ""container_title"": [""Advances in Applied Mathematics""], ""url"": ""https://doi.org/10.1016/j.aam.2004.03.002"", ""license"": [{""start"": {""date-parts"": [[2004, 10, 1]], ""date-time"": ""2004-10-01T00:00:00Z"", ""timestamp"": 1096588800000}, ""content-version"": ""tdm"", ""delay-in-days"": 0, ""URL"": ""https://www.elsevier.com/tdm/userlicense/1.0/""}, {""start"": {""date-parts"": [[2004, 10, 1]], ""date-time"": ""2004-10-01T00:00:00Z"", ""timestamp"": 1096588800000}, ""content-version"": ""tdm"", ""delay-in-days"": 0, ""URL"": ""https://www.elsevier.com/legal/tdmrep-license""}, {""start"": {""date-parts"": [[2013, 7, 17]], ""date-time"": ""2013-07-17T00:00:00Z"", ""timestamp"": 1374019200000}, ""content-version"": ""vor"", ""delay-in-days"": 3211, ""URL"": ""http://www.elsevier.com/open-access/userlicense/1.0/""}], ""source_url"": ""https://api.crossref.org/works/10.1016%2Fj.aam.2004.03.002""}}, {""provider"": ""arXiv original repository"", ""record"": {""arxiv_id"": ""math/0401418"", ""version"": 2, ""id_versioned"": ""math/0401418v2"", ""title"": ""On discrete orthogonal polynomials of several variables"", ""abstract"": ""Let $V$ be a set of isolated points in $\\RR^d$. Define a linear functional $\\CL$ on the space of real polynomials restricted on $V$, $\\CL f = \\sum_{x \\in V} f(x)ρ(x)$, where $ρ$ is a nonzero function on $V$. Polynomial subspaces that contain discrete orthogonal polynomials with respect to the bilinear form $<f,g> = \\CL(f g)$ are identified. One result shows that the discrete orthogonal polynomials still satisfy a three-term relation and Favard's theorem holds in this general setting."", ""authors"": [""Yuan Xu""], ""published"": ""2004-01-29T17:38:30Z"", ""updated"": ""2004-04-09T18:30:33Z"", ""primary_category"": ""math.CA"", ""categories"": [""math.CA""], ""doi"": null, ""journal_ref"": null, ""comment"": ""15 pages, 2 figures"", ""abs_url"": ""http://arxiv.org/abs/math/0401418v2"", ""pdf_url"": ""https://arxiv.org/pdf/math/0401418v2""}}]",https://api.crossref.org/works/10.1016%2Fj.aam.2004.03.002 | http://arxiv.org/abs/math/0401418v2,"[{""doi"": ""10.1016/j.aam.2004.03.002"", ""title"": ""On discrete orthogonal polynomials of several variables"", ""biblio"": {""volume"": ""33"", ""issue"": ""3"", ""first_page"": ""615"", ""last_page"": ""632""}, ""publication_year"": 2004, ""openalex_id"": ""W2019091792""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Average-Sensitivity-of-Polynomial-Threshold-Functions-September-25-2026/build/references.tex#L79,79,,,,[]
R037,127,Average-Sensitivity-of-Polynomial-Threshold-Functions-September-25-2026,Kane2014,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"\bibitem{Kane2014}
Daniel M. Kane,
\emph{The correct exponent for the Gotsman--Linial conjecture},
Computational Complexity \textbf{23} (2014), no.~2, 151--175.
\href{https://doi.org/10.1007/s00037-014-0086-z}{\nolinkurl{doi:10.1007/s00037-014-0086-z}}.
Preprint: \href{https://arxiv.org/abs/1210.1283v1}{arXiv:1210.1283v1}.","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1007/s00037-014-0086-z"", ""title"": [""The correct exponent for the Gotsman–Linial Conjecture""], ""authors"": [{""given"": ""Daniel M."", ""family"": ""Kane"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""Springer Science and Business Media LLC"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2014, 5, 13]]}, ""container_title"": [""computational complexity""], ""url"": ""https://doi.org/10.1007/s00037-014-0086-z"", ""license"": [{""start"": {""date-parts"": [[2014, 5, 13]], ""date-time"": ""2014-05-13T00:00:00Z"", ""timestamp"": 1399939200000}, ""content-version"": ""tdm"", ""delay-in-days"": 0, ""URL"": ""http://www.springer.com/tdm""}], ""source_url"": ""https://api.crossref.org/works/10.1007%2Fs00037-014-0086-z""}}, {""provider"": ""arXiv original repository"", ""record"": {""arxiv_id"": ""1210.1283"", ""version"": 1, ""id_versioned"": ""1210.1283v1"", ""title"": ""The Correct Exponent for the Gotsman-Linial Conjecture"", ""abstract"": ""We prove a new bound on the average sensitivity of polynomial threshold functions. In particular we show that a polynomial threshold function of degree $d$ in at most $n$ variables has average sensitivity at most $\\sqrt{n}(\\log(n))^{O(d\\log(d))}2^{O(d^2\\log(d)}$. For fixed $d$ the exponent in terms of $n$ in this bound is known to be optimal. This bound makes significant progress towards the Gotsman-Linial Conjecture which would put the correct bound at $Θ(d\\sqrt{n})$."", ""authors"": [""Daniel M. Kane""], ""published"": ""2012-10-04T03:08:19Z"", ""updated"": ""2012-10-04T03:08:19Z"", ""primary_category"": ""math.CO"", ""categories"": [""math.CO"", ""cs.CC"", ""math.PR""], ""doi"": null, ""journal_ref"": null, ""comment"": null, ""abs_url"": ""http://arxiv.org/abs/1210.1283v1"", ""pdf_url"": ""https://arxiv.org/pdf/1210.1283v1""}}]",https://api.crossref.org/works/10.1007%2Fs00037-014-0086-z | http://arxiv.org/abs/1210.1283v1,"[{""doi"": ""10.1007/s00037-014-0086-z"", ""title"": ""The correct exponent for the Gotsman–Linial Conjecture"", ""biblio"": {""volume"": ""23"", ""issue"": ""2"", ""first_page"": ""151"", ""last_page"": ""175""}, ""publication_year"": 2014, ""openalex_id"": ""W2071833075""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Average-Sensitivity-of-Polynomial-Threshold-Functions-September-25-2026/build/references.tex#L53,53,,,,[]
R038,127,Average-Sensitivity-of-Polynomial-Threshold-Functions-September-25-2026,TsengVolberg2026,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization. Identity verified at preprint level; claimed journal/chapter publication details are not independently certified by that record.,"\bibitem{TsengVolberg2026}
Chun-Kai Tseng and Alexander Volberg,
\emph{Small moments of the sensitivity of polynomial threshold functions},
preprint, 2026.
\href{https://arxiv.org/abs/2606.16004v2}{arXiv:2606.16004v2}.","[{""provider"": ""arXiv original repository"", ""record"": {""arxiv_id"": ""2606.16004"", ""version"": 2, ""id_versioned"": ""2606.16004v2"", ""title"": ""Small moments of the sensitivity of polynomial threshold functions"", ""abstract"": ""In the first version of Chang, Slote, Volberg, and Zhang's paper \\cite{BSA_of_PTF}, the authors modify a nice recursive approach due to Kane in \\cite{Correct_exponent_for_AS} where he bounded the average sensitivity of polynomial threshold functions. In \\cite{BSA_of_PTF} Kane's argument was adopted to estimate the boolean surface area of polynomial threshold function. The bridge is a combinatorial averaging lemma considering all balanced partitions. The lemma serves as a substitute for an additive property of average sensitivity. With the lemma, one can apply a Kane-type algorithm to derive a recurrence. Solving the recurrence then gives an upper bound of $e^{C_d \\sqrt{\\log n}}$ for the boolean surface area. In the second version of the same paper, the authors derive a polylog upper bound for BSA of PTFs. The difference is that they use a tail estimate for the sensitivity function. With the help of a polynomial restriction lemma in \\cite{poly_restriction} they sharpen the upper bound. It is noteworthy that when applying the polynomial restriction, each coordinate is put into each part independently with equal probability. As a result, a partition does not necessarily have equal-size blocks. In other words, it may not be balanced. In this note, we first investigate the effect of different partitioning. Second, we use the recursive method in the first version to derive a polylog upper bound for $\\mathbb E[s(x)^η]$ where $η< 1/2$. It is interesting to note the phase transition that happens at $η=1/2$ in both versions of the proof (but in a completely different form). Section 2.5 treats that."", ""authors"": [""Chun-Kai Tseng"", ""Alexander Volberg""], ""published"": ""2026-06-14T20:18:11Z"", ""updated"": ""2026-06-21T17:31:54Z"", ""primary_category"": ""math.PR"", ""categories"": [""math.PR"", ""math.AP"", ""math.CO""], ""doi"": null, ""journal_ref"": null, ""comment"": ""15 pages"", ""abs_url"": ""http://arxiv.org/abs/2606.16004v2"", ""pdf_url"": ""https://arxiv.org/pdf/2606.16004v2""}}]",http://arxiv.org/abs/2606.16004v2,[],Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Average-Sensitivity-of-Polynomial-Threshold-Functions-September-25-2026/build/references.tex#L73,73,,,,[]
R039,127,Average-Sensitivity-of-Polynomial-Threshold-Functions-September-25-2026,ChangSloteVolbergZhang2026,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization. Identity verified at preprint level; claimed journal/chapter publication details are not independently certified by that record.,"\bibitem{ChangSloteVolbergZhang2026}
Fan Chang, Joseph Slote, Alexander Volberg, and Haonan Zhang,
\emph{The Boolean surface area of polynomial threshold functions},
preprint, 2026.
\href{https://arxiv.org/abs/2604.08095v2}{arXiv:2604.08095v2}.","[{""provider"": ""arXiv original repository"", ""record"": {""arxiv_id"": ""2604.08095"", ""version"": 2, ""id_versioned"": ""2604.08095v2"", ""title"": ""The Boolean surface area of polynomial threshold functions"", ""abstract"": ""Polynomial threshold functions (PTFs) are an important low-complexity class of Boolean functions, with strong connections to learning theory and approximation theory. Recent work on learning and testing PTFs has exploited structural and isoperimetric properties of the class, especially bounds on average sensitivity, one of the central themes in the study of PTFs since the Gotsman--Linial conjecture. In this work we study PTFs through the lens of the Boolean surface area (or Talagrand boundary) \\[ \\mathbf{BSA}[f]=\\mathbb{E}|\\nabla f|=\\mathbb{E}\\sqrt{s_{f}(x)}, \\] a natural measure of vertex-boundary complexity on the discrete cube. Our main result is that every degree-$d$ PTF has polylogarithmic Boolean surface area: \\[ \\mathbf{BSA}[f]\\le C_d(\\log(en))^{C_d}. \\] The proof is based on the PTF Restriction Lemma of Kabanets, Kane, and Lu \\cite{KKL2017} and proceeds through a tail bound for the pointwise sensitivity. In particular, it controls all subcritical fractional moments of the sensitivity. We also record a random block partition principle for Boolean surface area and an alternative recursive argument following Kane's work \\cite{DK} on average sensitivity, which independently yields the weaker bound \\[ \\mathbf{BSA}[f]\\le \\exp(C_d\\sqrt{\\log n}). \\]"", ""authors"": [""Fan Chang"", ""Joseph Slote"", ""Alexander Volberg"", ""Haonan Zhang""], ""published"": ""2026-04-09T11:11:06Z"", ""updated"": ""2026-04-27T06:28:32Z"", ""primary_category"": ""cs.CC"", ""categories"": [""cs.CC"", ""math.AP"", ""math.CA"", ""math.PR""], ""doi"": null, ""journal_ref"": null, ""comment"": ""18 pages, 1 figure"", ""abs_url"": ""http://arxiv.org/abs/2604.08095v2"", ""pdf_url"": ""https://arxiv.org/pdf/2604.08095v2""}}]",http://arxiv.org/abs/2604.08095v2,[],Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Average-Sensitivity-of-Polynomial-Threshold-Functions-September-25-2026/build/references.tex#L3,3,,,,[]
R040,127,Average-Sensitivity-of-Polynomial-Threshold-Functions-September-25-2026,Chapman2018,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"\bibitem{Chapman2018}
Brynmor Chapman,
\emph{The Gotsman--Linial conjecture is false},
in Proceedings of the Twenty-Ninth Annual ACM--SIAM Symposium on Discrete
Algorithms (SODA 2018), Society for Industrial and Applied Mathematics,
2018, 692--699.
\href{https://doi.org/10.1137/1.9781611975031.45}{\nolinkurl{doi:10.1137/1.9781611975031.45}}.
Preprint: \href{https://arxiv.org/abs/2108.02288v1}{arXiv:2108.02288v1}.","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1137/1.9781611975031.45"", ""title"": [""The Gotsman-Linial Conjecture is False""], ""authors"": [{""given"": ""Brynmor"", ""family"": ""Chapman"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""role"": ""author"", ""vocabulary"": ""crossref""}]}], ""publisher"": ""Society for Industrial and Applied Mathematics"", ""type"": ""book-chapter"", ""published"": {""date-parts"": [[2018, 1]]}, ""container_title"": [""Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms""], ""url"": ""https://doi.org/10.1137/1.9781611975031.45"", ""license"": [], ""source_url"": ""https://api.crossref.org/works/10.1137%2F1.9781611975031.45""}}, {""provider"": ""arXiv original repository"", ""record"": {""arxiv_id"": ""2108.02288"", ""version"": 1, ""id_versioned"": ""2108.02288v1"", ""title"": ""The Gotsman-Linial Conjecture is False"", ""abstract"": ""In 1991, Craig Gotsman and Nathan Linial conjectured that for all $n$ and $d$, the average sensitivity of a degree-$d$ polynomial threshold function on $n$ variables is maximized by the degree-$d$ symmetric polynomial which computes the parity function on the $d$ layers of the hypercube with Hamming weight closest to $n/2$. We refute the conjecture for almost all $d$ and for almost all $n$, and we confirm the conjecture in many of the remaining cases."", ""authors"": [""Brynmor Chapman""], ""published"": ""2021-08-04T21:19:31Z"", ""updated"": ""2021-08-04T21:19:31Z"", ""primary_category"": ""math.CO"", ""categories"": [""math.CO"", ""cs.CC""], ""doi"": ""10.1137/1.9781611975031.45"", ""journal_ref"": ""Proceedings of the 2018 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 692-699, 2018"", ""comment"": ""Appeared in SODA 2018"", ""abs_url"": ""http://arxiv.org/abs/2108.02288v1"", ""pdf_url"": ""https://arxiv.org/pdf/2108.02288v1""}}]",https://api.crossref.org/works/10.1137%2F1.9781611975031.45 | http://arxiv.org/abs/2108.02288v1,"[{""doi"": ""10.1137/1.9781611975031.45"", ""title"": ""The Gotsman-Linial Conjecture is False"", ""biblio"": {""volume"": null, ""issue"": null, ""first_page"": ""692"", ""last_page"": ""699""}, ""publication_year"": 2018, ""openalex_id"": ""W2779077750""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Average-Sensitivity-of-Polynomial-Threshold-Functions-September-25-2026/build/references.tex#L9,9,,,,[]
R041,148,The-entropy-rate-dimension-formula-for-self-similar-measures-on-the-line-September-24-2026,RapaportVarju2024,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{RapaportVarju2024,
  author = {Rapaport, Ariel and Varj\'{u}, P\'{e}ter P.},
  title = {Self-similar measures associated to a homogeneous system of three maps},
  journal = {Duke Mathematical Journal},
  volume = {173},
  number = {3},
  year = {2024},
  pages = {513--602},
  doi = {10.1215/00127094-2023-0019},
  eprint = {2010.01022v3},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2010.01022v3},
  note = {\href{https://doi.org/10.1215/00127094-2023-0019}{doi:10.1215/00127094-2023-0019}}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1215/00127094-2023-0019"", ""title"": [""Self-similar measures associated to a homogeneous system of three maps""], ""authors"": [{""given"": ""Ariel"", ""family"": ""Rapaport"", ""sequence"": ""first"", ""affiliation"": [{""name"": ""Department of Mathematics, Technion, Haifa, Israel""}], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}, {""given"": ""Péter P."", ""family"": ""Varjú"", ""sequence"": ""additional"", ""affiliation"": [{""name"": ""Centre for Mathematical Sciences, University of Cambridge, Cambridge, UK""}], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""Duke University Press"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2024, 2, 15]]}, ""container_title"": [""Duke Mathematical Journal""], ""url"": ""https://doi.org/10.1215/00127094-2023-0019"", ""license"": [], ""source_url"": ""https://api.crossref.org/works/10.1215%2F00127094-2023-0019""}}, {""provider"": ""arXiv original repository"", ""record"": {""arxiv_id"": ""2010.01022"", ""version"": 3, ""id_versioned"": ""2010.01022v3"", ""title"": ""Self-similar measures associated to a homogeneous system of three maps"", ""abstract"": ""We study the dimension of self-similar measures associated to a homogeneous iterated function system of three contracting similarities on $\\bf R$ and other more general IFS's. We extend some of the theory recently developed for Bernoulli convolutions to this setting. In the setting of three maps a new phenomenon occurs, which has been highlighted by recent examples of Baker, and Bárány, Käenmäki. To overcome the difficulties stemming form these, we develop novel techniques, including an extension of Hochman's entropy increase method to a function field setup."", ""authors"": [""Ariel Rapaport"", ""Péter P. Varjú""], ""published"": ""2020-10-02T14:19:33Z"", ""updated"": ""2023-03-08T10:11:00Z"", ""primary_category"": ""math.DS"", ""categories"": [""math.DS""], ""doi"": null, ""journal_ref"": null, ""comment"": ""85 pages, minor revision based on referee's report, final accepted version to appear in Duke Math. J"", ""abs_url"": ""http://arxiv.org/abs/2010.01022v3"", ""pdf_url"": ""https://arxiv.org/pdf/2010.01022v3""}}]",https://api.crossref.org/works/10.1215%2F00127094-2023-0019 | http://arxiv.org/abs/2010.01022v3,"[{""doi"": ""10.1215/00127094-2023-0019"", ""title"": ""Self-similar measures associated to a homogeneous system of three maps"", ""biblio"": {""volume"": ""173"", ""issue"": ""3"", ""first_page"": null, ""last_page"": null}, ""publication_year"": 2024, ""openalex_id"": ""W3091280398""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-entropy-rate-dimension-formula-for-self-similar-measures-on-the-line-September-24-2026/build/references.bib#L78,78,,,,[]
R042,148,The-entropy-rate-dimension-formula-for-self-similar-measures-on-the-line-September-24-2026,Baker2021,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{Baker2021,
  author = {Baker, Simon},
  title = {Iterated function systems with super-exponentially close cylinders},
  journal = {Advances in Mathematics},
  volume = {379},
  year = {2021},
  pages = {107548},
  doi = {10.1016/j.aim.2020.107548},
  eprint = {1909.04343v2},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1909.04343v2},
