# How much sky does one IceCube track alert occupy?

Updated 2026-10-09 using the supplied GCN event-page archive and the subsequent HTML/text representation archive. This version resolves the earlier checksum-representation ambiguity and retains the audited event classifications; numerical map integrations are unchanged.

**The GCN records change the sample interpretation:** IceCube-260708A is reported as unlikely to be a high-energy neutrino, with signatures instead indicating multiple muons from a cosmic-ray air shower ([IceCube, GCN 45171](https://gcn.nasa.gov/circulars/45171)). It is retained as a flagged historical map but excluded from the candidate summary. For the **19 retained candidates**, median localization areas are **1.29 full Moons at 50%** and **4.34 full Moons at 90%**. These remain candidates, not confirmed astrophysical neutrinos. The ranges are unchanged: 0.27–37.5 Moons and 1.09–121.3 Moons, respectively.

For the historical inventory of all 20 supplied 2026 maps, the recalculated 50% regions span approximately **0.27–37.5 full-Moon areas**, with a median of **1.24**. The 90% regions span **1.09–121.3 full-Moon areas**, with a median of **4.20**. These are separate probability levels. They describe uncertainty in the incoming direction, not the probability that any particular astronomical object produced the event.

The sample comprises the supplied maps dated 2026-01-15 through 2026-09-30. It is not a verified complete or latest catalog as of 2026-10-09.

![Areas of the 20 supplied alerts](icecube-2026-areas-audited.png)

## Conversion and definitions

A Moon with angular diameter 0.5 degrees has apparent area π(0.25°)² = **0.19634954 square degrees**. Thus N_Moon = 5.09295818 × A_deg². The exact spherical-cap Moon area differs by only approximately 0.00016%, far below the map discretization effects. A hypothetical 1-degree-radius circle occupies about 16 Moons; a 1-degree-diameter circle occupies about 4.

The supplied copy of [GCN's IceCube documentation](https://gcn.nasa.gov/missions/icecube) describes several distinct quantities:

| Quantity | Meaning and treatment |
|---|---|
| Map PROBDENSITY | Directional probability density per steradian. Multiply by each pixel's solid angle to obtain probability mass. |
| 50% and 90% map regions | Every supplied FITS header explicitly calls these highest-posterior-density credible regions. The documentation also describes confidence contours and simulation-calibrated coverage. This report uses the files' HPD probability definition; it does not independently recalibrate frequentist coverage. |
| RA/Dec asymmetric errors | Error-rectangle boundaries at the stated level; not independent Gaussian standard deviations. |
| Revised notice ra_dec_error | Approximate circularized 90% radius from mean RA/Dec errors, corrected for cos(declination). It need not enclose 90% of the map probability. |
| Preliminary vs revised uncertainty | The documentation says revision 0 excludes systematics and normally has no map URL; revision 1 includes systematics and links a map. All 20 supplied event circulars describe offline-refined directions matching the maps. Exact notice payloads and FITS version identity remain unavailable; the 260217A preliminary notice is specifically documented as having a wrong record number. |
| p_astro / signalness | An astrophysical-origin metric defined using simulated signal/background populations and an assumed spectrum. It is separate from directional containment and is not a probability assigned to a specific counterpart. |

At a given probability level, the highest-density region is the smallest-area region under the piecewise-constant map model. A 90% region includes more of the directional probability than a 50% region. There is no universal area ratio: the recalculated A90/A50 ranges from **3.23 to 4.11** in this sample. The circular Gaussian value, ln(10)/ln(2) ≈ 3.32, is a model assumption, not a rule for real maps.

## Calculation and integrity audit

The ZIP SHA-256 is `6bff0e4fecdbed2e146249abc2cf9ecfae0aa3c123a9c9b0d8089acb3e40a7d0`. All 20 compressed-map byte counts and SHA-256 checksums match the supplied manifest; all 20 decompressed checksums also match. This verifies consistency with the supplied manifest, not independent authentication against the live server. The manifest supplies direct URLs under [the official alert directory](https://roc-2.icecube.wisc.edu/public/alerts/); those URLs and checksums are retained in the CSV.