  note = {\href{https://doi.org/10.1016/j.aim.2020.107548}{doi:10.1016/j.aim.2020.107548}}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1016/j.aim.2020.107548"", ""title"": [""Iterated function systems with super-exponentially close cylinders""], ""authors"": [{""given"": ""Simon"", ""family"": ""Baker"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""Elsevier BV"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2021, 3]]}, ""container_title"": [""Advances in Mathematics""], ""url"": ""https://doi.org/10.1016/j.aim.2020.107548"", ""license"": [{""start"": {""date-parts"": [[2021, 3, 1]], ""date-time"": ""2021-03-01T00:00:00Z"", ""timestamp"": 1614556800000}, ""content-version"": ""tdm"", ""delay-in-days"": 0, ""URL"": ""https://www.elsevier.com/tdm/userlicense/1.0/""}, {""start"": {""date-parts"": [[2021, 3, 1]], ""date-time"": ""2021-03-01T00:00:00Z"", ""timestamp"": 1614556800000}, ""content-version"": ""tdm"", ""delay-in-days"": 0, ""URL"": ""https://www.elsevier.com/legal/tdmrep-license""}, {""start"": {""date-parts"": [[2025, 3, 5]], ""date-time"": ""2025-03-05T00:00:00Z"", ""timestamp"": 1741132800000}, ""content-version"": ""vor"", ""delay-in-days"": 1465, ""URL"": ""http://www.elsevier.com/open-access/userlicense/1.0/""}, {""start"": {""date-parts"": [[2021, 3, 1]], ""date-time"": ""2021-03-01T00:00:00Z"", ""timestamp"": 1614556800000}, ""content-version"": ""stm-asf"", ""delay-in-days"": 0, ""URL"": ""https://doi.org/10.15223/policy-017""}, {""start"": {""date-parts"": [[2021, 3, 1]], ""date-time"": ""2021-03-01T00:00:00Z"", ""timestamp"": 1614556800000}, ""content-version"": ""stm-asf"", ""delay-in-days"": 0, ""URL"": ""https://doi.org/10.15223/policy-037""}, {""start"": {""date-parts"": [[2021, 3, 1]], ""date-time"": ""2021-03-01T00:00:00Z"", ""timestamp"": 1614556800000}, ""content-version"": ""stm-asf"", ""delay-in-days"": 0, ""URL"": ""https://doi.org/10.15223/policy-012""}, {""start"": {""date-parts"": [[2021, 3, 1]], ""date-time"": ""2021-03-01T00:00:00Z"", ""timestamp"": 1614556800000}, ""content-version"": ""stm-asf"", ""delay-in-days"": 0, ""URL"": ""https://doi.org/10.15223/policy-029""}, {""start"": {""date-parts"": [[2021, 3, 1]], ""date-time"": ""2021-03-01T00:00:00Z"", ""timestamp"": 1614556800000}, ""content-version"": ""stm-asf"", ""delay-in-days"": 0, ""URL"": ""https://doi.org/10.15223/policy-004""}], ""source_url"": ""https://api.crossref.org/works/10.1016%2Fj.aim.2020.107548""}}, {""provider"": ""arXiv original repository"", ""record"": {""arxiv_id"": ""1909.04343"", ""version"": 2, ""id_versioned"": ""1909.04343v2"", ""title"": ""Iterated function systems with super-exponentially close cylinders"", ""abstract"": ""Several important conjectures in Fractal Geometry can be summarised as follows: If the dimension of a self-similar measure in $\\mathbb{R}$ does not equal its expected value, then the underlying iterated function system contains an exact overlap. In recent years significant progress has been made towards these conjectures. Hochman proved that if the Hausdorff dimension of a self-similar measure in $\\mathbb{R}$ does not equal its expected value, then there are cylinders which are super-exponentially close at all small scales. Several years later, Shmerkin proved an analogous statement for the $L^q$ dimension of self-similar measures in $\\mathbb{R}$. With these statements in mind, it is natural to wonder whether there exist iterated function systems that do not contain exact overlaps, yet there are cylinders which are super-exponentially close at all small scales. In this paper we show that such iterated function systems do exist. In fact we prove much more. We prove that for any sequence $(ε_n)_{n=1}^{\\infty}$ of positive real numbers, there exists an iterated function system $\\{φ_i\\}_{i\\in \\mathcal{I}}$ that does not contain exact overlaps and $$\\min\\left\\{|φ_{\\mathbf{a}}(0)-φ_{\\mathbf{b}}(0)|: \\mathbf{a},\\mathbf{b}\\in \\mathcal{I}^n,\\, \\mathbf{a}\\neq \\mathbf{b},\\, r_{\\mathbf{a}}=r_{\\mathbf{b}}\\right\\}\\leq ε_n$$ for all $n\\in \\mathbb{N}.$"", ""authors"": [""Simon Baker""], ""published"": ""2019-09-10T08:08:58Z"", ""updated"": ""2019-09-12T12:05:04Z"", ""primary_category"": ""math.DS"", ""categories"": [""math.DS"", ""math.CA"", ""math.MG""], ""doi"": null, ""journal_ref"": null, ""comment"": null, ""abs_url"": ""http://arxiv.org/abs/1909.04343v2"", ""pdf_url"": ""https://arxiv.org/pdf/1909.04343v2""}}]",https://api.crossref.org/works/10.1016%2Fj.aim.2020.107548 | http://arxiv.org/abs/1909.04343v2,"[{""doi"": ""10.1016/j.aim.2020.107548"", ""title"": ""Iterated function systems with super-exponentially close cylinders"", ""biblio"": {""volume"": ""379"", ""issue"": null, ""first_page"": ""107548"", ""last_page"": ""107548""}, ""publication_year"": 2021, ""openalex_id"": ""W3119097474""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-entropy-rate-dimension-formula-for-self-similar-measures-on-the-line-September-24-2026/build/references.bib#L251,251,,,,[]
R043,148,The-entropy-rate-dimension-formula-for-self-similar-measures-on-the-line-September-24-2026,Hutchinson1981,unverified,"DOI exists and registry author/year agree, but both Crossref and OpenAlex return an empty title. Work identity is only partially corroborated; title and full pagination remain unverified.","@article{Hutchinson1981,
  author = {Hutchinson, John E.},
  title = {Fractals and self-similarity},
  journal = {Indiana University Mathematics Journal},
  volume = {30},
  number = {5},
  year = {1981},
  pages = {713--747},
  doi = {10.1512/iumj.1981.30.30055},
  url = {https://doi.org/10.1512/iumj.1981.30.30055},
  note = {\href{https://doi.org/10.1512/iumj.1981.30.30055}{doi:10.1512/iumj.1981.30.30055}}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1512/iumj.1981.30.30055"", ""title"": [""""], ""authors"": [{""given"": ""John"", ""family"": ""Hutchinson"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""Indiana University Mathematics Journal"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[1981]]}, ""container_title"": [""Indiana University Mathematics Journal""], ""url"": ""https://doi.org/10.1512/iumj.1981.30.30055"", ""license"": [], ""source_url"": ""https://api.crossref.org/works/10.1512%2Fiumj.1981.30.30055""}}]",https://api.crossref.org/works/10.1512%2Fiumj.1981.30.30055,"[{""doi"": ""10.1512/iumj.1981.30.30055"", ""title"": """", ""biblio"": {""volume"": ""30"", ""issue"": ""5"", ""first_page"": ""713"", ""last_page"": ""713""}, ""publication_year"": 1981, ""openalex_id"": ""W4249775755""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-entropy-rate-dimension-formula-for-self-similar-measures-on-the-line-September-24-2026/build/references.bib#L158,158,,,,[]
R044,148,The-entropy-rate-dimension-formula-for-self-similar-measures-on-the-line-September-24-2026,FengHu2009,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{FengHu2009,
  author = {Feng, De-Jun and Hu, Huyi},
  title = {Dimension theory of iterated function systems},
  journal = {Communications on Pure and Applied Mathematics},
  volume = {62},
  number = {11},
  year = {2009},
  pages = {1435--1500},
  doi = {10.1002/cpa.20276},
  eprint = {1002.2036v1},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1002.2036v1},
  note = {\href{https://doi.org/10.1002/cpa.20276}{doi:10.1002/cpa.20276}}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1002/cpa.20276"", ""title"": [""Dimension theory of iterated function systems""], ""authors"": [{""given"": ""De‐Jun"", ""family"": ""Feng"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}, {""given"": ""Huyi"", ""family"": ""Hu"", ""sequence"": ""additional"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""Wiley"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2009, 3, 3]]}, ""container_title"": [""Communications on Pure and Applied Mathematics""], ""url"": ""https://doi.org/10.1002/cpa.20276"", ""license"": [{""start"": {""date-parts"": [[2009, 3, 3]], ""date-time"": ""2009-03-03T00:00:00Z"", ""timestamp"": 1236038400000}, ""content-version"": ""vor"", ""delay-in-days"": 0, ""URL"": ""http://onlinelibrary.wiley.com/termsAndConditions#vor""}], ""source_url"": ""https://api.crossref.org/works/10.1002%2Fcpa.20276""}}, {""provider"": ""arXiv original repository"", ""record"": {""arxiv_id"": ""1002.2036"", ""version"": 1, ""id_versioned"": ""1002.2036v1"", ""title"": ""Dimension theory of iterated function systems"", ""abstract"": ""Let $\\{S_i\\}_{i=1}^\\ell$ be an iterated function system (IFS) on $\\R^d$ with attractor $K$. Let $(Σ,σ)$ denote the one-sided full shift over the alphabet $\\{1,..., \\ell\\}$. We define the projection entropy function $h_π$ on the space of invariant measures on $Σ$ associated with the coding map $π: Σ\\to K$, and develop some basic ergodic properties about it. This concept turns out to be crucial in the study of dimensional properties of invariant measures on $K$. We show that for any conformal IFS (resp., the direct product of finitely many conformal IFS), without any separation condition, the projection of an ergodic measure under $π$ is always exactly dimensional and, its Hausdorff dimension can be represented as the ratio of its projection entropy to its Lyapunov exponent (resp., the linear combination of projection entropies associated with several coding maps). Furthermore, for any conformal IFS and certain affine IFS, we prove a variational principle between the Hausdorff dimension of the attractors and that of projections of ergodic measures."", ""authors"": [""De-Jun Feng"", ""Huyi Hu""], ""published"": ""2010-02-10T07:56:12Z"", ""updated"": ""2010-02-10T07:56:12Z"", ""primary_category"": ""math.DS"", ""categories"": [""math.DS"", ""math.CA""], ""doi"": null, ""journal_ref"": ""Comm. Pure Appl. Math., 62 (2009), no. 11, 1435--1500"", ""comment"": ""60 pages"", ""abs_url"": ""http://arxiv.org/abs/1002.2036v1"", ""pdf_url"": ""https://arxiv.org/pdf/1002.2036v1""}}]",https://api.crossref.org/works/10.1002%2Fcpa.20276 | http://arxiv.org/abs/1002.2036v1,"[{""doi"": ""10.1002/cpa.20276"", ""title"": ""Dimension theory of iterated function systems"", ""biblio"": {""volume"": ""62"", ""issue"": ""11"", ""first_page"": ""1435"", ""last_page"": ""1500""}, ""publication_year"": 2009, ""openalex_id"": ""W2962852664""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-entropy-rate-dimension-formula-for-self-similar-measures-on-the-line-September-24-2026/build/references.bib#L1,1,,,,[]
R045,148,The-entropy-rate-dimension-formula-for-self-similar-measures-on-the-line-September-24-2026,BaranyVerma2026,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization. Identity verified at preprint level; claimed journal/chapter publication details are not independently certified by that record.,"@misc{BaranyVerma2026,
  author = {B\'{a}r\'{a}ny, Bal\'{a}zs and Verma, Manuj},
  title = {Hausdorff dimension of self-similar measures and sets with common fixed point structure},
  year = {2026},
  eprint = {2507.05835v2},
  note = {\href{https://arxiv.org/abs/2507.05835v2}{arXiv:2507.05835v2}},
  archivePrefix = {arXiv},
  primaryClass = {math.DS},
  url = {https://arxiv.org/abs/2507.05835v2}
}","[{""provider"": ""arXiv original repository"", ""record"": {""arxiv_id"": ""2507.05835"", ""version"": 2, ""id_versioned"": ""2507.05835v2"", ""title"": ""Hausdorff dimension of self-similar measures and sets with common fixed point structure"", ""abstract"": ""In this paper, we study the Hausdorff dimension of self-similar measures and sets on the real line, where the generating iterated function system consists of some maps that share the same fixed point. In particular, we will show that out of a Hausdorff co-dimension one exceptional set of natural parameters, such systems satisfy a weak exponential separation. This significantly strengthens the previous result of the first author and Szvák. As an application, we give the Hausdorff dimension of self-affine measures supported on the generalised 4-corner set."", ""authors"": [""Balázs Bárány"", ""Manuj Verma""], ""published"": ""2025-07-08T09:57:46Z"", ""updated"": ""2026-07-14T09:06:38Z"", ""primary_category"": ""math.DS"", ""categories"": [""math.DS""], ""doi"": null, ""journal_ref"": null, ""comment"": null, ""abs_url"": ""http://arxiv.org/abs/2507.05835v2"", ""pdf_url"": ""https://arxiv.org/pdf/2507.05835v2""}}]",http://arxiv.org/abs/2507.05835v2,[],Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-entropy-rate-dimension-formula-for-self-similar-measures-on-the-line-September-24-2026/build/references.bib#L119,119,unverifiable,Barany–Verma Theorem 3.5 proves the entropy-rate formula under weak exponential separation while allowing exact collisions.,"The original abstract discusses weak exponential separation and dimension results, but does not state the entropy-rate formula, exact-collision allowance, or Theorem 3.5. Topic overlap is not adequate support for the exact claim.","[{""url"": ""http://arxiv.org/abs/2507.05835v2"", ""id_versioned"": ""2507.05835v2"", ""abstract"": ""In this paper, we study the Hausdorff dimension of self-similar measures and sets on the real line, where the generating iterated function system consists of some maps that share the same fixed point. In particular, we will show that out of a Hausdorff co-dimension one exceptional set of natural parameters, such systems satisfy a weak exponential separation. This significantly strengthens the previous result of the first author and Szvák. As an application, we give the Hausdorff dimension of self-affine measures supported on the generalised 4-corner set.""}]"
R046,154,Pointwise-Multiple-Ergodic-Averages-for-Mixing-Transformations-October-4-2026,Jamneshan2023,minor_difference,"Same Jamneshan work and DOI. Citation uses 2023; Crossref published date is 2022-06-21. Revised arXiv v4 identity also matches. Likely online-first/issue-year difference, not a wrong-work citation.","@article{Jamneshan2023,
  author = {Jamneshan, A.},
  title = {An uncountable {Furstenberg--Zimmer} structure theory},
  journal = {Ergodic Theory Dynam. Systems},
  volume = {43},
  number = {7},
  year = {2023},
  pages = {2404--2436},
  doi = {10.1017/etds.2022.43},
  note = {Corrected version: arXiv:2103.17167v4}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1017/etds.2022.43"", ""title"": [""An uncountable Furstenberg–Zimmer structure theory""], ""authors"": [{""given"": ""ASGAR"", ""family"": ""JAMNESHAN"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""role"": ""author"", ""vocabulary"": ""crossref""}]}], ""publisher"": ""Cambridge University Press (CUP)"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2022, 6, 21]]}, ""container_title"": [""Ergodic Theory and Dynamical Systems""], ""url"": ""https://doi.org/10.1017/etds.2022.43"", ""license"": [{""start"": {""date-parts"": [[2022, 6, 21]], ""date-time"": ""2022-06-21T00:00:00Z"", ""timestamp"": 1655769600000}, ""content-version"": ""unspecified"", ""delay-in-days"": 0, ""URL"": ""https://creativecommons.org/licenses/by/4.0""}], ""source_url"": ""https://api.crossref.org/works/10.1017%2Fetds.2022.43""}}, {""provider"": ""arXiv original repository"", ""record"": {""arxiv_id"": ""2103.17167"", ""version"": 4, ""id_versioned"": ""2103.17167v4"", ""title"": ""An uncountable Furstenberg--Zimmer structure theory"", ""abstract"": ""Furstenberg--Zimmer structure theory refers to the extension of the dichotomy between the compact and weakly mixing parts of a measure preserving dynamical system and the algebraic and geometric descriptions of such parts to a conditional setting, where such dichotomy is established relative to a factor and conditional analogues of those algebraic and geometric descriptions are sought. Although the unconditional dichotomy and the characterizations are known for arbitrary systems, the relative situation is understood under certain countability and separability hypotheses on the underlying groups and spaces. The aim of this article is to remove these restrictions in the relative situation and establish a Furstenberg--Zimmer structure theory in full generality. As an independent byproduct, we establish a connection between the relative analysis of systems in ergodic theory and the internal logic in certain Boolean topoi."", ""authors"": [""Asgar Jamneshan""], ""published"": ""2021-03-31T15:40:57Z"", ""updated"": ""2025-09-27T14:06:05Z"", ""primary_category"": ""math.DS"", ""categories"": [""math.DS"", ""math.LO""], ""doi"": ""10.1017/etds.2022.43"", ""journal_ref"": null, ""comment"": ""38 pages, 4 figures, 1 table; [v4] After publication the author found two issues; we refer to the erratum, appeared online at https://doi.org/10.1017/etds.2025.10214 . The main results remain unchanged, and this version contains all the corrections outlined in the erratum"", ""abs_url"": ""http://arxiv.org/abs/2103.17167v4"", ""pdf_url"": ""https://arxiv.org/pdf/2103.17167v4""}}]",https://api.crossref.org/works/10.1017%2Fetds.2022.43 | http://arxiv.org/abs/2103.17167v4,"[{""doi"": ""10.1017/etds.2022.43"", ""title"": ""An uncountable Furstenberg–Zimmer structure theory"", ""biblio"": {""volume"": ""43"", ""issue"": ""7"", ""first_page"": ""2404"", ""last_page"": ""2436""}, ""publication_year"": 2022, ""openalex_id"": ""W3150594803""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Pointwise-Multiple-Ergodic-Averages-for-Mixing-Transformations-October-4-2026/build/references.bib#L129,129,partial_support_abstract_only,The cited results include a nonergodic Furstenberg–Zimmer structure theorem; nearby pointwise distal convergence is separately attributed to Huang–Shao–Ye and a companion proposition.,"The original arXiv abstract says the relative compact/weak-mixing structure theory removes countability and separability restrictions and holds in full generality. This supports the broad structure-theory attribution. It does not verify the detailed nonergodic decomposition, joining, rational-time, or pointwise assertions. Those should not all be attributed to Jamneshan.","[{""url"": ""http://arxiv.org/abs/2103.17167v4"", ""id_versioned"": ""2103.17167v4"", ""abstract"": ""Furstenberg--Zimmer structure theory refers to the extension of the dichotomy between the compact and weakly mixing parts of a measure preserving dynamical system and the algebraic and geometric descriptions of such parts to a conditional setting, where such dichotomy is established relative to a factor and conditional analogues of those algebraic and geometric descriptions are sought. Although the unconditional dichotomy and the characterizations are known for arbitrary systems, the relative situation is understood under certain countability and separability hypotheses on the underlying groups and spaces. The aim of this article is to remove these restrictions in the relative situation and establish a Furstenberg--Zimmer structure theory in full generality. As an independent byproduct, we establish a connection between the relative analysis of systems in ergodic theory and the internal logic in certain Boolean topoi.""}]"
R047,154,Pointwise-Multiple-Ergodic-Averages-for-Mixing-Transformations-October-4-2026,HuangShaoYe2019,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{HuangShaoYe2019,
  author = {Huang, W. and Shao, S. and Ye, X.},
  title = {Pointwise convergence of multiple ergodic averages and strictly ergodic models},
  journal = {J. Anal. Math.},
  volume = {139},
  number = {1},
  year = {2019},
  pages = {265--305},
  doi = {10.1007/s11854-019-0061-3}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1007/s11854-019-0061-3"", ""title"": [""Pointwise convergence of multiple ergodic averages and strictly ergodic models""], ""authors"": [{""given"": ""Wen"", ""family"": ""Huang"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""role"": ""author"", ""vocabulary"": ""crossref""}]}, {""given"": ""Song"", ""family"": ""Shao"", ""sequence"": ""additional"", ""affiliation"": [], ""role"": [{""role"": ""author"", ""vocabulary"": ""crossref""}]}, {""given"": ""Xiangdong"", ""family"": ""Ye"", ""sequence"": ""additional"", ""affiliation"": [], ""role"": [{""role"": ""author"", ""vocabulary"": ""crossref""}]}], ""publisher"": ""Springer Science and Business Media LLC"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2019, 10]]}, ""container_title"": [""Journal d'Analyse Mathématique""], ""url"": ""https://doi.org/10.1007/s11854-019-0061-3"", ""license"": [{""start"": {""date-parts"": [[2019, 10, 1]], ""date-time"": ""2019-10-01T00:00:00Z"", ""timestamp"": 1569888000000}, ""content-version"": ""tdm"", ""delay-in-days"": 0, ""URL"": ""http://www.springer.com/tdm""}, {""start"": {""date-parts"": [[2019, 10, 1]], ""date-time"": ""2019-10-01T00:00:00Z"", ""timestamp"": 1569888000000}, ""content-version"": ""vor"", ""delay-in-days"": 0, ""URL"": ""http://www.springer.com/tdm""}], ""source_url"": ""https://api.crossref.org/works/10.1007%2Fs11854-019-0061-3""}}]",https://api.crossref.org/works/10.1007%2Fs11854-019-0061-3,"[{""doi"": ""10.1007/s11854-019-0061-3"", ""title"": ""Pointwise convergence of multiple ergodic averages and strictly ergodic models"", ""biblio"": {""volume"": ""139"", ""issue"": ""1"", ""first_page"": ""265"", ""last_page"": ""305""}, ""publication_year"": 2019, ""openalex_id"": ""W2979633430""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Pointwise-Multiple-Ergodic-Averages-for-Mixing-Transformations-October-4-2026/build/references.bib#L97,97,,,,[]
R048,154,Pointwise-Multiple-Ergodic-Averages-for-Mixing-Transformations-October-4-2026,Austin2015,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{Austin2015,
  author = {Austin, T.},
  title = {Pleasant extensions retaining algebraic structure, {I}},
  journal = {J. Anal. Math.},
  volume = {125},
  year = {2015},
  pages = {1--36},
  doi = {10.1007/s11854-015-0001-9}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1007/s11854-015-0001-9"", ""title"": [""Pleasant extensions retaining algebraic structure, I""], ""authors"": [{""given"": ""Tim"", ""family"": ""Austin"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""role"": ""author"", ""vocabulary"": ""crossref""}]}], ""publisher"": ""Springer Science and Business Media LLC"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2015, 1]]}, ""container_title"": [""Journal d'Analyse Mathématique""], ""url"": ""https://doi.org/10.1007/s11854-015-0001-9"", ""license"": [{""start"": {""date-parts"": [[2015, 1, 1]], ""date-time"": ""2015-01-01T00:00:00Z"", ""timestamp"": 1420070400000}, ""content-version"": ""tdm"", ""delay-in-days"": 0, ""URL"": ""http://www.springer.com/tdm""}], ""source_url"": ""https://api.crossref.org/works/10.1007%2Fs11854-015-0001-9""}}]",https://api.crossref.org/works/10.1007%2Fs11854-015-0001-9,"[{""doi"": ""10.1007/s11854-015-0001-9"", ""title"": ""Pleasant extensions retaining algebraic structure, I"", ""biblio"": {""volume"": ""125"", ""issue"": ""1"", ""first_page"": ""1"", ""last_page"": ""36""}, ""publication_year"": 2015, ""openalex_id"": ""W4244930114""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Pointwise-Multiple-Ergodic-Averages-for-Mixing-Transformations-October-4-2026/build/references.bib#L108,108,,,,[]
R049,154,Pointwise-Multiple-Ergodic-Averages-for-Mixing-Transformations-October-4-2026,Tropp2018,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{Tropp2018,
  author = {Tropp, J. A.},
  title = {Second-order matrix concentration inequalities},
  journal = {Appl. Comput. Harmon. Anal.},
  volume = {44},
  number = {3},
  year = {2018},
  pages = {700--736},
  doi = {10.1016/j.acha.2016.07.005}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1016/j.acha.2016.07.005"", ""title"": [""Second-order matrix concentration inequalities""], ""authors"": [{""given"": ""Joel A."", ""family"": ""Tropp"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""Elsevier BV"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2018, 5]]}, ""container_title"": [""Applied and Computational Harmonic Analysis""], ""url"": ""https://doi.org/10.1016/j.acha.2016.07.005"", ""license"": [{""start"": {""date-parts"": [[2018, 5, 1]], ""date-time"": ""2018-05-01T00:00:00Z"", ""timestamp"": 1525132800000}, ""content-version"": ""tdm"", ""delay-in-days"": 0, ""URL"": ""https://www.elsevier.com/tdm/userlicense/1.0/""}, {""start"": {""date-parts"": [[2018, 5, 1]], ""date-time"": ""2018-05-01T00:00:00Z"", ""timestamp"": 1525132800000}, ""content-version"": ""tdm"", ""delay-in-days"": 0, ""URL"": ""https://www.elsevier.com/legal/tdmrep-license""}, {""start"": {""date-parts"": [[2022, 5, 1]], ""date-time"": ""2022-05-01T00:00:00Z"", ""timestamp"": 1651363200000}, ""content-version"": ""vor"", ""delay-in-days"": 1461, ""URL"": ""http://www.elsevier.com/open-access/userlicense/1.0/""}, {""start"": {""date-parts"": [[2018, 5, 1]], ""date-time"": ""2018-05-01T00:00:00Z"", ""timestamp"": 1525132800000}, ""content-version"": ""stm-asf"", ""delay-in-days"": 0, ""URL"": ""https://doi.org/10.15223/policy-017""}, {""start"": {""date-parts"": [[2018, 5, 1]], ""date-time"": ""2018-05-01T00:00:00Z"", ""timestamp"": 1525132800000}, ""content-version"": ""stm-asf"", ""delay-in-days"": 0, ""URL"": ""https://doi.org/10.15223/policy-037""}, {""start"": {""date-parts"": [[2018, 5, 1]], ""date-time"": ""2018-05-01T00:00:00Z"", ""timestamp"": 1525132800000}, ""content-version"": ""stm-asf"", ""delay-in-days"": 0, ""URL"": ""https://doi.org/10.15223/policy-012""}, {""start"": {""date-parts"": [[2018, 5, 1]], ""date-time"": ""2018-05-01T00:00:00Z"", ""timestamp"": 1525132800000}, ""content-version"": ""stm-asf"", ""delay-in-days"": 0, ""URL"": ""https://doi.org/10.15223/policy-029""}, {""start"": {""date-parts"": [[2018, 5, 1]], ""date-time"": ""2018-05-01T00:00:00Z"", ""timestamp"": 1525132800000}, ""content-version"": ""stm-asf"", ""delay-in-days"": 0, ""URL"": ""https://doi.org/10.15223/policy-004""}], ""source_url"": ""https://api.crossref.org/works/10.1016%2Fj.acha.2016.07.005""}}]",https://api.crossref.org/works/10.1016%2Fj.acha.2016.07.005,"[{""doi"": ""10.1016/j.acha.2016.07.005"", ""title"": ""Second-order matrix concentration inequalities"", ""biblio"": {""volume"": ""44"", ""issue"": ""3"", ""first_page"": ""700"", ""last_page"": ""736""}, ""publication_year"": 2016, ""openalex_id"": ""W1922270005""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Pointwise-Multiple-Ergodic-Averages-for-Mixing-Transformations-October-4-2026/build/references.bib#L174,174,,,,[]
R050,154,Pointwise-Multiple-Ergodic-Averages-for-Mixing-Transformations-October-4-2026,DerrienLesigne1996,unverified,Derrien and Lesigne 1996: bounded discovery searches did not retrieve an original publication record; no matching original was inspected.,"@article{DerrienLesigne1996,
  author = {Derrien, J.-M. and Lesigne, E.},
  title = {Un th{\'e}or{\`e}me ergodique polyn{\^o}mial ponctuel pour les endomorphismes exacts et les {$K$}-syst{\`e}mes},
  journal = {Ann. Inst. H. Poincar{\'e} Probab. Statist.},
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  pages = {765--778}
}",[],,[],Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Pointwise-Multiple-Ergodic-Averages-for-Mixing-Transformations-October-4-2026/build/references.bib#L66,66,,,,[]
R051,164,Monochromatic-finite-sums-and-products-in-the-positive-integers-September-23-2026,ZorinKranich,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"\bibitem{ZorinKranich}
P.~Zorin-Kranich,
\emph{A nilpotent IP polynomial multiple recurrence theorem},
J. Anal. Math. \textbf{123} (2014), 183--225.
\url{https://doi.org/10.1007/s11854-014-0018-5}.
Revised version: arXiv:1206.0287v4, 4 June 2018,
\url{https://arxiv.org/abs/1206.0287v4}.","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1007/s11854-014-0018-5"", ""title"": [""A nilpotent IP polynomial multiple recurrence theorem""], ""authors"": [{""given"": ""Pavel"", ""family"": ""Zorin-Kranich"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""Springer Science and Business Media LLC"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2014, 7]]}, ""container_title"": [""Journal d'Analyse Mathématique""], ""url"": ""https://doi.org/10.1007/s11854-014-0018-5"", ""license"": [{""start"": {""date-parts"": [[2014, 7, 1]], ""date-time"": ""2014-07-01T00:00:00Z"", ""timestamp"": 1404172800000}, ""content-version"": ""tdm"", ""delay-in-days"": 0, ""URL"": ""http://www.springer.com/tdm""}], ""source_url"": ""https://api.crossref.org/works/10.1007%2Fs11854-014-0018-5""}}, {""provider"": ""arXiv original repository"", ""record"": {""arxiv_id"": ""1206.0287"", ""version"": 4, ""id_versioned"": ""1206.0287v4"", ""title"": ""A nilpotent IP polynomial multiple recurrence theorem"", ""abstract"": ""We generalize the IP-polynomial Szemerédi theorem due to Bergelson and McCutcheon and the nilpotent Szemerédi theorem due to Leibman. Important tools in our proof include a generalization of Leibman's result that polynomial mappings into a nilpotent group form a group and a multiparameter version of the nilpotent Hales-Jewett theorem due to Bergelson and Leibman."", ""authors"": [""Pavel Zorin-Kranich""], ""published"": ""2012-06-01T19:35:30Z"", ""updated"": ""2018-06-04T20:30:42Z"", ""primary_category"": ""math.DS"", ""categories"": [""math.DS"", ""math.CO""], ""doi"": ""10.1007/s11854-014-0018-5"", ""journal_ref"": ""Journal d'Analyse Mathématique 123 (2014) 183-225"", ""comment"": ""v4: switch to TeXlive 2016 and biblatex"", ""abs_url"": ""http://arxiv.org/abs/1206.0287v4"", ""pdf_url"": ""https://arxiv.org/pdf/1206.0287v4""}}]",https://api.crossref.org/works/10.1007%2Fs11854-014-0018-5 | http://arxiv.org/abs/1206.0287v4,"[{""doi"": ""10.1007/s11854-014-0018-5"", ""title"": ""A nilpotent IP polynomial multiple recurrence theorem"", ""biblio"": {""volume"": ""123"", ""issue"": ""1"", ""first_page"": ""183"", ""last_page"": ""225""}, ""publication_year"": 2014, ""openalex_id"": ""W2163779747""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Monochromatic-finite-sums-and-products-in-the-positive-integers-September-23-2026/build/references.tex#L229,229,,,,[]
R052,164,Monochromatic-finite-sums-and-products-in-the-positive-integers-September-23-2026,GreenTaoRegularity,minor_difference,Same Green–Tao work/authors and explicitly cited arXiv v3. Citation title includes “an associated counting lemma”; arXiv title omits “an”. Journal/book chapter metadata were not independently verified. Identity verified at preprint level; claimed journal/chapter publication details are not independently certified by that record.,"\bibitem{GreenTaoRegularity}
B.~Green and T.~Tao,
\emph{An arithmetic regularity lemma, an associated counting lemma, and applications},
in \emph{An Irregular Mind: Szemer\'edi is 70},
Bolyai Society Mathematical Studies, Springer, 2010, pp.~261--334.
Corrected version: arXiv:1002.2028v3, 24 November 2020,
\url{https://arxiv.org/abs/1002.2028v3}.","[{""provider"": ""arXiv original repository"", ""record"": {""arxiv_id"": ""1002.2028"", ""version"": 3, ""id_versioned"": ""1002.2028v3"", ""title"": ""An arithmetic regularity lemma, associated counting lemma, and applications"", ""abstract"": ""Szemeredi's regularity lemma can be viewed as a rough structure theorem for arbitrary dense graphs, decomposing such graphs into a structured piece (a partition into cells with edge densities), a small error (corresponding to irregular cells), and a uniform piece (the pseudorandom deviations from the edge densities). We establish an arithmetic regularity lemma that similarly decomposes bounded functions f : [N] -> C, into a (well-equidistributed, virtual) -step nilsequence, an error which is small in L^2 and a further error which is miniscule in the Gowers U^{s+1}-norm, where s is a positive integer. We then establish a complementary arithmetic counting lemma that counts arithmetic patterns in the nilsequence component of f. We provide a number of applications of these lemmas: a proof of Szemeredi's theorem on arithmetic progressions, a proof of a conjecture of Bergelson, Host and Kra, and a generalisation of certain results of Gowers and Wolf. Our result is dependent on the inverse conjecture for the Gowers U^{s+1} norm, recently established for general s by the authors and T. Ziegler. REVISED November 2020: This paper has been revised so that only systems of linear forms satisfying a condition called the flag property are covered by the counting lemma. Translation-invariant systems, as well as systems of Cauchy-Schwarz complexity 1 and some other naturally-occurring systems have this property. We thank Daniel Altman for drawing our attention to what appeared to be a minor technical issue in one of our proofs but which ultimately led us to realise that the the counting lemma fails quite badly (with rather simple examples, which we shall describe) without some assumption of this type. Additionally, we supply a short appendix showing that the Gowers-Wolf complexity of a system is bounded by its Cauchy-Schwarz complexity."", ""authors"": [""Ben Green"", ""Terence Tao""], ""published"": ""2010-02-10T17:45:01Z"", ""updated"": ""2020-11-24T22:44:32Z"", ""primary_category"": ""math.CO"", ""categories"": [""math.CO"", ""math.DS""], ""doi"": null, ""journal_ref"": null, ""comment"": ""61 pages, corrected version of article which appeared in An Irregular Mind, Szemeredi is 70"", ""abs_url"": ""http://arxiv.org/abs/1002.2028v3"", ""pdf_url"": ""https://arxiv.org/pdf/1002.2028v3""}}]",http://arxiv.org/abs/1002.2028v3,[],Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Monochromatic-finite-sums-and-products-in-the-positive-integers-September-23-2026/build/references.tex#L98,98,,,,[]
R053,164,Monochromatic-finite-sums-and-products-in-the-positive-integers-September-23-2026,HostKra,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"\bibitem{HostKra}
B.~Host and B.~Kra,
\emph{Nonconventional ergodic averages and nilmanifolds},
Ann. of Math. (2) \textbf{161} (2005), no.~1, 397--488.
\url{https://doi.org/10.4007/annals.2005.161.397}.","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.4007/annals.2005.161.397"", ""title"": [""Nonconventional ergodic averages and nilmanifolds""], ""authors"": [{""given"": ""Bernard"", ""family"": ""Host"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}, {""given"": ""Bryna"", ""family"": ""Kra"", ""sequence"": ""additional"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""Annals of Mathematics"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2005, 1, 1]]}, ""container_title"": [""Annals of Mathematics""], ""url"": ""https://doi.org/10.4007/annals.2005.161.397"", ""license"": [], ""source_url"": ""https://api.crossref.org/works/10.4007%2Fannals.2005.161.397""}}]",https://api.crossref.org/works/10.4007%2Fannals.2005.161.397,"[{""doi"": ""10.4007/annals.2005.161.397"", ""title"": ""Nonconventional ergodic averages and nilmanifolds"", ""biblio"": {""volume"": ""161"", ""issue"": ""1"", ""first_page"": ""397"", ""last_page"": ""488""}, ""publication_year"": 2005, ""openalex_id"": ""W2141304880""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Monochromatic-finite-sums-and-products-in-the-positive-integers-September-23-2026/build/references.tex#L150,150,,,,[]
R054,164,Monochromatic-finite-sums-and-products-in-the-positive-integers-September-23-2026,GowersDense,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"\bibitem{GowersDense}
W.~T.~Gowers,
\emph{Decompositions, approximate structure, transference, and the Hahn--Banach theorem},
Bull. Lond. Math. Soc. \textbf{42} (2010), no.~4, 573--606.
\url{https://doi.org/10.1112/blms/bdq018}.","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1112/blms/bdq018"", ""title"": [""Decompositions, approximate structure, transference, and the Hahn-Banach theorem""], ""authors"": [{""given"": ""W. T."", ""family"": ""Gowers"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""Wiley"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2010, 6, 27]]}, ""container_title"": [""Bulletin of the London Mathematical Society""], ""url"": ""https://doi.org/10.1112/blms/bdq018"", ""license"": [{""start"": {""date-parts"": [[2010, 6, 27]], ""date-time"": ""2010-06-27T00:00:00Z"", ""timestamp"": 1277596800000}, ""content-version"": ""tdm"", ""delay-in-days"": 0, ""URL"": ""http://doi.wiley.com/10.1002/tdm_license_1.1""}, {""start"": {""date-parts"": [[2010, 6, 27]], ""date-time"": ""2010-06-27T00:00:00Z"", ""timestamp"": 1277596800000}, ""content-version"": ""vor"", ""delay-in-days"": 0, ""URL"": ""http://onlinelibrary.wiley.com/termsAndConditions#vor""}], ""source_url"": ""https://api.crossref.org/works/10.1112%2Fblms%2Fbdq018""}}]",https://api.crossref.org/works/10.1112%2Fblms%2Fbdq018,"[{""doi"": ""10.1112/blms/bdq018"", ""title"": ""Decompositions, approximate structure, transference, and the Hahn-Banach theorem"", ""biblio"": {""volume"": ""42"", ""issue"": ""4"", ""first_page"": ""573"", ""last_page"": ""606""}, ""publication_year"": 2010, ""openalex_id"": ""W2150482562""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Monochromatic-finite-sums-and-products-in-the-positive-integers-September-23-2026/build/references.tex#L60,60,,,,[]
R055,164,Monochromatic-finite-sums-and-products-in-the-positive-integers-September-23-2026,GTZ,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"\bibitem{GTZ}
B.~Green, T.~Tao and T.~Ziegler,
\emph{An inverse theorem for the Gowers $U^{s+1}[N]$-norm},
Ann. of Math. (2) \textbf{176} (2012), no.~2, 1231--1372.
\url{https://doi.org/10.4007/annals.2012.176.2.11}.