For each NUNIQ pixel, decode its HEALPix order k and use Ω = 4π/(12 × 4^k) steradians. This uses each pixel's actual resolution rather than treating every row as having the header NSIDE. Check that densities are nonnegative where finite and that pixels have no duplicate or overlapping sky coverage. All maps pass those checks.

As directed by the headers, ignore non-finite density pixels. Let S = ΣρᵢΩᵢ over the remaining pixels, and normalize the retained density by S. Sort by descending **density**, not descending pixel probability mass. Sum ρᵢΩᵢ/S to the desired probability and sum the selected solid angles. Interpolate linearly within the crossing pixel to quote an exact target-probability area. This fractional-pixel convention yields a scalar area but does not determine where inside that pixel the partial region lies. The CSV also records the areas excluding and including the crossing pixel. The shape figure displays whole crossing pixels.

The original finite-pixel probability sums range from **0.978338 to 1.001875**, rather than all being exactly unity. Using unnormalized cumulative mass thresholds changes some 90% areas by as much as **9.95%** relative to normalized integration. Both versions are retained in the CSV. Normalizing defines a probability distribution on the supplied valid support; it cannot recover missing probability or repair an underlying failed reconstruction.

Four files contain non-finite pixels: **260610A (2), 260807A (20), 260827A (21), and 260919A (29)**. The files instruct readers to ignore such values, attributing them to minimizer convergence failures. Six maps' native pixel sets cover slightly less than the full sphere: 260610A, 260722A, 260805A, 260807A, 260821A, and 260919A. The minimum represented fraction is 0.999893. Unrepresented or non-finite locations are not scientifically established zero-probability directions; the normalization and reported regions are conditional on the supplied valid values.

Relative to CONTOUR_AREA_50 and CONTOUR_AREA_90, normalized interpolated areas differ by:

| Level | Minimum signed difference | Median signed difference | Maximum signed difference |
|---|---:|---:|---:|
| 50% | −4.08% | +2.22% | +5.89% |
| 90% | −2.63% | +1.67% | +4.03% |

The values are close, but not identical. Only 10 of 20 header 50% areas and 7 of 20 header 90% areas fall within the corresponding crossing-pixel bracket expanded by 0.005 square degrees for two-decimal rounding. Therefore, simple rounding plus this particular boundary-pixel convention does not explain every discrepancy. Differences in normalization, contour construction, and map sampling are possible contributors; the exact upstream convention cannot be established from these inputs. Neither header areas nor recalculated areas have been silently substituted for the other.

Pixel size limits precision. For 260807A, the crossing pixel covers 0.8393 square degrees (4.27 Moons). Its 50% area bracket is 6.9537–7.7930 square degrees, and its 90% bracket is 23.7658–24.6051. For 260919A, the corresponding brackets are 0.04918–0.05246 and 0.20982–0.22294 square degrees. These are discretization brackets, not additional statistical confidence intervals.

## Event results

“Map” values below use normalized probability and fractional crossing pixels. Header values are copied without modification. “Circle mass” is the actual normalized map probability inside the circularized nominal 90% radius, integrated with subpixel refinement; it is not the target 90% assigned by construction.