Further revision: arXiv:1009.3998v5, 23 April 2026,
\url{https://arxiv.org/abs/1009.3998v5}.","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.4007/annals.2012.176.2.11"", ""title"": [""An inverse theorem for the Gowers U^(s+1)[N]-norm""], ""authors"": [{""given"": ""Ben"", ""family"": ""Green"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}, {""given"": ""Terence"", ""family"": ""Tao"", ""sequence"": ""additional"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}, {""given"": ""Tamar"", ""family"": ""Ziegler"", ""sequence"": ""additional"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""Annals of Mathematics"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2012, 9, 1]]}, ""container_title"": [""Annals of Mathematics""], ""url"": ""https://doi.org/10.4007/annals.2012.176.2.11"", ""license"": [], ""source_url"": ""https://api.crossref.org/works/10.4007%2Fannals.2012.176.2.11""}}, {""provider"": ""arXiv original repository"", ""record"": {""arxiv_id"": ""1009.3998"", ""version"": 5, ""id_versioned"": ""1009.3998v5"", ""title"": ""An inverse theorem for the Gowers U^{s+1}[N]-norm"", ""abstract"": ""We prove the inverse conjecture for the Gowers U^{s+1}[N]-norm for all s >= 3; this is new for s > 3, and the cases s<3 have also been previously established. More precisely, we establish that if f : [N] -> [-1,1] is a function with || f ||_{U^{s+1}[N]} > δthen there is a bounded-complexity s-step nilsequence F(g(n)Γ) which correlates with f, where the bounds on the complexity and correlation depend only on s and δ. From previous results, this conjecture implies the Hardy-Littlewood prime tuples conjecture for any linear system of finite complexity. A 6-page erratum to the original paper was provided in April 2024 and is available as a separate PDF on the webpages of the first and second authors."", ""authors"": [""Ben Green"", ""Terence Tao"", ""Tamar Ziegler""], ""published"": ""2010-09-21T05:41:11Z"", ""updated"": ""2026-04-23T12:20:55Z"", ""primary_category"": ""math.CO"", ""categories"": [""math.CO"", ""math.DS""], ""doi"": null, ""journal_ref"": null, ""comment"": ""Appeared as Annals of Math. 176 (2012), 1231--1372. Preprint is 116 pages. This version corrects a mistake in the proof of Lemma 13.2 (the wrong filtration was specified) and two small typos on page 28"", ""abs_url"": ""http://arxiv.org/abs/1009.3998v5"", ""pdf_url"": ""https://arxiv.org/pdf/1009.3998v5""}}]",https://api.crossref.org/works/10.4007%2Fannals.2012.176.2.11 | http://arxiv.org/abs/1009.3998v5,"[{""doi"": ""10.4007/annals.2012.176.2.11"", ""title"": ""An inverse theorem for the Gowers U^(s+1)[N]-norm"", ""biblio"": {""volume"": ""176"", ""issue"": ""2"", ""first_page"": ""1231"", ""last_page"": ""1372""}, ""publication_year"": 2012, ""openalex_id"": ""W2777506625""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Monochromatic-finite-sums-and-products-in-the-positive-integers-September-23-2026/build/references.tex#L106,106,,,,[]
R056,192,Unbounded-Violations-of-the-Square-Root-Degree-Bound-September-26-2026,ODonnellServedio,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"\bibitem{ODonnellServedio}
R. O'Donnell and R. A. Servedio,
Learning monotone decision trees in polynomial time,
\emph{SIAM Journal on Computing} \textbf{37} (2007), 827--844.
\url{https://doi.org/10.1137/060669309}.","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1137/060669309"", ""title"": [""Learning Monotone Decision Trees in Polynomial Time""], ""authors"": [{""given"": ""Ryan"", ""family"": ""O'Donnell"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}, {""given"": ""Rocco A."", ""family"": ""Servedio"", ""sequence"": ""additional"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""Society for Industrial & Applied Mathematics (SIAM)"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2007, 1]]}, ""container_title"": [""SIAM Journal on Computing""], ""url"": ""https://doi.org/10.1137/060669309"", ""license"": [], ""source_url"": ""https://api.crossref.org/works/10.1137%2F060669309""}}]",https://api.crossref.org/works/10.1137%2F060669309,"[{""doi"": ""10.1137/060669309"", ""title"": ""Learning Monotone Decision Trees in Polynomial Time"", ""biblio"": {""volume"": ""37"", ""issue"": ""3"", ""first_page"": ""827"", ""last_page"": ""844""}, ""publication_year"": 2007, ""openalex_id"": ""W2029370139""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Unbounded-Violations-of-the-Square-Root-Degree-Bound-September-26-2026/build/bibliography.tex#L45,45,unverifiable,Theorem 3 and Lemma 3 bound a Boolean readout’s signed singleton sum by the square root of the expected number of fixed coordinates.,The original theorem and lemma text were not retrieved. OpenAlex withheld its abstract because the license was not verified-open.,[]
R057,192,Unbounded-Violations-of-the-Square-Root-Degree-Bound-September-26-2026,Wang,unverified,Wang ePrint 2020/002: original ePrint site access denied; discovery results did not establish this report.,"\bibitem{Wang}
Q. Wang, \emph{On a Conjecture of O'Donnell},
Cryptology ePrint Archive, Report 2020/002 (2020).
\url{https://eprint.iacr.org/2020/002}.",[],,[],Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Unbounded-Violations-of-the-Square-Root-Degree-Bound-September-26-2026/build/bibliography.tex#L51,51,,,,[]
R058,192,Unbounded-Violations-of-the-Square-Root-Degree-Bound-September-26-2026,Durrett,unverified,Durrett fifth edition: author-hosted version access denied; bounded discovery did not establish the exact cited edition/version.,"\bibitem{Durrett}
R. Durrett, \emph{Probability: Theory and Examples}, fifth edition,
Cambridge University Press, 2019.
Author's Version~5, January~11, 2019,
\url{https://sites.math.duke.edu/~rtd/PTE/PTE5_011119.pdf}.",[],,[],Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Unbounded-Violations-of-the-Square-Root-Degree-Bound-September-26-2026/build/bibliography.tex#L8,8,,,,[]
R059,192,Unbounded-Violations-of-the-Square-Root-Degree-Bound-September-26-2026,KudinPasalic,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"\bibitem{KudinPasalic}
S. Kudin and E. Pa\v{s}ali\'c,
Proving the conjecture of O'Donnell in certain cases and disproving
its general validity,
\emph{Discrete Applied Mathematics} \textbf{289} (2021), 345--353.
\url{https://doi.org/10.1016/j.dam.2020.11.005}.","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1016/j.dam.2020.11.005"", ""title"": [""Proving the conjecture of O’Donnell in certain cases and disproving its general validity""], ""authors"": [{""given"": ""S."", ""family"": ""Kudin"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""role"": ""author"", ""vocabulary"": ""crossref""}]}, {""given"": ""E."", ""family"": ""Pasalic"", ""sequence"": ""additional"", ""affiliation"": [], ""role"": [{""role"": ""author"", ""vocabulary"": ""crossref""}]}], ""publisher"": ""Elsevier BV"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2021, 1]]}, ""container_title"": [""Discrete Applied Mathematics""], ""url"": ""https://doi.org/10.1016/j.dam.2020.11.005"", ""license"": [{""start"": {""date-parts"": [[2021, 1, 1]], ""date-time"": ""2021-01-01T00:00:00Z"", ""timestamp"": 1609459200000}, ""content-version"": ""tdm"", ""delay-in-days"": 0, ""URL"": ""https://www.elsevier.com/tdm/userlicense/1.0/""}, {""start"": {""date-parts"": [[2021, 1, 1]], ""date-time"": ""2021-01-01T00:00:00Z"", ""timestamp"": 1609459200000}, ""content-version"": ""tdm"", ""delay-in-days"": 0, ""URL"": ""https://www.elsevier.com/legal/tdmrep-license""}, {""start"": {""date-parts"": [[2025, 1, 31]], ""date-time"": ""2025-01-31T00:00:00Z"", ""timestamp"": 1738281600000}, ""content-version"": ""vor"", ""delay-in-days"": 1491, ""URL"": ""http://www.elsevier.com/open-access/userlicense/1.0/""}, {""start"": {""date-parts"": [[2021, 1, 1]], ""date-time"": ""2021-01-01T00:00:00Z"", ""timestamp"": 1609459200000}, ""content-version"": ""stm-asf"", ""delay-in-days"": 0, ""URL"": ""https://doi.org/10.15223/policy-017""}, {""start"": {""date-parts"": [[2021, 1, 1]], ""date-time"": ""2021-01-01T00:00:00Z"", ""timestamp"": 1609459200000}, ""content-version"": ""stm-asf"", ""delay-in-days"": 0, ""URL"": ""https://doi.org/10.15223/policy-037""}, {""start"": {""date-parts"": [[2021, 1, 1]], ""date-time"": ""2021-01-01T00:00:00Z"", ""timestamp"": 1609459200000}, ""content-version"": ""stm-asf"", ""delay-in-days"": 0, ""URL"": ""https://doi.org/10.15223/policy-012""}, {""start"": {""date-parts"": [[2021, 1, 1]], ""date-time"": ""2021-01-01T00:00:00Z"", ""timestamp"": 1609459200000}, ""content-version"": ""stm-asf"", ""delay-in-days"": 0, ""URL"": ""https://doi.org/10.15223/policy-029""}, {""start"": {""date-parts"": [[2021, 1, 1]], ""date-time"": ""2021-01-01T00:00:00Z"", ""timestamp"": 1609459200000}, ""content-version"": ""stm-asf"", ""delay-in-days"": 0, ""URL"": ""https://doi.org/10.15223/policy-004""}], ""source_url"": ""https://api.crossref.org/works/10.1016%2Fj.dam.2020.11.005""}}]",https://api.crossref.org/works/10.1016%2Fj.dam.2020.11.005,"[{""doi"": ""10.1016/j.dam.2020.11.005"", ""title"": ""Proving the conjecture of O’Donnell in certain cases and disproving its general validity"", ""biblio"": {""volume"": ""289"", ""issue"": null, ""first_page"": ""345"", ""last_page"": ""353""}, ""publication_year"": 2020, ""openalex_id"": ""W3100495479""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Unbounded-Violations-of-the-Square-Root-Degree-Bound-September-26-2026/build/bibliography.tex#L27,27,,,,[]
R060,192,Unbounded-Violations-of-the-Square-Root-Degree-Bound-September-26-2026,Jha,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization. Identity verified at preprint level; claimed journal/chapter publication details are not independently certified by that record.,"\bibitem{Jha}
S. K. Jha, \emph{On the Sum of Linear Coefficients of a Boolean Valued
Function}, arXiv:1611.01029v2 (2016).
\url{https://arxiv.org/abs/1611.01029v2}.","[{""provider"": ""arXiv original repository"", ""record"": {""arxiv_id"": ""1611.01029"", ""version"": 2, ""id_versioned"": ""1611.01029v2"", ""title"": ""On the Sum of Linear Coefficients of a Boolean Valued Function"", ""abstract"": ""Let $f:\\{-1,1\\}^{n}\\rightarrow \\{-1,1\\}$ be a Boolean valued function having total degree $d$. Then a conjecture due to Servedio and Gopalan asserts that $\\sum_{i=1}^{n}\\widehat{f}(i)\\leq \\sum_{j=1}^{d}\\widehat{\\text{Maj}}_{d}(j)$ where $\\text{Maj}_{d}$ is the majority function on $d$ bits. Here we give some alternative formalisms of this conjecture involving the discrete derivative operators on $f$."", ""authors"": [""Sumit Kumar Jha""], ""published"": ""2016-11-03T14:10:17Z"", ""updated"": ""2016-11-06T09:06:47Z"", ""primary_category"": ""cs.CC"", ""categories"": [""cs.CC""], ""doi"": null, ""journal_ref"": null, ""comment"": null, ""abs_url"": ""http://arxiv.org/abs/1611.01029v2"", ""pdf_url"": ""https://arxiv.org/pdf/1611.01029v2""}}]",http://arxiv.org/abs/1611.01029v2,[],Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Unbounded-Violations-of-the-Square-Root-Degree-Bound-September-26-2026/build/bibliography.tex#L22,22,,,,[]
R061,210,Foulkes-Conjecture-for-the-Sixth-Symmetric-Power-September-25-2026,McKay2008,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{McKay2008,
  author = {McKay, Tom},
  title = {On plethysm conjectures of {Stanley} and {Foulkes}},
  journal = {Journal of Algebra},
  volume = {319},
  number = {5},
  year = {2008},
  pages = {2050--2071},
  note = {\href{https://doi.org/10.1016/j.jalgebra.2007.12.003}{doi: 10.1016/j.jalgebra.2007.12.003}},
  doi = {10.1016/j.jalgebra.2007.12.003}
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R062,210,Foulkes-Conjecture-for-the-Sixth-Symmetric-Power-September-25-2026,DentSiemons2000,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{DentSiemons2000,
  author = {Dent, Suzie C. and Siemons, Johannes},
  title = {On a conjecture of {Foulkes}},
  journal = {Journal of Algebra},
  volume = {226},
  number = {1},
  year = {2000},
  pages = {236--249},
  note = {\href{https://doi.org/10.1006/jabr.1999.8169}{doi: 10.1006/jabr.1999.8169}},
  doi = {10.1006/jabr.1999.8169}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1006/jabr.1999.8169"", ""title"": [""On a Conjecture of Foulkes""], ""authors"": [{""given"": ""Suzie C."", ""family"": ""Dent"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""role"": ""author"", ""vocabulary"": ""crossref""}]}, {""given"": ""Johannes"", ""family"": ""Siemons"", ""sequence"": ""additional"", ""affiliation"": [], ""role"": [{""role"": ""author"", ""vocabulary"": ""crossref""}]}], ""publisher"": ""Elsevier BV"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2000, 4]]}, ""container_title"": [""Journal of Algebra""], ""url"": ""https://doi.org/10.1006/jabr.1999.8169"", ""license"": [{""start"": {""date-parts"": [[2000, 4, 1]], ""date-time"": ""2000-04-01T00:00:00Z"", ""timestamp"": 954547200000}, ""content-version"": ""tdm"", ""delay-in-days"": 0, ""URL"": ""https://www.elsevier.com/tdm/userlicense/1.0/""}, {""start"": {""date-parts"": [[2013, 7, 17]], ""date-time"": ""2013-07-17T00:00:00Z"", ""timestamp"": 1374019200000}, ""content-version"": ""vor"", ""delay-in-days"": 4855, ""URL"": ""https://www.elsevier.com/open-access/userlicense/1.0/""}], ""source_url"": ""https://api.crossref.org/works/10.1006%2Fjabr.1999.8169""}}]",https://api.crossref.org/works/10.1006%2Fjabr.1999.8169,"[{""doi"": ""10.1006/jabr.1999.8169"", ""title"": ""On a Conjecture of Foulkes"", ""biblio"": {""volume"": ""226"", ""issue"": ""1"", ""first_page"": ""236"", ""last_page"": ""249""}, ""publication_year"": 2000, ""openalex_id"": ""W2057979593""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Foulkes-Conjecture-for-the-Sixth-Symmetric-Power-September-25-2026/build/references.bib#L48,48,,,,[]
R063,210,Foulkes-Conjecture-for-the-Sixth-Symmetric-Power-September-25-2026,MatolcsiRuzsa2010,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@incollection{MatolcsiRuzsa2010,
  author = {Matolcsi, M{\'a}t{\'e} and Ruzsa, Imre Z.},
  title = {Sumsets and the convex hull},
  booktitle = {Additive Number Theory: Festschrift in Honor of the Sixtieth Birthday of Melvyn B. Nathanson},
  editor = {Chudnovsky, David and Chudnovsky, Gregory},
  publisher = {Springer},
  year = {2010},
  pages = {221--227},
  note = {\href{https://arxiv.org/abs/0810.1485v1}{arXiv:0810.1485v1}. \href{https://doi.org/10.1007/978-0-387-68361-4_16}{doi: 10.1007/978-0-387-68361-4\_16}},
  doi = {10.1007/978-0-387-68361-4_16},
  eprint = {0810.1485v1},
  archivePrefix = {arXiv},
  primaryClass = {math.CO},
  url = {https://arxiv.org/abs/0810.1485v1}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1007/978-0-387-68361-4_16"", ""title"": [""Sumsets and the Convex Hull""], ""authors"": [{""given"": ""Máté"", ""family"": ""Matolcsi"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""role"": ""author"", ""vocabulary"": ""crossref""}]}, {""given"": ""Imre Z."", ""family"": ""Ruzsa"", ""sequence"": ""additional"", ""affiliation"": [], ""role"": [{""role"": ""author"", ""vocabulary"": ""crossref""}]}], ""publisher"": ""Springer New York"", ""type"": ""book-chapter"", ""published"": {""date-parts"": [[2010]]}, ""container_title"": [""Additive Number Theory""], ""url"": ""https://doi.org/10.1007/978-0-387-68361-4_16"", ""license"": [], ""source_url"": ""https://api.crossref.org/works/10.1007%2F978-0-387-68361-4_16""}}, {""provider"": ""arXiv original repository"", ""record"": {""arxiv_id"": ""0810.1485"", ""version"": 1, ""id_versioned"": ""0810.1485v1"", ""title"": ""Sumsets and the convex hull"", ""abstract"": ""We extend Freiman's inequality on the cardinality of the sumset of a $d$ dimensional set. We consider different sets related by an inclusion of their convex hull, and one of them added possibly several times."", ""authors"": [""Mate Matolcsi"", ""Imre Z. Ruzsa""], ""published"": ""2008-10-08T17:09:42Z"", ""updated"": ""2008-10-08T17:09:42Z"", ""primary_category"": ""math.CO"", ""categories"": [""math.CO""], ""doi"": null, ""journal_ref"": null, ""comment"": ""6 pages"", ""abs_url"": ""http://arxiv.org/abs/0810.1485v1"", ""pdf_url"": ""https://arxiv.org/pdf/0810.1485v1""}}]",https://api.crossref.org/works/10.1007%2F978-0-387-68361-4_16 | http://arxiv.org/abs/0810.1485v1,"[{""doi"": ""10.1007/978-0-387-68361-4_16"", ""title"": ""Sumsets and the Convex Hull"", ""biblio"": {""volume"": null, ""issue"": null, ""first_page"": ""221"", ""last_page"": ""227""}, ""publication_year"": 2010, ""openalex_id"": ""W1723055616""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Foulkes-Conjecture-for-the-Sixth-Symmetric-Power-September-25-2026/build/references.bib#L216,216,,,,[]
R064,210,Foulkes-Conjecture-for-the-Sixth-Symmetric-Power-September-25-2026,MuellerNeunhoeffer2005,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{MuellerNeunhoeffer2005,
  author = {M{\""u}ller, J{\""u}rgen and Neunh{\""o}ffer, Max},
  title = {Some computations regarding {Foulkes}' conjecture},
  journal = {Experimental Mathematics},
  volume = {14},
  number = {3},
  year = {2005},
  pages = {277--283},
  note = {\href{https://doi.org/10.1080/10586458.2005.10128928}{doi: 10.1080/10586458.2005.10128928}},
  doi = {10.1080/10586458.2005.10128928}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1080/10586458.2005.10128928"", ""title"": [""Some Computations Regarding Foulkes' Conjecture""], ""authors"": [{""given"": ""Jurgen"", ""family"": ""Müller"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""role"": ""author"", ""vocabulary"": ""crossref""}]}, {""given"": ""Max"", ""family"": ""Neunhöffer"", ""sequence"": ""additional"", ""affiliation"": [], ""role"": [{""role"": ""author"", ""vocabulary"": ""crossref""}]}], ""publisher"": ""Informa UK Limited"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2005, 1]]}, ""container_title"": [""Experimental Mathematics""], ""url"": ""https://doi.org/10.1080/10586458.2005.10128928"", ""license"": [], ""source_url"": ""https://api.crossref.org/works/10.1080%2F10586458.2005.10128928""}}]",https://api.crossref.org/works/10.1080%2F10586458.2005.10128928,"[{""doi"": ""10.1080/10586458.2005.10128928"", ""title"": ""Some Computations Regarding Foulkes' Conjecture"", ""biblio"": {""volume"": ""14"", ""issue"": ""3"", ""first_page"": ""277"", ""last_page"": ""283""}, ""publication_year"": 2005, ""openalex_id"": ""W1997431816""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Foulkes-Conjecture-for-the-Sixth-Symmetric-Power-September-25-2026/build/references.bib#L60,60,,,,[]
R065,210,Foulkes-Conjecture-for-the-Sixth-Symmetric-Power-September-25-2026,BurgisserChristandlIkenmeyer2011,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{BurgisserChristandlIkenmeyer2011,
  author = {B{\""u}rgisser, Peter and Christandl, Matthias and Ikenmeyer, Christian},
  title = {Even partitions in plethysms},
  journal = {Journal of Algebra},
  volume = {328},
  number = {1},
  year = {2011},
  pages = {322--329},
  note = {\href{https://arxiv.org/abs/1003.4474v2}{arXiv:1003.4474v2}. \href{https://doi.org/10.1016/j.jalgebra.2010.10.031}{doi: 10.1016/\allowbreak j.jalgebra.2010.10.031}},
  doi = {10.1016/j.jalgebra.2010.10.031},
  eprint = {1003.4474v2},
  archivePrefix = {arXiv},
  primaryClass = {math.GR}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1016/j.jalgebra.2010.10.031"", ""title"": [""Even partitions in plethysms""], ""authors"": [{""given"": ""Peter"", ""family"": ""Bürgisser"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""role"": ""author"", ""vocabulary"": ""crossref""}]}, {""given"": ""Matthias"", ""family"": ""Christandl"", ""sequence"": ""additional"", ""affiliation"": [], ""role"": [{""role"": ""author"", ""vocabulary"": ""crossref""}]}, {""given"": ""Christian"", ""family"": ""Ikenmeyer"", ""sequence"": ""additional"", ""affiliation"": [], ""role"": [{""role"": ""author"", ""vocabulary"": ""crossref""}]}], ""publisher"": ""Elsevier BV"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2011, 2]]}, ""container_title"": [""Journal of Algebra""], ""url"": ""https://doi.org/10.1016/j.jalgebra.2010.10.031"", ""license"": [{""start"": {""date-parts"": [[2011, 2, 1]], ""date-time"": ""2011-02-01T00:00:00Z"", ""timestamp"": 1296518400000}, ""content-version"": ""tdm"", ""delay-in-days"": 0, ""URL"": ""https://www.elsevier.com/tdm/userlicense/1.0/""}, {""start"": {""date-parts"": [[2015, 2, 15]], ""date-time"": ""2015-02-15T00:00:00Z"", ""timestamp"": 1423958400000}, ""content-version"": ""vor"", ""delay-in-days"": 1475, ""URL"": ""https://www.elsevier.com/open-access/userlicense/1.0/""}], ""source_url"": ""https://api.crossref.org/works/10.1016%2Fj.jalgebra.2010.10.031""}}, {""provider"": ""arXiv original repository"", ""record"": {""arxiv_id"": ""1003.4474"", ""version"": 2, ""id_versioned"": ""1003.4474v2"", ""title"": ""Even Partitions in Plethysms"", ""abstract"": ""We prove that for all natural numbers k,n,d with k <= d and every partition lambda of size kn with at most k parts there exists an irreducible GL(d, C)-representation of highest weight 2*lambda in the plethysm Sym^k(Sym^(2n) (C^d)). This gives an affirmative answer to a conjecture by Weintraub (J. Algebra, 129 (1):103-114, 1990). Our investigation is motivated by questions of geometric complexity theory and uses ideas from quantum information theory."", ""authors"": [""Peter Bürgisser"", ""Matthias Christandl"", ""Christian Ikenmeyer""], ""published"": ""2010-03-23T17:24:49Z"", ""updated"": ""2010-12-15T10:55:48Z"", ""primary_category"": ""math.GR"", ""categories"": [""math.GR"", ""quant-ph""], ""doi"": ""10.1016/j.jalgebra.2010.10.031"", ""journal_ref"": ""Journal of Algebra 328, 322-329 (2011)"", ""comment"": ""9 pages"", ""abs_url"": ""http://arxiv.org/abs/1003.4474v2"", ""pdf_url"": ""https://arxiv.org/pdf/1003.4474v2""}}]",https://api.crossref.org/works/10.1016%2Fj.jalgebra.2010.10.031 | http://arxiv.org/abs/1003.4474v2,"[{""doi"": ""10.1016/j.jalgebra.2010.10.031"", ""title"": ""Even partitions in plethysms"", ""biblio"": {""volume"": ""328"", ""issue"": ""1"", ""first_page"": ""322"", ""last_page"": ""329""}, ""publication_year"": 2010, ""openalex_id"": ""W2094971045""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Foulkes-Conjecture-for-the-Sixth-Symmetric-Power-September-25-2026/build/references.bib#L262,262,,,,[]
R066,215,The-canonical-massive-continuum-limit-of-the-two-dimensional-O3-model-October-4-2026,GawedzkiKupiainen,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{GawedzkiKupiainen,
  author = {Gaw{\k e}dzki, Krzysztof and Kupiainen, Antti},
  title = {Continuum limit of the hierarchical {$O(N)$} non-linear {$\sigma$}-model},
  journal = {Communications in Mathematical Physics}, volume = {106}, pages = {533--550}, year = {1986},
  doi = {10.1007/BF01463394}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1007/bf01463394"", ""title"": [""Continuum limit of the hierarchicalO(N) non-linear ?-model""], ""authors"": [{""given"": ""K."", ""family"": ""Gawedzki"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}, {""given"": ""A."", ""family"": ""Kupiainen"", ""sequence"": ""additional"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""Springer Science and Business Media LLC"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[1986, 12]]}, ""container_title"": [""Communications In Mathematical Physics""], ""url"": ""https://doi.org/10.1007/bf01463394"", ""license"": [{""start"": {""date-parts"": [[1986, 12, 1]], ""date-time"": ""1986-12-01T00:00:00Z"", ""timestamp"": 533779200000}, ""content-version"": ""tdm"", ""delay-in-days"": 0, ""URL"": ""http://www.springer.com/tdm""}], ""source_url"": ""https://api.crossref.org/works/10.1007%2Fbf01463394""}}]",https://api.crossref.org/works/10.1007%2Fbf01463394,"[{""doi"": ""10.1007/bf01463394"", ""title"": ""Continuum limit of the hierarchicalO(N) non-linear ?-model"", ""biblio"": {""volume"": ""106"", ""issue"": ""4"", ""first_page"": ""533"", ""last_page"": ""550""}, ""publication_year"": 1986, ""openalex_id"": ""W1497066249""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-canonical-massive-continuum-limit-of-the-two-dimensional-O3-model-October-4-2026/build/references.bib#L79,79,,,,[]
R067,215,The-canonical-massive-continuum-limit-of-the-two-dimensional-O3-model-October-4-2026,Ginibre1970,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{Ginibre1970,
  author = {Ginibre, J.},
  title = {General formulation of {Griffiths'} inequalities},
  journal = {Communications in Mathematical Physics}, volume = {16}, number = {4}, pages = {310--328}, year = {1970},
  doi = {10.1007/BF01646537}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1007/bf01646537"", ""title"": [""General formulation of Griffiths' inequalities""], ""authors"": [{""given"": ""J."", ""family"": ""Ginibre"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""Springer Science and Business Media LLC"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[1970, 12]]}, ""container_title"": [""Communications in Mathematical Physics""], ""url"": ""https://doi.org/10.1007/bf01646537"", ""license"": [{""start"": {""date-parts"": [[1970, 12, 1]], ""date-time"": ""1970-12-01T00:00:00Z"", ""timestamp"": 28857600000}, ""content-version"": ""tdm"", ""delay-in-days"": 0, ""URL"": ""http://www.springer.com/tdm""}], ""source_url"": ""https://api.crossref.org/works/10.1007%2Fbf01646537""}}]",https://api.crossref.org/works/10.1007%2Fbf01646537,"[{""doi"": ""10.1007/bf01646537"", ""title"": ""General formulation of Griffiths' inequalities"", ""biblio"": {""volume"": ""16"", ""issue"": ""4"", ""first_page"": ""310"", ""last_page"": ""328""}, ""publication_year"": 1970, ""openalex_id"": ""W1974689275""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-canonical-massive-continuum-limit-of-the-two-dimensional-O3-model-October-4-2026/build/references.bib#L172,172,,,,[]
R068,215,The-canonical-massive-continuum-limit-of-the-two-dimensional-O3-model-October-4-2026,OS75,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{OS75,
  author = {Osterwalder, Konrad and Schrader, Robert},
  title = {Axioms for {Euclidean} {Green}'s functions {II}},
  journal = {Communications in Mathematical Physics},
  volume = {42},
  number = {3},
  pages = {281--305},
  year = {1975},
  note = {With an Appendix by Stephen Summers},
  doi = {10.1007/BF01608978}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1007/bf01608978"", ""title"": [""Axioms for Euclidean Green's functions II""], ""authors"": [{""given"": ""Konrad"", ""family"": ""Osterwalder"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}, {""given"": ""Robert"", ""family"": ""Schrader"", ""sequence"": ""additional"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""Springer Science and Business Media LLC"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[1975, 10]]}, ""container_title"": [""Communications in Mathematical Physics""], ""url"": ""https://doi.org/10.1007/bf01608978"", ""license"": [{""start"": {""date-parts"": [[1975, 10, 1]], ""date-time"": ""1975-10-01T00:00:00Z"", ""timestamp"": 181353600000}, ""content-version"": ""tdm"", ""delay-in-days"": 0, ""URL"": ""http://www.springer.com/tdm""}], ""source_url"": ""https://api.crossref.org/works/10.1007%2Fbf01608978""}}]",https://api.crossref.org/works/10.1007%2Fbf01608978,"[{""doi"": ""10.1007/bf01608978"", ""title"": ""Axioms for Euclidean Green's functions II"", ""biblio"": {""volume"": ""42"", ""issue"": ""3"", ""first_page"": ""281"", ""last_page"": ""305""}, ""publication_year"": 1975, ""openalex_id"": ""W2002435891""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-canonical-massive-continuum-limit-of-the-two-dimensional-O3-model-October-4-2026/build/references.bib#L134,134,unverifiable,The corrected Osterwalder–Schrader reconstruction framework uses the linear growth condition in Section IV.1.,"The cited Section IV.1 was not retrieved. Metadata verifies the paper identity, but cannot establish the correction or its precise hypotheses.",[]
R069,215,The-canonical-massive-continuum-limit-of-the-two-dimensional-O3-model-October-4-2026,OpenAI-O4,unverified,OpenAI companion preprint: original repository retrieval blocked by network policy; the supplied attachment alone does not independently verify it.,"@misc{OpenAI-O4,
  author = {{OpenAI}},
  title = {{Sharp mass bounds for the two-dimensional O(4) model}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Sharp-mass-bounds-for-the-two-dimensional-O4-model-September-23-2026/paper.pdf}{OAI:Sharp-mass-bounds-for-the-two-dimensional-O4-model-September-23-2026}},
  year = {2026}
}",[],,[],Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-canonical-massive-continuum-limit-of-the-two-dimensional-O3-model-October-4-2026/build/references.bib#L186,186,,,,[]
R070,215,The-canonical-massive-continuum-limit-of-the-two-dimensional-O3-model-October-4-2026,Kupiainen,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{Kupiainen,
  author = {Kupiainen, Antti J.},
  title = {On the {$1/n$} expansion},
  journal = {Communications in Mathematical Physics}, volume = {73}, pages = {273--294}, year = {1980},
  doi = {10.1007/BF01197703}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1007/bf01197703"", ""title"": [""On the 1/n expansion""], ""authors"": [{""given"": ""Antti J."", ""family"": ""Kupiainen"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""Springer Science and Business Media LLC"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[1980, 10]]}, ""container_title"": [""Communications in Mathematical Physics""], ""url"": ""https://doi.org/10.1007/bf01197703"", ""license"": [{""start"": {""date-parts"": [[1980, 10, 1]], ""date-time"": ""1980-10-01T00:00:00Z"", ""timestamp"": 339206400000}, ""content-version"": ""tdm"", ""delay-in-days"": 0, ""URL"": ""http://www.springer.com/tdm""}], ""source_url"": ""https://api.crossref.org/works/10.1007%2Fbf01197703""}}]",https://api.crossref.org/works/10.1007%2Fbf01197703,"[{""doi"": ""10.1007/bf01197703"", ""title"": ""On the 1/n expansion"", ""biblio"": {""volume"": ""73"", ""issue"": ""3"", ""first_page"": ""273"", ""last_page"": ""294""}, ""publication_year"": 1980, ""openalex_id"": ""W2047723697""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-canonical-massive-continuum-limit-of-the-two-dimensional-O3-model-October-4-2026/build/references.bib#L73,73,,,,[]
R071,230,An-exact-Hausdorff-gauge-for-SLE-September-25-2026,RohdeSchramm2005,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{RohdeSchramm2005,
  author = {Rohde, Steffen and Schramm, Oded},
  title = {Basic properties of {SLE}},
  journal = {Annals of Mathematics},
  series = {2},
  volume = {161},
  number = {2},
  year = {2005},
  pages = {883--924},
  doi = {10.4007/annals.2005.161.883},
  url = {https://annals.math.princeton.edu/wp-content/uploads/annals-v161-n2-p07.pdf},
  note = {\href{https://doi.org/10.4007/annals.2005.161.883}{doi:10.4007/annals.2005.161.883}. Published Theorem 5.1, p. 899; normalization in Section 2.1, pp. 886--887}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.4007/annals.2005.161.883"", ""title"": [""Basic properties of SLE""], ""authors"": [{""given"": ""Steffen"", ""family"": ""Rohde"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}, {""given"": ""Oded"", ""family"": ""Schramm"", ""sequence"": ""additional"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""Annals of Mathematics"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2005, 3, 1]]}, ""container_title"": [""Annals of Mathematics""], ""url"": ""https://doi.org/10.4007/annals.2005.161.883"", ""license"": [], ""source_url"": ""https://api.crossref.org/works/10.4007%2Fannals.2005.161.883""}}]",https://api.crossref.org/works/10.4007%2Fannals.2005.161.883,"[{""doi"": ""10.4007/annals.2005.161.883"", ""title"": ""Basic properties of SLE"", ""biblio"": {""volume"": ""161"", ""issue"": ""2"", ""first_page"": ""883"", ""last_page"": ""924""}, ""publication_year"": 2005, ""openalex_id"": ""W2949895073""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-exact-Hausdorff-gauge-for-SLE-September-25-2026/build/refs/sources.bib#L103,103,,,,[]
R072,230,An-exact-Hausdorff-gauge-for-SLE-September-25-2026,OpenAI2026Explicit,unverified,OpenAI companion preprint: original repository retrieval blocked by network policy; the supplied attachment alone does not independently verify it.,"@misc{OpenAI2026Explicit,
  author = {{OpenAI}},
  title = {{An explicit exact Hausdorff gauge for SLE: A regular formula from quantitative tails and dense visits}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/An-explicit-exact-Hausdorff-gauge-for-SLE-September-26-2026/An-explicit-exact-Hausdorff-gauge-for-SLE-September-26-2026.pdf}{OAI:An-explicit-exact-Hausdorff-gauge-for-SLE-September-26-2026}},
  year = {2026}
}",[],,[],Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-exact-Hausdorff-gauge-for-SLE-September-25-2026/build/refs/sources.bib#L214,214,,,,[]
R073,230,An-exact-Hausdorff-gauge-for-SLE-September-25-2026,PeresSolomyak2005,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{PeresSolomyak2005,
  author = {Peres, Yuval and Solomyak, Boris},
  title = {The sharp {Hausdorff} measure condition for length of projections},
  journal = {Proceedings of the American Mathematical Society},
  volume = {133},
  number = {11},
  year = {2005},
  pages = {3371--3379},
  doi = {10.1090/S0002-9939-05-08073-1},
  url = {https://arxiv.org/abs/math/0406375v1},
  note = {\href{https://doi.org/10.1090/S0002-9939-05-08073-1}{Published version}.
          Numbered references use \href{https://arxiv.org/abs/math/0406375v1}{arXiv:math/0406375v1},
          18 June 2004, Lemma 1.2 and Section 5}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1090/s0002-9939-05-08073-1"", ""title"": [""The sharp Hausdorff measure condition for length of projections""], ""authors"": [{""given"": ""Yuval"", ""family"": ""Peres"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""role"": ""author"", ""vocabulary"": ""crossref""}]}, {""given"": ""Boris"", ""family"": ""Solomyak"", ""sequence"": ""additional"", ""affiliation"": [], ""role"": [{""role"": ""author"", ""vocabulary"": ""crossref""}]}], ""publisher"": ""American Mathematical Society (AMS)"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2005, 6, 20]]}, ""container_title"": [""Proceedings of the American Mathematical Society""], ""url"": ""https://doi.org/10.1090/s0002-9939-05-08073-1"", ""license"": [{""start"": {""date-parts"": [[2006, 6, 20]], ""date-time"": ""2006-06-20T00:00:00Z"", ""timestamp"": 1150761600000}, ""content-version"": ""am"", ""delay-in-days"": 365, ""URL"": ""https://www.ams.org/publications/copyright-and-permissions""}], ""source_url"": ""https://api.crossref.org/works/10.1090%2Fs0002-9939-05-08073-1""}}, {""provider"": ""arXiv original repository"", ""record"": {""arxiv_id"": ""math/0406375"", ""version"": 1, ""id_versioned"": ""math/0406375v1"", ""title"": ""The sharp Hausdorff measure condition for length of projections"", ""abstract"": ""In a recent paper, Pertti Mattila asked which gauge functions $φ$ have the property that for any planar Borel set $A$ with positive Hausdorff measure in gauge $φ$, the projection of $A$ to almost every line has positive length. We show that integrability near zero of $φ(r)/(r^2)$, which is known to be sufficient for this property, is also necessary if $φ$ is regularly varying. Our proof is based on a random construction adapted to the gauge function."", ""authors"": [""Yuval Peres"", ""Boris Solomyak""], ""published"": ""2004-06-18T17:24:45Z"", ""updated"": ""2004-06-18T17:24:45Z"", ""primary_category"": ""math.CA"", ""categories"": [""math.CA""], ""doi"": null, ""journal_ref"": ""Proc. Amer. Math. Soc. 133 (2005), no. 11, 3371--3379"", ""comment"": ""11 pages, 1 figure"", ""abs_url"": ""http://arxiv.org/abs/math/0406375v1"", ""pdf_url"": ""https://arxiv.org/pdf/math/0406375v1""}}]",https://api.crossref.org/works/10.1090%2Fs0002-9939-05-08073-1 | http://arxiv.org/abs/math/0406375v1,"[{""doi"": ""10.1090/s0002-9939-05-08073-1"", ""title"": ""The sharp Hausdorff measure condition for length of projections"", ""biblio"": {""volume"": ""133"", ""issue"": ""11"", ""first_page"": ""3371"", ""last_page"": ""3379""}, ""publication_year"": 2005, ""openalex_id"": ""W1708185612""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-exact-Hausdorff-gauge-for-SLE-September-25-2026/build/refs/sources.bib#L126,126,,,,[]
R074,230,An-exact-Hausdorff-gauge-for-SLE-September-25-2026,Zhan2019Decomposition,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{Zhan2019Decomposition,
  author = {Zhan, Dapeng},
  title = {Decomposition of {Schramm--Loewner} evolution along its curve},
  journal = {Stochastic Processes and their Applications},
  volume = {129}, year = {2019}, pages = {129--152},
  doi = {10.1016/j.spa.2018.02.010},
  note = {\href{https://doi.org/10.1016/j.spa.2018.02.010}{doi:10.1016/j.spa.2018.02.010}.
          Numbered references use the \href{https://users.math.msu.edu/users/zhan/decomposition-SLE.pdf}{author-hosted published article}}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1016/j.spa.2018.02.010"", ""title"": [""Decomposition of Schramm–Loewner evolution along its curve""], ""authors"": [{""ORCID"": ""https://orcid.org/0000-0001-5528-8142"", ""authenticated-orcid"": false, ""given"": ""Dapeng"", ""family"": ""Zhan"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""Elsevier BV"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2019, 1]]}, ""container_title"": [""Stochastic Processes and their Applications""], ""url"": ""https://doi.org/10.1016/j.spa.2018.02.010"", ""license"": [{""start"": {""date-parts"": [[2019, 1, 1]], ""date-time"": ""2019-01-01T00:00:00Z"", ""timestamp"": 1546300800000}, ""content-version"": ""tdm"", ""delay-in-days"": 0, ""URL"": ""https://www.elsevier.com/tdm/userlicense/1.0/""}, {""start"": {""date-parts"": [[2019, 1, 1]], ""date-time"": ""2019-01-01T00:00:00Z"", ""timestamp"": 1546300800000}, ""content-version"": ""tdm"", ""delay-in-days"": 0, ""URL"": ""https://www.elsevier.com/legal/tdmrep-license""}, {""start"": {""date-parts"": [[2023, 1, 1]], ""date-time"": ""2023-01-01T00:00:00Z"", ""timestamp"": 1672531200000}, ""content-version"": ""vor"", ""delay-in-days"": 1461, ""URL"": ""http://www.elsevier.com/open-access/userlicense/1.0/""}, {""start"": {""date-parts"": [[2019, 1, 1]], ""date-time"": ""2019-01-01T00:00:00Z"", ""timestamp"": 1546300800000}, ""content-version"": ""stm-asf"", ""delay-in-days"": 0, ""URL"": ""https://doi.org/10.15223/policy-017""}, {""start"": {""date-parts"": [[2019, 1, 1]], ""date-time"": ""2019-01-01T00:00:00Z"", ""timestamp"": 1546300800000}, ""content-version"": ""stm-asf"", ""delay-in-days"": 0, ""URL"": ""https://doi.org/10.15223/policy-037""}, {""start"": {""date-parts"": [[2019, 1, 1]], ""date-time"": ""2019-01-01T00:00:00Z"", ""timestamp"": 1546300800000}, ""content-version"": ""stm-asf"", ""delay-in-days"": 0, ""URL"": ""https://doi.org/10.15223/policy-012""}, {""start"": {""date-parts"": [[2019, 1, 1]], ""date-time"": ""2019-01-01T00:00:00Z"", ""timestamp"": 1546300800000}, ""content-version"": ""stm-asf"", ""delay-in-days"": 0, ""URL"": ""https://doi.org/10.15223/policy-029""}, {""start"": {""date-parts"": [[2019, 1, 1]], ""date-time"": ""2019-01-01T00:00:00Z"", ""timestamp"": 1546300800000}, ""content-version"": ""stm-asf"", ""delay-in-days"": 0, ""URL"": ""https://doi.org/10.15223/policy-004""}], ""source_url"": ""https://api.crossref.org/works/10.1016%2Fj.spa.2018.02.010""}}]",https://api.crossref.org/works/10.1016%2Fj.spa.2018.02.010,"[{""doi"": ""10.1016/j.spa.2018.02.010"", ""title"": ""Decomposition of Schramm–Loewner evolution along its curve"", ""biblio"": {""volume"": ""129"", ""issue"": ""1"", ""first_page"": ""129"", ""last_page"": ""152""}, ""publication_year"": 2018, ""openalex_id"": ""W2963970729""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-exact-Hausdorff-gauge-for-SLE-September-25-2026/build/refs/sources.bib#L169,169,partial_support_abstract_only,"For 0<kappa<8, integrated Green-weighted two-sided radial SLE laws give natural-length-biased chordal SLE; Theorem 4.1 and specific equations implement a remaining-mass mechanism.","The original arXiv abstract states the claimed integrated-law identity and the range (0,8). It does not verify Theorem 4.1, Proposition 2.2, equations (2.1)/(4.3)–(4.5), or the derived past-mass identity.","[{""url"": ""http://arxiv.org/abs/1509.05015v3"", ""id_versioned"": ""1509.05015v3"", ""abstract"": ""We show that, for $κ\\in(0,8)$, the integral of the laws of two-sided radial SLE$_κ$ curves through different interior points against a measure with SLE$_κ$ Green function density is the law of a chordal SLE$_κ$ curve, biased by the path's natural length. We also show that, for $κ>0$, the integral of the laws of extended SLE$_κ(-8)$ curves through different interior points against a measure with a closed formula density restricted in a bounded set is the law of a chordal SLE$_κ$ curve, biased by the path's capacity length restricted in that set. Another result is that, for $κ\\in(4,8)$, if one integrates the laws of two-sided chordal SLE$_κ$ curves through different force points on $\\mathbb R$ against a measure with density on $\\mathbb R$, then one also gets a law that is absolutely continuous w.r.t. that of a chordal SLE$_κ$ curve. To obtain these results, we develop a framework to study stochastic processes with random lifetime, and improve the traditional Girsanov's Theorem.""}]"
R075,230,An-exact-Hausdorff-gauge-for-SLE-September-25-2026,RezaeiZhan2017,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{RezaeiZhan2017,
 author={Rezaei, Mohammad A. and Zhan, Dapeng},
 title={Higher moments of the natural parameterization for {SLE} curves},
 journal={Annales de l'Institut Henri Poincar{\'e}, Probabilit{\'e}s et Statistiques},
 volume={53}, number={1}, year={2017}, pages={182--199},
 doi={10.1214/15-AIHP712}, url={https://arxiv.org/abs/1412.3700},
 note={\href{https://doi.org/10.1214/15-AIHP712}{doi:10.1214/15-AIHP712}. Numbered references use \href{https://arxiv.org/abs/1412.3700v2}{arXiv:1412.3700v2}}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1214/15-aihp712"", ""title"": [""Higher moments of the natural parameterization for SLE curves""], ""authors"": [{""given"": ""Mohammad A."", ""family"": ""Rezaei"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}, {""given"": ""Dapeng"", ""family"": ""Zhan"", ""sequence"": ""additional"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""Institute of Mathematical Statistics"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2017, 2, 1]]}, ""container_title"": [""Annales de l'Institut Henri Poincaré, Probabilités et Statistiques""], ""url"": ""https://doi.org/10.1214/15-aihp712"", ""license"": [], ""source_url"": ""https://api.crossref.org/works/10.1214%2F15-aihp712""}}, {""provider"": ""arXiv original repository"", ""record"": {""arxiv_id"": ""1412.3700"", ""version"": 2, ""id_versioned"": ""1412.3700v2"", ""title"": ""Higher moments of the natural parameterization for SLE curves"", ""abstract"": ""In this paper, we will show that the higher moments of the natural parametrization of SLE curves in any bounded domain in the upper half plane is finite. We prove this by estimating the probability that an SLE curve gets near n given points."", ""authors"": [""Mohammad A. Rezaei"", ""Dapeng Zhan""], ""published"": ""2014-12-11T16:08:29Z"", ""updated"": ""2017-07-21T15:40:35Z"", ""primary_category"": ""math.PR"", ""categories"": [""math.PR""], ""doi"": ""10.1214/15-AIHP712"", ""journal_ref"": ""Ann. IHP. 53(1), 182-199, 2017"", ""comment"": ""23 pages, 5 figures"", ""abs_url"": ""http://arxiv.org/abs/1412.3700v2"", ""pdf_url"": ""https://arxiv.org/pdf/1412.3700v2""}}]",https://api.crossref.org/works/10.1214%2F15-aihp712 | http://arxiv.org/abs/1412.3700v2,"[{""doi"": ""10.1214/15-aihp712"", ""title"": ""Higher moments of the natural parameterization for SLE curves"", ""biblio"": {""volume"": ""53"", ""issue"": ""1"", ""first_page"": null, ""last_page"": null}, ""publication_year"": 2017, ""openalex_id"": ""W1671294127""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-exact-Hausdorff-gauge-for-SLE-September-25-2026/build/refs/sources.bib#L150,150,,,,[]
R076,245,Weak-and-strong-normalization-in-pure-type-systems-September-25-2026,Sorensen1997,unverified,Sorensen dissertation/revised report: university-hosted original access denied; bounded discovery did not establish the cited record/version.,"@phdthesis{Sorensen1997,
  author = {S{\o}rensen, M. H. B.},
  title = {Normalization in {$\lambda$}-Calculus and Type Theory},
  school = {University of Copenhagen},
  year = {1997},
  note = {Consulted revised edition, April 1998, DIKU Report 97/27},
  url = {https://di.ku.dk/forskning/Publikationer/tekniske_rapporter/tekniske-rapporter-1997/97-27.pdf}
}",[],,[],Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Weak-and-strong-normalization-in-pure-type-systems-September-25-2026/build/references.bib#L20,20,,,,[]
R077,245,Weak-and-strong-normalization-in-pure-type-systems-September-25-2026,Poll1994,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@phdthesis{Poll1994,
  author = {Poll, Erik},
  title = {A Programming Logic Based on Type Theory},
  school = {Technische Universiteit Eindhoven},
  year = {1994},
  doi = {10.6100/IR423044},
  url = {https://pure.tue.nl/ws/files/1718573/423044.pdf}
}","[{""provider"": ""DataCite original deposit"", ""record"": {""record"": {""doi"": ""10.6100/ir423044"", ""titles"": [{""title"": ""A programming logic based on type theory""}], ""creators"": [{""name"": ""Poll, E (Erik)"", ""nameType"": ""Personal"", ""affiliation"": [], ""nameIdentifiers"": []}], ""publisher"": ""Technische Universiteit Eindhoven"", ""publication_year"": 1994, ""resource_type"": {""ris"": ""GEN"", ""bibtex"": ""misc"", ""citeproc"": ""article"", ""schemaOrg"": ""CreativeWork""}, ""url"": ""https://research.tue.nl/en/publications/a-programming-logic-based-on-type-theory(c72f515d-fbbb-4b2e-af98-50ed5fb9b735).html"", ""rights"": [], ""related_identifiers"": [], ""version"": null}, ""source_url"": ""https://api.datacite.org/dois/10.6100%2Fir423044""}}]",https://api.datacite.org/dois/10.6100%2Fir423044,[],Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Weak-and-strong-normalization-in-pure-type-systems-September-25-2026/build/references.bib#L128,128,,,,[]
R078,245,Weak-and-strong-normalization-in-pure-type-systems-September-25-2026,BartheCoquand2006,minor_difference,"Same Barthe–Coquand work and DOI. Citation says 2006; Crossref published date is 2003-09-16. Volume 16(2), 137–155 is corroborated by OpenAlex; actual print-date reconciliation is unresolved.","@article{BartheCoquand2006,
  author = {Barthe, Gilles and Coquand, Thierry},
  title = {Remarks on the equational theory of non-normalizing pure type systems},
  journal = {Journal of Functional Programming},
  volume = {16},
  number = {2},
  pages = {137--155},
  year = {2006},
  doi = {10.1017/S0956796803004726}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1017/s0956796803004726"", ""title"": [""Remarks on the equational theory of non-normalizing pure type systems""], ""authors"": [{""given"": ""GILLES"", ""family"": ""BARTHE"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}, {""given"": ""THIERRY"", ""family"": ""COQUAND"", ""sequence"": ""additional"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""Cambridge University Press (CUP)"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2003, 9, 16]]}, ""container_title"": [""Journal of Functional Programming""], ""url"": ""https://doi.org/10.1017/s0956796803004726"", ""license"": [{""start"": {""date-parts"": [[2003, 9, 16]], ""date-time"": ""2003-09-16T00:00:00Z"", ""timestamp"": 1063670400000}, ""content-version"": ""unspecified"", ""delay-in-days"": 0, ""URL"": ""https://www.cambridge.org/core/terms""}], ""source_url"": ""https://api.crossref.org/works/10.1017%2Fs0956796803004726""}}]",https://api.crossref.org/works/10.1017%2Fs0956796803004726,"[{""doi"": ""10.1017/s0956796803004726"", ""title"": ""Remarks on the equational theory of non-normalizing pure type systems"", ""biblio"": {""volume"": ""16"", ""issue"": ""2"", ""first_page"": ""137"", ""last_page"": ""155""}, ""publication_year"": 2003, ""openalex_id"": ""W2168328957""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Weak-and-strong-normalization-in-pure-type-systems-September-25-2026/build/references.bib#L107,107,,,,[]
R079,245,Weak-and-strong-normalization-in-pure-type-systems-September-25-2026,Geuvers1993,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@phdthesis{Geuvers1993,
  author = {Geuvers, Jan Herman},
  title = {Logics and Type Systems},
  school = {Katholieke Universiteit Nijmegen},
  year = {1993},
  url = {https://www.cs.ru.nl/~herman/PUBS/Proefschrift.pdf}
}","[{""provider"": ""DataCite original deposit"", ""record"": {""record"": {""doi"": ""10.6100/ir414311"", ""titles"": [{""title"": ""Logics and type systems""}], ""creators"": [{""name"": ""Geuvers, JH Herman"", ""nameType"": ""Personal"", ""givenName"": ""JH Herman"", ""familyName"": ""Geuvers"", ""affiliation"": [], ""nameIdentifiers"": []}], ""publisher"": ""Katholieke Universiteit Nijmegen"", ""publication_year"": 1993, ""resource_type"": {""ris"": ""GEN"", ""bibtex"": ""misc"", ""citeproc"": ""article"", ""schemaOrg"": ""CreativeWork""}, ""url"": ""https://research.tue.nl/en/publications/logics-and-type-systems(37f0d72a-56bc-41b8-9796-e67c1e1c18e7).html"", ""rights"": [], ""related_identifiers"": [], ""version"": null}, ""source_url"": ""https://api.datacite.org/dois/10.6100%2Fir414311""}}]",https://api.datacite.org/dois/10.6100%2Fir414311,[],Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Weak-and-strong-normalization-in-pure-type-systems-September-25-2026/build/references.bib#L1,1,,,,[]
R080,245,Weak-and-strong-normalization-in-pure-type-systems-September-25-2026,Mull2023,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@inproceedings{Mull2023,
  author = {Mull, Nathan},
  title = {An Irrelevancy-Eliminating Translation of Pure Type Systems},
  booktitle = {28th International Conference on Types for Proofs and Programs (TYPES 2022)},
  series = {Leibniz International Proceedings in Informatics},
  volume = {269},
  pages = {7:1--7:21},
  publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\""u}r Informatik},
  year = {2023},
  doi = {10.4230/LIPIcs.TYPES.2022.7}
}","[{""provider"": ""DataCite original deposit"", ""record"": {""record"": {""doi"": ""10.4230/lipics.types.2022.7"", ""titles"": [{""title"": ""An Irrelevancy-Eliminating Translation of Pure Type Systems"", ""lang"": ""en""}], ""creators"": [{""name"": ""Mull, Nathan"", ""nameType"": ""Personal"", ""givenName"": ""Nathan"", ""familyName"": ""Mull"", ""affiliation"": [""University of Chicago, IL, USA""], ""nameIdentifiers"": []}], ""publisher"": ""Schloss Dagstuhl – Leibniz-Zentrum für Informatik"", ""publication_year"": 2023, ""resource_type"": {""resourceTypeGeneral"": ""ConferencePaper"", ""ris"": ""CPAPER"", ""bibtex"": ""inproceedings"", ""citeproc"": """", ""schemaOrg"": ""Article""}, ""url"": ""https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2022.7"", ""rights"": [{""lang"": ""en"", ""rights"": ""Creative Commons Attribution 4.0 International license"", ""rightsUri"": ""https://creativecommons.org/licenses/by/4.0/legalcode"", ""rightsIdentifier"": ""cc by 4.0""}, {""rights"": ""info:eu-repo/semantics/openAccess""}], ""related_identifiers"": [{""relationType"": ""IsPartOf"", ""relatedIdentifier"": ""10.4230/LIPIcs.TYPES.2022"", ""relatedIdentifierType"": ""DOI""}, {""relationType"": ""IsPartOf"", ""relatedIdentifier"": ""978-3-95977-285-3"", ""relatedIdentifierType"": ""ISBN""}, {""relationType"": ""IsPartOf"", ""relatedIdentifier"": ""1868-8969"", ""relatedIdentifierType"": ""ISSN""}], ""version"": null}, ""source_url"": ""https://api.datacite.org/dois/10.4230%2Flipics.types.2022.7""}}]",https://api.datacite.org/dois/10.4230%2Flipics.types.2022.7,[],Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Weak-and-strong-normalization-in-pure-type-systems-September-25-2026/build/references.bib#L43,43,,,,[]
R081,296,Relative-generation-and-the-generator-problem-for-finite-factors-September-23-2026,DSSW2008,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{DSSW2008,
  author = {Dykema, Ken and Sinclair, Allan and Smith, Roger and White, Stuart},
  title = {Generators of {$\mathrm{II}_1$} factors},
  journal = {Operators and Matrices},
  volume = {2}, number = {4}, pages = {555--582}, year = {2008},
  doi = {10.7153/oam-02-35}, eprint = {0706.1953}, archivePrefix = {arXiv},
  url = {https://files.ele-math.com/articles/oam-02-35.pdf}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.7153/oam-02-35"", ""title"": [""Generators of II_1 factors""], ""authors"": [{""given"": ""Ken"", ""family"": ""Dykema"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}, {""given"": ""Allan"", ""family"": ""Sinclair"", ""sequence"": ""additional"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}, {""given"": ""Roger"", ""family"": ""Smith"", ""sequence"": ""additional"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}, {""given"": ""Stuart"", ""family"": ""White"", ""sequence"": ""additional"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""Element d.o.o."", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2008]]}, ""container_title"": [""Operators and Matrices""], ""url"": ""https://doi.org/10.7153/oam-02-35"", ""license"": [], ""source_url"": ""https://api.crossref.org/works/10.7153%2Foam-02-35""}}, {""provider"": ""arXiv original repository"", ""record"": {""arxiv_id"": ""0706.1953"", ""version"": 2, ""id_versioned"": ""0706.1953v2"", ""title"": ""Generators of II_1 Factors"", ""abstract"": ""In 2005, Shen introduced a new invariant, $\\mathcal G(N)$, of a diffuse von Neumann algebra $N$ with a fixed faithful trace, and he used this invariant to give a unified approach to showing that large classes of ${\\mathrm{II}}_1$ factors $M$ are singly generated. This paper focuses on properties of this invariant. We relate $\\mathcal G(M)$ to the number of self-adjoint generators of a ${\\mathrm{II}}_1$ factor $M$: if $\\mathcal G(M)<n/2$, then $M$ is generated by $n+1$ self-adjoint operators, whereas if $M$ is generated by $n+1$ self-adjoint operators, then $\\mathcal G(M)\\leq n/2$. The invariant $\\mathcal G(\\cdot)$ is well-behaved under amplification, satisfying $\\mathcal G(M_t)=t^{-2}\\mathcal G(M)$ for all $t>0$. In particular, if $\\mathcal G(\\mathcal L\\mathbb F_r)>0$ for any particular $r>1$, then the free group factors are pairwise non-isomorphic and are not singly generated for sufficiently large values of $r$. Estimates are given for forming free products and passing to finite index subfactors and the basic construction. We also examine a version of the invariant $\\mathcal G_{\\text{sa}}(M)$ defined only using self-adjoint operators; this is proved to satisfy $\\mathcal G_{\\text{sa}}(M)=2\\mathcal G(M)$. Finally we give inequalities relating a quantity involved in the calculation of $\\mathcal G(M)$ to the free-entropy dimension $δ_0$ of a collection of generators for $M$."", ""authors"": [""Ken Dykema"", ""Allan Sinclair"", ""Roger Smith"", ""Stuart White""], ""published"": ""2007-06-13T17:10:39Z"", ""updated"": ""2007-11-02T03:17:59Z"", ""primary_category"": ""math.OA"", ""categories"": [""math.OA""], ""doi"": null, ""journal_ref"": ""Oper. Matrices 2, no 4 (2008), 555-582."", ""comment"": ""36 Pages, section 8 rewritten"", ""abs_url"": ""http://arxiv.org/abs/0706.1953v2"", ""pdf_url"": ""https://arxiv.org/pdf/0706.1953v2""}}]",https://api.crossref.org/works/10.7153%2Foam-02-35 | http://arxiv.org/abs/0706.1953v2,"[{""doi"": ""10.7153/oam-02-35"", ""title"": ""Generators of II_1 factors"", ""biblio"": {""volume"": null, ""issue"": ""4"", ""first_page"": ""555"", ""last_page"": ""582""}, ""publication_year"": 2008, ""openalex_id"": ""W1996458343""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Relative-generation-and-the-generator-problem-for-finite-factors-September-23-2026/build/references.bib#L116,116,,,,[]
R082,296,Relative-generation-and-the-generator-problem-for-finite-factors-September-23-2026,Popa1995,minor_difference,"Same Popa work/author/venue. Citation says 1995; publisher-deposited Crossref record says 2018-11-06, potentially a digitization/edition date. Original historical issue inaccessible; do not count this as a demonstrated citation error.","@incollection{Popa1995,
  author = {Popa, Sorin},
  title = {Free-independent sequences in type {$\mathrm{II}_1$} factors and related problems},
  booktitle = {Recent advances in operator algebras---Orl{\'e}ans, 1992},
  series = {Ast{\'e}risque},
  number = {232},
  publisher = {Soci{\'e}t{\'e} math{\'e}matique de France},
  pages = {187--202},
  year = {1995},
  url = {https://www.numdam.org/item/AST_1995__232__187_0/}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.24033/ast.318"", ""title"": [""Free-independent sequences in type $II_1$ factors and related problems""], ""authors"": [{""given"": ""S."", ""family"": ""POPA"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""role"": ""author"", ""vocabulary"": ""crossref""}]}], ""publisher"": ""Societe Mathematique de France"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2018, 11, 6]]}, ""container_title"": [""Astérisque""], ""url"": ""https://doi.org/10.24033/ast.318"", ""license"": [], ""source_url"": ""https://api.crossref.org/works/10.24033%2Fast.318""}}]",https://api.crossref.org/works/10.24033%2Fast.318,[],Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Relative-generation-and-the-generator-problem-for-finite-factors-September-23-2026/build/references.bib#L85,85,,,,[]
R083,296,Relative-generation-and-the-generator-problem-for-finite-factors-September-23-2026,BrannanEtAl2023,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{BrannanEtAl2023,
  author = {Brannan, Michael and Elzinga, Floris and Harris, Samuel J. and Yamashita, Makoto},
  title = {Crossed product equivalence of quantum automorphism groups of finite dimensional {$C^*$}-algebras},
  journal = {International Mathematics Research Notices},
  volume = {2023}, number = {20}, pages = {17749--17787}, year = {2023},
  doi = {10.1093/imrn/rnad060},
  url = {https://doi.org/10.1093/imrn/rnad060}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1093/imrn/rnad060"", ""title"": [""Crossed Product Equivalence of Quantum Automorphism Groups of Finite Dimensional C*-Algebras""], ""authors"": [{""given"": ""Michael"", ""family"": ""Brannan"", ""sequence"": ""first"", ""affiliation"": [{""name"": ""Department of Pure Mathematics and The Institute for Quantum Computing, University of Waterloo , Waterloo, Ontario N2L 3G1, Canada""}], ""role"": [{""role"": ""author"", ""vocabulary"": ""crossref""}]}, {""given"": ""Floris"", ""family"": ""Elzinga"", ""sequence"": ""additional"", ""affiliation"": [{""name"": ""Department of Mathematics, University of Oslo , P.O box 1053, Blindern, 0316 Oslo, Norway""}], ""role"": [{""role"": ""author"", ""vocabulary"": ""crossref""}]}, {""given"": ""Samuel J"", ""family"": ""Harris"", ""sequence"": ""additional"", ""affiliation"": [{""name"": ""Department of Mathematics & Statistics, Northern Arizona University , PO Box 5717, Flagstaff, AZ, 86011 USA""}], ""role"": [{""role"": ""author"", ""vocabulary"": ""crossref""}]}, {""given"": ""Makoto"", ""family"": ""Yamashita"", ""sequence"": ""additional"", ""affiliation"": [{""name"": ""Department of Mathematics, University of Oslo , P.O box 1053, Blindern, 0316 Oslo, Norway""}], ""role"": [{""role"": ""author"", ""vocabulary"": ""crossref""}]}], ""publisher"": ""Oxford University Press (OUP)"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2023, 3, 30]]}, ""container_title"": [""International Mathematics Research Notices""], ""url"": ""https://doi.org/10.1093/imrn/rnad060"", ""license"": [{""start"": {""date-parts"": [[2023, 3, 31]], ""date-time"": ""2023-03-31T00:00:00Z"", ""timestamp"": 1680220800000}, ""content-version"": ""vor"", ""delay-in-days"": 1, ""URL"": ""https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model""}], ""source_url"": ""https://api.crossref.org/works/10.1093%2Fimrn%2Frnad060""}}]",https://api.crossref.org/works/10.1093%2Fimrn%2Frnad060,"[{""doi"": ""10.1093/imrn/rnad060"", ""title"": ""Crossed Product Equivalence of Quantum Automorphism Groups of Finite Dimensional C*-Algebras"", ""biblio"": {""volume"": ""2023"", ""issue"": ""20"", ""first_page"": ""17749"", ""last_page"": ""17787""}, ""publication_year"": 2023, ""openalex_id"": ""W4362192376""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Relative-generation-and-the-generator-problem-for-finite-factors-September-23-2026/build/references.bib#L190,190,,,,[]
R084,296,Relative-generation-and-the-generator-problem-for-finite-factors-September-23-2026,Wogen1969,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{Wogen1969,
  author = {Wogen, Warren},
  title = {On generators for von {Neumann} algebras},
  journal = {Bulletin of the American Mathematical Society},
  volume = {75}, number = {1}, pages = {95--99}, year = {1969},
  doi = {10.1090/S0002-9904-1969-12157-9}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1090/s0002-9904-1969-12157-9"", ""title"": [""On generators for von Neumann algebras""], ""authors"": [{""given"": ""Warren"", ""family"": ""Wogen"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""American Mathematical Society (AMS)"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[1969]]}, ""container_title"": [""Bulletin of the American Mathematical Society""], ""url"": ""https://doi.org/10.1090/s0002-9904-1969-12157-9"", ""license"": [], ""source_url"": ""https://api.crossref.org/works/10.1090%2Fs0002-9904-1969-12157-9""}}]",https://api.crossref.org/works/10.1090%2Fs0002-9904-1969-12157-9,"[{""doi"": ""10.1090/s0002-9904-1969-12157-9"", ""title"": ""On generators for von Neumann algebras"", ""biblio"": {""volume"": ""75"", ""issue"": ""1"", ""first_page"": ""95"", ""last_page"": ""99""}, ""publication_year"": 1969, ""openalex_id"": ""W2027507010""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Relative-generation-and-the-generator-problem-for-finite-factors-September-23-2026/build/references.bib#L109,109,,,,[]
R085,296,Relative-generation-and-the-generator-problem-for-finite-factors-September-23-2026,Sherman2012,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{Sherman2012,
  author = {Sherman, David},
  title = {On cardinal invariants and generators for von {Neumann} algebras},
  journal = {Canadian Journal of Mathematics},
  volume = {64},
  number = {2},
  pages = {455--480},
  year = {2012},
  doi = {10.4153/CJM-2011-048-2},
  eprint = {0908.4565},
  archivePrefix = {arXiv},
  primaryClass = {math.OA},
  url = {https://arxiv.org/abs/0908.4565}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.4153/cjm-2011-048-2"", ""title"": [""On Cardinal Invariants and Generators for von Neumann Algebras""], ""authors"": [{""given"": ""David"", ""family"": ""Sherman"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""role"": ""author"", ""vocabulary"": ""crossref""}]}], ""publisher"": ""Canadian Mathematical Society"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2012, 4, 16]]}, ""container_title"": [""Canadian Journal of Mathematics""], ""url"": ""https://doi.org/10.4153/cjm-2011-048-2"", ""license"": [{""start"": {""date-parts"": [[2018, 11, 20]], ""date-time"": ""2018-11-20T00:00:00Z"", ""timestamp"": 1542672000000}, ""content-version"": ""unspecified"", ""delay-in-days"": 2409, ""URL"": ""https://www.cambridge.org/core/terms""}], ""source_url"": ""https://api.crossref.org/works/10.4153%2Fcjm-2011-048-2""}}, {""provider"": ""arXiv original repository"", ""record"": {""arxiv_id"": ""0908.4565"", ""version"": 2, ""id_versioned"": ""0908.4565v2"", ""title"": ""On cardinal invariants and generators for von Neumann algebras"", ""abstract"": ""We demonstrate how virtually all common cardinal invariants associated to a von Neumann algebra M can be computed from the decomposability number, dec(M), and the minimal cardinality of a generating set, gen(M). Applications include the equivalence of the well-known generator problem, \""Is every separably-acting von Neumann algebra singly-generated?\"", with the formally stronger questions, \""Is every countably-generated von Neumann algebra singly-generated?\"" and \""Is the gen invariant monotone?\"" Modulo the generator problem, we determine the range of the invariant (gen(M), dec(M)), which is mostly governed by the inequality dec(M) leq c^{gen(M)}."", ""authors"": [""David Sherman""], ""published"": ""2009-08-31T15:53:12Z"", ""updated"": ""2009-12-18T16:46:13Z"", ""primary_category"": ""math.OA"", ""categories"": [""math.OA"", ""math.FA""], ""doi"": ""10.4153/CJM-2011-048-2"", ""journal_ref"": ""Can. J. Math.-J. Can. Math. 64 (2012) 455-480"", ""comment"": ""22 pages; the main additions are Theorem 3.8 and Section 8"", ""abs_url"": ""http://arxiv.org/abs/0908.4565v2"", ""pdf_url"": ""https://arxiv.org/pdf/0908.4565v2""}}]",https://api.crossref.org/works/10.4153%2Fcjm-2011-048-2 | http://arxiv.org/abs/0908.4565v2,"[{""doi"": ""10.4153/cjm-2011-048-2"", ""title"": ""On Cardinal Invariants and Generators for von Neumann Algebras"", ""biblio"": {""volume"": ""64"", ""issue"": ""2"", ""first_page"": ""455"", ""last_page"": ""480""}, ""publication_year"": 2011, ""openalex_id"": ""W2038231956""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Relative-generation-and-the-generator-problem-for-finite-factors-September-23-2026/build/references.bib#L28,28,,,,[]
R086,351,A-closed-Ricci-flow-with-bounded-scalar-curvature-and-finite-time-curvature-blowup-September-24-2026,GuZhu2008,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization. Identity verified at preprint level; claimed journal/chapter publication details are not independently certified by that record.,"\bibitem{GuZhu2008}
H.-L.~Gu and X.-P. Zhu,
\emph{The existence of Type II singularities for the Ricci flow on
\(S^{n+1}\)},
Comm. Anal. Geom. \textbf{16} (2008), no.~3, 467--494.
\href{https://arxiv.org/abs/0707.0033v1}{arXiv:0707.0033v1}.","[{""provider"": ""arXiv original repository"", ""record"": {""arxiv_id"": ""0707.0033"", ""version"": 1, ""id_versioned"": ""0707.0033v1"", ""title"": ""The Existence of Type II Singularities for the Ricci Flow on $S^{n+1}$"", ""abstract"": ""In this paper we prove the existence of Type II singularities for the Ricci flow on $S^{n+1}$ for all $n\\geq 2$."", ""authors"": [""Hui-Ling Gu"", ""Xi-Ping Zhu""], ""published"": ""2007-06-30T01:55:31Z"", ""updated"": ""2007-06-30T01:55:31Z"", ""primary_category"": ""math.DG"", ""categories"": [""math.DG"", ""math.AP""], ""doi"": null, ""journal_ref"": null, ""comment"": ""28 pages"", ""abs_url"": ""http://arxiv.org/abs/0707.0033v1"", ""pdf_url"": ""https://arxiv.org/pdf/0707.0033v1""}}]",http://arxiv.org/abs/0707.0033v1,[],Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-closed-Ricci-flow-with-bounded-scalar-curvature-and-finite-time-curvature-blowup-September-24-2026/build/references/bibliography.tex#L36,36,,,,[]
R087,351,A-closed-Ricci-flow-with-bounded-scalar-curvature-and-finite-time-curvature-blowup-September-24-2026,Stolarski2019,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"\bibitem{Stolarski2019}
M.~Stolarski,
\emph{Curvature Blow-up in Doubly-warped Product Metrics Evolving by Ricci Flow},
\href{https://arxiv.org/abs/1905.00087v1}{arXiv:1905.00087v1}, 2019.
All numbered source references in this paper use this version.
Published in Mem. Amer. Math. Soc. \textbf{295} (2024), no.~1470.
\href{https://doi.org/10.1090/memo/1470}{doi:10.1090/memo/1470}.","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1090/memo/1470"", ""title"": [""Curvature Blow-up in Doubly-warped Product Metrics Evolving by Ricci Flow""], ""authors"": [{""given"": ""Maxwell"", ""family"": ""Stolarski"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""American Mathematical Society (AMS)"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2024, 3, 19]]}, ""container_title"": [""Memoirs of the American Mathematical Society""], ""url"": ""https://doi.org/10.1090/memo/1470"", ""license"": [{""start"": {""date-parts"": [[2025, 3, 19]], ""date-time"": ""2025-03-19T00:00:00Z"", ""timestamp"": 1742342400000}, ""content-version"": ""am"", ""delay-in-days"": 365, ""URL"": ""https://www.ams.org/publications/copyright-and-permissions""}], ""source_url"": ""https://api.crossref.org/works/10.1090%2Fmemo%2F1470""}}, {""provider"": ""arXiv original repository"", ""record"": {""arxiv_id"": ""1905.00087"", ""version"": 1, ""id_versioned"": ""1905.00087v1"", ""title"": ""Curvature Blow-up in Doubly-warped Product Metrics Evolving by Ricci Flow"", ""abstract"": ""For any manifold $N^p$ admitting an Einstein metric with positive Einstein constant, we study the behavior of the Ricci flow on high-dimensional products $M = N^p \\times S^{q+1}$ with doubly-warped product metrics. In particular, we provide a rigorous construction of local, type II, conical singularity formation on such spaces. It is shown that for any $k > 1$ there exists a solution with curvature blow-up rate $\\| Rm \\|_{\\infty} (t) \\gtrsim (T-t)^{-k}$ with singularity modeled on a Ricci-flat cone at parabolic scales."", ""authors"": [""Maxwell Stolarski""], ""published"": ""2019-04-30T20:07:41Z"", ""updated"": ""2019-04-30T20:07:41Z"", ""primary_category"": ""math.DG"", ""categories"": [""math.DG""], ""doi"": null, ""journal_ref"": null, ""comment"": ""134 pages. Comments welcome"", ""abs_url"": ""http://arxiv.org/abs/1905.00087v1"", ""pdf_url"": ""https://arxiv.org/pdf/1905.00087v1""}}]",https://api.crossref.org/works/10.1090%2Fmemo%2F1470 | http://arxiv.org/abs/1905.00087v1,"[{""doi"": ""10.1090/memo/1470"", ""title"": ""Curvature Blow-up in Doubly-warped Product Metrics Evolving by Ricci Flow"", ""biblio"": {""volume"": ""295"", ""issue"": ""1470"", ""first_page"": null, ""last_page"": null}, ""publication_year"": 2024, ""openalex_id"": ""W4392943161""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-closed-Ricci-flow-with-bounded-scalar-curvature-and-finite-time-curvature-blowup-September-24-2026/build/references/bibliography.tex#L80,80,,,,[]
R088,351,A-closed-Ricci-flow-with-bounded-scalar-curvature-and-finite-time-curvature-blowup-September-24-2026,Hamilton1995,minor_difference,"Same Hamilton work/author/venue. Citation says “formation”, 1995; Crossref says “formations”, 1993. Publication/conference/volume dating unresolved; no evidence of a different work.","\bibitem{Hamilton1995}
R.~S. Hamilton,
\emph{The formation of singularities in the Ricci flow},
Surveys in Differential Geometry, Vol.~II (Cambridge, MA, 1993),
International Press, Cambridge, MA, 1995, 7--136.
\href{https://intlpress.com/site/pub/files/_fulltext/journals/sdg/1993/0002/0001/SDG-1993-0002-0001-a002.pdf}{Full text}.","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.4310/sdg.1993.v2.n1.a2"", ""title"": [""The formations of singularities in the Ricci Flow""], ""authors"": [{""given"": ""Richard"", ""family"": ""Hamilton"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""International Press of Boston"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[1993]]}, ""container_title"": [""Surveys in Differential Geometry""], ""url"": ""https://doi.org/10.4310/sdg.1993.v2.n1.a2"", ""license"": [], ""source_url"": ""https://api.crossref.org/works/10.4310%2Fsdg.1993.v2.n1.a2""}}]",https://api.crossref.org/works/10.4310%2Fsdg.1993.v2.n1.a2,[],Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-closed-Ricci-flow-with-bounded-scalar-curvature-and-finite-time-curvature-blowup-September-24-2026/build/references/bibliography.tex#L43,43,,,,[]
R089,351,A-closed-Ricci-flow-with-bounded-scalar-curvature-and-finite-time-curvature-blowup-September-24-2026,Shi1989,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"\bibitem{Shi1989}
W.-X. Shi,
\emph{Deforming the metric on complete Riemannian manifolds},
J. Differential Geom. \textbf{30} (1989), no.~1, 223--301.
\href{https://doi.org/10.4310/jdg/1214443292}{doi:10.4310/jdg/1214443292}.","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.4310/jdg/1214443292"", ""title"": [""Deforming the metric on complete Riemannian manifolds""], ""authors"": [{""given"": ""Wan-Xiong"", ""family"": ""Shi"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""International Press of Boston"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[1989, 1, 1]]}, ""container_title"": [""Journal of Differential Geometry""], ""url"": ""https://doi.org/10.4310/jdg/1214443292"", ""license"": [], ""source_url"": ""https://api.crossref.org/works/10.4310%2Fjdg%2F1214443292""}}]",https://api.crossref.org/works/10.4310%2Fjdg%2F1214443292,"[{""doi"": ""10.4310/jdg/1214443292"", ""title"": ""Deforming the metric on complete Riemannian manifolds"", ""biblio"": {""volume"": ""30"", ""issue"": ""1"", ""first_page"": null, ""last_page"": null}, ""publication_year"": 1989, ""openalex_id"": ""W1611092396""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-closed-Ricci-flow-with-bounded-scalar-curvature-and-finite-time-curvature-blowup-September-24-2026/build/references/bibliography.tex#L74,74,,,,[]
R090,351,A-closed-Ricci-flow-with-bounded-scalar-curvature-and-finite-time-curvature-blowup-September-24-2026,Sesum2005,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"\bibitem{Sesum2005}
N.~\v{S}e\v{s}um,
\emph{Curvature tensor under the Ricci flow},
Amer. J. Math. \textbf{127} (2005), no.~6, 1315--1324.
\href{https://doi.org/10.1353/ajm.2005.0042}{doi:10.1353/ajm.2005.0042}.","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1353/ajm.2005.0042"", ""title"": [""Curvature tensor under the Ricci flow""], ""authors"": [{""given"": ""Nataša"", ""family"": ""Šešum"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""Project MUSE"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2005, 12]]}, ""container_title"": [""American Journal of Mathematics""], ""url"": ""https://doi.org/10.1353/ajm.2005.0042"", ""license"": [], ""source_url"": ""https://api.crossref.org/works/10.1353%2Fajm.2005.0042""}}]",https://api.crossref.org/works/10.1353%2Fajm.2005.0042,"[{""doi"": ""10.1353/ajm.2005.0042"", ""title"": ""Curvature tensor under the Ricci flow"", ""biblio"": {""volume"": ""127"", ""issue"": ""6"", ""first_page"": ""1315"", ""last_page"": ""1324""}, ""publication_year"": 2005, ""openalex_id"": ""W2093041805""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-closed-Ricci-flow-with-bounded-scalar-curvature-and-finite-time-curvature-blowup-September-24-2026/build/references/bibliography.tex#L68,68,,,,[]
R091,369,Strict-hot-spots-and-absence-of-interior-critical-points-on-smooth-simply-connected-planar-domains-September-24-2026,Filonov2005,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{Filonov2005,
  author = {Filonov, N.},
  title = {On an inequality between {Dirichlet} and {Neumann} eigenvalues for the {Laplace} operator},
  journal = {St. Petersburg Mathematical Journal},
  volume = {16}, number = {2}, pages = {413--416}, year = {2005},
  doi = {10.1090/S1061-0022-05-00857-5},
  url = {https://doi.org/10.1090/S1061-0022-05-00857-5},
  note = {Russian original: Algebra i Analiz 16 (2004), no. 2, 172--176}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1090/s1061-0022-05-00857-5"", ""title"": [""On an inequality between Dirichlet and Neumann eigenvalues for the Laplace operator""], ""authors"": [{""given"": ""N."", ""family"": ""Filonov"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""American Mathematical Society (AMS)"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2005, 3, 9]]}, ""container_title"": [""St. Petersburg Mathematical Journal""], ""url"": ""https://doi.org/10.1090/s1061-0022-05-00857-5"", ""license"": [], ""source_url"": ""https://api.crossref.org/works/10.1090%2Fs1061-0022-05-00857-5""}}]",https://api.crossref.org/works/10.1090%2Fs1061-0022-05-00857-5,"[{""doi"": ""10.1090/s1061-0022-05-00857-5"", ""title"": ""On an inequality between Dirichlet and Neumann eigenvalues for the Laplace operator"", ""biblio"": {""volume"": ""16"", ""issue"": ""2"", ""first_page"": ""413"", ""last_page"": ""416""}, ""publication_year"": 2005, ""openalex_id"": ""W1521793072""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Strict-hot-spots-and-absence-of-interior-critical-points-on-smooth-simply-connected-planar-domains-September-24-2026/build/references/references.bib#L130,130,,,,[]
R092,369,Strict-hot-spots-and-absence-of-interior-critical-points-on-smooth-simply-connected-planar-domains-September-24-2026,BanuelosBurdzy1999,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{BanuelosBurdzy1999,
  author  = {Ba{\~n}uelos, Rodrigo and Burdzy, Krzysztof},
  title   = {On the ``hot spots'' conjecture of {J. Rauch}},
  journal = {Journal of Functional Analysis},
  volume  = {164},
  number  = {1},
  pages   = {1--33},
  year    = {1999},
  doi     = {10.1006/jfan.1999.3397},
  url     = {https://doi.org/10.1006/jfan.1999.3397}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1006/jfan.1999.3397"", ""title"": [""On the “Hot Spots” Conjecture of J. Rauch""], ""authors"": [{""given"": ""Rodrigo"", ""family"": ""Banuelos"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}, {""given"": ""Krzysztof"", ""family"": ""Burdzy"", ""sequence"": ""additional"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""Elsevier BV"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[1999, 5]]}, ""container_title"": [""Journal of Functional Analysis""], ""url"": ""https://doi.org/10.1006/jfan.1999.3397"", ""license"": [{""start"": {""date-parts"": [[1999, 5, 1]], ""date-time"": ""1999-05-01T00:00:00Z"", ""timestamp"": 925516800000}, ""content-version"": ""tdm"", ""delay-in-days"": 0, ""URL"": ""https://www.elsevier.com/tdm/userlicense/1.0/""}, {""start"": {""date-parts"": [[2013, 7, 17]], ""date-time"": ""2013-07-17T00:00:00Z"", ""timestamp"": 1374019200000}, ""content-version"": ""vor"", ""delay-in-days"": 5191, ""URL"": ""https://www.elsevier.com/open-access/userlicense/1.0/""}], ""source_url"": ""https://api.crossref.org/works/10.1006%2Fjfan.1999.3397""}}]",https://api.crossref.org/works/10.1006%2Fjfan.1999.3397,"[{""doi"": ""10.1006/jfan.1999.3397"", ""title"": ""On the “Hot Spots” Conjecture of J. Rauch"", ""biblio"": {""volume"": ""164"", ""issue"": ""1"", ""first_page"": ""1"", ""last_page"": ""33""}, ""publication_year"": 1999, ""openalex_id"": ""W2005045710""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Strict-hot-spots-and-absence-of-interior-critical-points-on-smooth-simply-connected-planar-domains-September-24-2026/build/references/references.bib#L16,16,,,,[]
R093,369,Strict-hot-spots-and-absence-of-interior-critical-points-on-smooth-simply-connected-planar-domains-September-24-2026,Rauch1975,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@incollection{Rauch1975,
  author    = {Rauch, Jeffrey},
  title     = {Lecture \#1. {Five} problems: An introduction to the qualitative theory of partial differential equations},
  editor    = {Goldstein, Jerome A.},
  booktitle = {Partial Differential Equations and Related Topics},
  series    = {Lecture Notes in Mathematics},
  volume    = {446},
  pages     = {355--369},
  publisher = {Springer},
  address   = {Berlin, Heidelberg},
  year      = {1975},
  doi       = {10.1007/BFb0070610},
  url       = {https://doi.org/10.1007/BFb0070610}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1007/bfb0070610"", ""title"": [""Lecture #1. Five problems: An introduction to the qualitative theory of partial differential equations""], ""authors"": [{""given"": ""Jeffrey"", ""family"": ""Rauch"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""role"": ""author"", ""vocabulary"": ""crossref""}]}], ""publisher"": ""Springer Berlin Heidelberg"", ""type"": ""book-chapter"", ""published"": {""date-parts"": [[1975]]}, ""container_title"": [""Lecture Notes in Mathematics"", ""Partial Differential Equations and Related Topics""], ""url"": ""https://doi.org/10.1007/bfb0070610"", ""license"": [{""start"": {""date-parts"": [[1975, 1, 1]], ""date-time"": ""1975-01-01T00:00:00Z"", ""timestamp"": 157766400000}, ""content-version"": ""unspecified"", ""delay-in-days"": 0, ""URL"": ""http://www.springer.com/tdm""}], ""source_url"": ""https://api.crossref.org/works/10.1007%2Fbfb0070610""}}]",https://api.crossref.org/works/10.1007%2Fbfb0070610,"[{""doi"": ""10.1007/bfb0070610"", ""title"": ""Lecture #1. Five problems: An introduction to the qualitative theory of partial differential equations"", ""biblio"": {""volume"": null, ""issue"": null, ""first_page"": ""355"", ""last_page"": ""369""}, ""publication_year"": 1975, ""openalex_id"": ""W999437016""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Strict-hot-spots-and-absence-of-interior-critical-points-on-smooth-simply-connected-planar-domains-September-24-2026/build/references/references.bib#L1,1,,,,[]
R094,369,Strict-hot-spots-and-absence-of-interior-critical-points-on-smooth-simply-connected-planar-domains-September-24-2026,Pommerenke1992,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@book{Pommerenke1992,
  author = {Pommerenke, Christian},
  title = {Boundary Behaviour of Conformal Maps},
  series = {Grundlehren der mathematischen Wissenschaften},
  volume = {299}, publisher = {Springer}, address = {Berlin, Heidelberg},
  year = {1992}, doi = {10.1007/978-3-662-02770-7},
  url = {https://doi.org/10.1007/978-3-662-02770-7}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1007/978-3-662-02770-7"", ""title"": [""Boundary Behaviour of Conformal Maps""], ""authors"": [{""given"": ""Christian"", ""family"": ""Pommerenke"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""Springer Berlin Heidelberg"", ""type"": ""book"", ""published"": {""date-parts"": [[1992]]}, ""container_title"": [""Grundlehren der mathematischen Wissenschaften""], ""url"": ""https://doi.org/10.1007/978-3-662-02770-7"", ""license"": [{""start"": {""date-parts"": [[1992, 1, 1]], ""date-time"": ""1992-01-01T00:00:00Z"", ""timestamp"": 694224000000}, ""content-version"": ""tdm"", ""delay-in-days"": 0, ""URL"": ""http://www.springer.com/tdm""}], ""source_url"": ""https://api.crossref.org/works/10.1007%2F978-3-662-02770-7""}}]",https://api.crossref.org/works/10.1007%2F978-3-662-02770-7,"[{""doi"": ""10.1007/978-3-662-02770-7"", ""title"": ""Boundary Behaviour of Conformal Maps"", ""biblio"": {""volume"": null, ""issue"": null, ""first_page"": null, ""last_page"": null}, ""publication_year"": 1992, ""openalex_id"": ""W2064685239""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Strict-hot-spots-and-absence-of-interior-critical-points-on-smooth-simply-connected-planar-domains-September-24-2026/build/references/references.bib#L149,149,,,,[]
R095,369,Strict-hot-spots-and-absence-of-interior-critical-points-on-smooth-simply-connected-planar-domains-September-24-2026,Miyamoto2007,unverified,Miyamoto RIMS1591: original preprint access denied. Discovery found a related 2009 journal article with a different title; that is not sufficient to verify this 2007 preprint.,"@misc{Miyamoto2007,
  author = {Miyamoto, Yasuhito},
  title = {The ``hot spots'' conjecture for nearly circular planar convex domains},
  year = {2007},
  howpublished = {RIMS Preprint 1591},
  note = {Revised 30 May 2007},
  url = {https://www.kurims.kyoto-u.ac.jp/preprint/file/RIMS1591.pdf}
}",[],,[],Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Strict-hot-spots-and-absence-of-interior-critical-points-on-smooth-simply-connected-planar-domains-September-24-2026/build/references/references.bib#L295,295,unverifiable,Miyamoto Lemma 1.2 and Theorem A exclude interior critical points under a spectral-diameter condition and give nonsymmetric nearly circular convex examples.,The cited RIMS1591 preprint was not accessible and its identity was not independently established. A related later journal article is insufficient to validate these exact locators.,[]
R096,372,Global-Uniqueness-for-the-Smooth-Isotropic-Elasticity-Inverse-Problem-September-24-2026,Grauert1958,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{Grauert1958,
  author  = {Grauert, Hans},
  title   = {Analytische {Faserungen} {\""u}ber holomorph-vollst{\""a}ndigen {R{\""a}umen}},
  journal = {Mathematische Annalen},
  volume  = {135},
  year    = {1958},
  pages   = {263--273},
  doi     = {10.1007/BF01351803},
  note    = {\href{https://doi.org/10.1007/BF01351803}{doi:10.1007/BF01351803}}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1007/bf01351803"", ""title"": [""Analytische Faserungen �ber holomorph-vollst�ndigen R�umen""], ""authors"": [{""given"": ""Hans"", ""family"": ""Grauert"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""Springer Science and Business Media LLC"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[1958, 6]]}, ""container_title"": [""Mathematische Annalen""], ""url"": ""https://doi.org/10.1007/bf01351803"", ""license"": [{""start"": {""date-parts"": [[1958, 6, 1]], ""date-time"": ""1958-06-01T00:00:00Z"", ""timestamp"": -365644800000}, ""content-version"": ""tdm"", ""delay-in-days"": 0, ""URL"": ""http://www.springer.com/tdm""}], ""source_url"": ""https://api.crossref.org/works/10.1007%2Fbf01351803""}}]",https://api.crossref.org/works/10.1007%2Fbf01351803,"[{""doi"": ""10.1007/bf01351803"", ""title"": ""Analytische Faserungen �ber holomorph-vollst�ndigen R�umen"", ""biblio"": {""volume"": ""135"", ""issue"": ""3"", ""first_page"": ""263"", ""last_page"": ""273""}, ""publication_year"": 1958, ""openalex_id"": ""W2914074126""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Global-Uniqueness-for-the-Smooth-Isotropic-Elasticity-Inverse-Problem-September-24-2026/build/references.bib#L100,100,,,,[]
R097,372,Global-Uniqueness-for-the-Smooth-Isotropic-Elasticity-Inverse-Problem-September-24-2026,Eskin2001,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{Eskin2001,
  author  = {Eskin, Gregory},
  title   = {Global uniqueness in the inverse scattering problem for the {Schr{\""o}dinger} operator with external {Yang--Mills} potentials},
  journal = {Communications in Mathematical Physics},
  volume  = {222},
  number  = {3},
  year    = {2001},
  pages   = {503--531},
  doi     = {10.1007/s002200100522},
  note    = {\href{https://doi.org/10.1007/s002200100522}{doi:10.1007/s002200100522}}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1007/s002200100522"", ""title"": [""Global Uniqueness in the Inverse Scattering Problem¶for the Schrödinger Operator¶with External Yang-Mills Potentials""], ""authors"": [{""given"": ""G."", ""family"": ""Eskin"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""Springer Science and Business Media LLC"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2001, 9, 1]]}, ""container_title"": [""Communications in Mathematical Physics""], ""url"": ""https://doi.org/10.1007/s002200100522"", ""license"": [{""start"": {""date-parts"": [[2001, 9, 1]], ""date-time"": ""2001-09-01T00:00:00Z"", ""timestamp"": 999302400000}, ""content-version"": ""tdm"", ""delay-in-days"": 0, ""URL"": ""http://www.springer.com/tdm""}], ""source_url"": ""https://api.crossref.org/works/10.1007%2Fs002200100522""}}]",https://api.crossref.org/works/10.1007%2Fs002200100522,"[{""doi"": ""10.1007/s002200100522"", ""title"": ""Global Uniqueness in the Inverse Scattering Problem¶for the Schrödinger Operator¶with External Yang-Mills Potentials"", ""biblio"": {""volume"": ""222"", ""issue"": ""3"", ""first_page"": ""503"", ""last_page"": ""531""}, ""publication_year"": 2001, ""openalex_id"": ""W2053745339""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Global-Uniqueness-for-the-Smooth-Isotropic-Elasticity-Inverse-Problem-September-24-2026/build/references.bib#L73,73,unverifiable,Cekic’s holomorphic-direction parameter argument follows Eskin’s Yang–Mills analysis.,No abstract or full-text passage was available to inspect the claimed methodological relationship. Bibliographic identity alone cannot verify it.,[]
R098,372,Global-Uniqueness-for-the-Smooth-Isotropic-Elasticity-Inverse-Problem-September-24-2026,Weck1969,unverified,Weck 1969: EuDML access denied; initial discovery failed and follow-up searches did not establish an original record.,"@article{Weck1969,
  author  = {Weck, Norbert},
  title   = {Au{\ss}enraumaufgaben in der {Theorie} station{\""a}rer {Schwingungen} inhomogener elastischer {K{\""o}rper}},
  journal = {Mathematische Zeitschrift},
  volume  = {111},
  year    = {1969},
  pages   = {387--398},
  url     = {https://eudml.org/doc/171213},
  note    = {\href{https://eudml.org/doc/171213}{EuDML record}}
}",[],,[],Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Global-Uniqueness-for-the-Smooth-Isotropic-Elasticity-Inverse-Problem-September-24-2026/build/references.bib#L123,123,,,,[]
R099,372,Global-Uniqueness-for-the-Smooth-Isotropic-Elasticity-Inverse-Problem-September-24-2026,NU2003,minor_difference,Same Nakamura–Uhlmann DOI/authors and 2003 publication. Citation prefixes “Erratum:”; Crossref omits that label from the title. OpenAlex pages 205–207 agree; registry title alone cannot certify correction scope.,"@article{NU2003,
  author  = {Nakamura, Gen and Uhlmann, Gunther},
  title   = {Erratum: {Global} uniqueness for an inverse boundary value problem arising in elasticity},
  journal = {Inventiones Mathematicae},
  volume  = {152},
  number  = {1},
  year    = {2003},
  pages   = {205--207},
  doi     = {10.1007/s00222-002-0276-1},
  note    = {\href{https://doi.org/10.1007/s00222-002-0276-1}{doi:10.1007/s00222-002-0276-1}}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1007/s00222-002-0276-1"", ""title"": [""Global uniqueness for an inverse boundary value problem arising in elasticity""], ""authors"": [{""given"": ""Gen"", ""family"": ""Nakamura"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}, {""given"": ""Gunther"", ""family"": ""Uhlmann"", ""sequence"": ""additional"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""Springer Science and Business Media LLC"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2003, 4, 1]]}, ""container_title"": [""Inventiones Mathematicae""], ""url"": ""https://doi.org/10.1007/s00222-002-0276-1"", ""license"": [{""start"": {""date-parts"": [[2003, 4, 1]], ""date-time"": ""2003-04-01T00:00:00Z"", ""timestamp"": 1049155200000}, ""content-version"": ""tdm"", ""delay-in-days"": 0, ""URL"": ""http://www.springer.com/tdm""}], ""source_url"": ""https://api.crossref.org/works/10.1007%2Fs00222-002-0276-1""}}]",https://api.crossref.org/works/10.1007%2Fs00222-002-0276-1,"[{""doi"": ""10.1007/s00222-002-0276-1"", ""title"": ""Global uniqueness for an inverse boundary value problem arising in elasticity"", ""biblio"": {""volume"": ""152"", ""issue"": ""1"", ""first_page"": ""205"", ""last_page"": ""207""}, ""publication_year"": 2003, ""openalex_id"": ""W2061570073""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Global-Uniqueness-for-the-Smooth-Isotropic-Elasticity-Inverse-Problem-September-24-2026/build/references.bib#L12,12,,,,[]
R100,372,Global-Uniqueness-for-the-Smooth-Isotropic-Elasticity-Inverse-Problem-September-24-2026,Forstneric2009,match,Original record supports work identity (title and authors); available venue/date information is consistent after ordinary formatting normalization.,"@article{Forstneric2009,
  author  = {Forstneri{\v c}, Franc},
  title   = {Oka manifolds},
  journal = {Comptes Rendus. Math\'{e}matique},
  volume  = {347},
  number  = {17--18},
  year    = {2009},
  pages   = {1017--1020},
  doi     = {10.1016/j.crma.2009.07.005},
  note    = {\href{https://doi.org/10.1016/j.crma.2009.07.005}{doi:10.1016/j.crma.2009.07.005}}
}","[{""provider"": ""Crossref publisher deposit"", ""record"": {""doi"": ""10.1016/j.crma.2009.07.005"", ""title"": [""Oka manifolds""], ""authors"": [{""given"": ""Franc"", ""family"": ""Forstnerič"", ""sequence"": ""first"", ""affiliation"": [], ""role"": [{""vocabulary"": ""crossref"", ""role"": ""author""}]}], ""publisher"": ""MathDoc/Centre Mersenne"", ""type"": ""journal-article"", ""published"": {""date-parts"": [[2009, 8, 5]]}, ""container_title"": [""Comptes Rendus. Mathématique""], ""url"": ""https://doi.org/10.1016/j.crma.2009.07.005"", ""license"": [], ""source_url"": ""https://api.crossref.org/works/10.1016%2Fj.crma.2009.07.005""}}]",https://api.crossref.org/works/10.1016%2Fj.crma.2009.07.005,"[{""doi"": ""10.1016/j.crma.2009.07.005"", ""title"": ""Oka manifolds"", ""biblio"": {""volume"": ""347"", ""issue"": ""17-18"", ""first_page"": ""1017"", ""last_page"": ""1020""}, ""publication_year"": 2009, ""openalex_id"": ""W4235939950""}]",Identity audit. Missing fields are not assumed correct. Crossref connector omits volume/issue/pages; OpenAlex locators are secondary corroboration only. Full text was not retrieved.,https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Global-Uniqueness-for-the-Smooth-Isotropic-Elasticity-Inverse-Problem-September-24-2026/build/references.bib#L111,111,,,,[]