| IceCube event | Map 50%, deg² | Map 50%, Moons | Header 50%, deg² | Map 90%, deg² | Map 90%, Moons | Header 90%, deg² | Circle mass |
|---|---:|---:|---:|---:|---:|---:|---:|
| 260115A | 1.9547 | 9.96 | 1.92 | 6.5120 | 33.17 | 6.48 | 81.9% |
| 260125A | 0.3116 | 1.59 | 0.31 | 1.0466 | 5.33 | 1.03 | 89.1% |
| 260217A | 0.2180 | 1.11 | 0.21 | 0.7382 | 3.76 | 0.72 | 88.6% |
| 260315A | 0.2360 | 1.20 | 0.23 | 0.7961 | 4.05 | 0.77 | 88.7% |
| 260425A | 0.3150 | 1.60 | 0.31 | 1.0580 | 5.39 | 1.05 | 89.0% |
| 260504A | 0.2115 | 1.08 | 0.21 | 0.7120 | 3.63 | 0.70 | 88.6% |
| 260610A | 1.3254 | 6.75 | 1.30 | 4.5901 | 23.38 | 4.61 | 87.4% |
| 260622A | 0.2791 | 1.42 | 0.27 | 0.9439 | 4.81 | 0.92 | 88.9% |
| 260704A | 0.2010 | 1.02 | 0.19 | 0.6763 | 3.44 | 0.67 | 89.1% |
| 260708A † | 0.2015 | 1.03 | 0.20 | 0.6970 | 3.55 | 0.67 | 88.1% |
| 260712A | 0.1947 | 0.99 | 0.19 | 0.6631 | 3.38 | 0.64 | 88.8% |
| 260722A | 0.5836 | 2.97 | 0.58 | 2.0293 | 10.34 | 2.05 | 87.1% |
| 260805A | 0.3933 | 2.00 | 0.41 | 1.3499 | 6.87 | 1.36 | 87.3% |
| 260807A | 7.3666 | 37.52 | 7.24 | 23.8162 | 121.30 | 24.46 | 64.1% |
| 260821A | 0.2012 | 1.02 | 0.19 | 0.6824 | 3.48 | 0.67 | 88.9% |
| 260825A | 0.2524 | 1.29 | 0.25 | 0.8520 | 4.34 | 0.84 | 89.1% |
| 260827A | 0.1896 | 0.97 | 0.18 | 0.6829 | 3.48 | 0.68 | 88.2% |
| 260916A | 0.2189 | 1.11 | 0.21 | 0.7426 | 3.78 | 0.73 | 89.1% |
| 260919A | 0.0521 | 0.27 | 0.05 | 0.2140 | 1.09 | 0.21 | 89.6% |
| 260930A | 0.2573 | 1.31 | 0.25 | 0.8689 | 4.43 | 0.85 | 88.9% |

All figures in this table are numerical summaries of the supplied maps; the displayed digits do not imply finer physical localization than their pixels or calibrated reconstruction allow. The original 20-map medians are retained only as historical inventory statistics. The current candidate medians exclude † 260708A because of the cosmic-ray muon interpretation in GCN 45171. The table and figure retain this map as a visibly flagged audit record. This exclusion does not change any other event's calculated area.

## What circularization misses

The GCN documentation gives the revised 90% radius as

r90 = sqrt(mean(|ΔRA90|) × cos(dec) × mean(|ΔDec90|)),

where each mean averages the plus and minus errors. Calculate the circle's spherical area as 2π[1−cos(r90)] steradians. Its small-angle form is πr90² square degrees, or about 16r90² Moons for radius in degrees. The 50% circles in the area plot use the same formula applied to the 50% bounds as an explicitly derived comparison, not an independently documented 50% notice field.

![Map shapes and circular approximations](icecube-2026-shapes.png)

For **260115A**, the circle has radius **1.4394°** and area **33.15 Moons**, almost identical to the 90% map area's **33.17 Moons**. Yet it encloses only **81.9%** of the normalized map probability. The circle spends area above and below the elongated region and misses probability at its sides.

For **260807A**, the circle has radius **2.8818°** and area **132.85 Moons**, **9.53% larger** than the actual 90% map area of **121.30 Moons**. It nevertheless contains only **64.1%** of the normalized map probability. The long, asymmetric extension extends far outside the circle. Coarse pixels and invalid or absent map samples also produce visible irregularities; those should not automatically be interpreted as separate astrophysical sources.

The two headline circle probabilities were checked using recursive HEALPix subdivision to orders 12 and 15. Both changed by less than 0.00006 in probability (0.006 percentage point). This validates numerical integration of the supplied piecewise-constant maps, not the underlying reconstruction. The CSV retains a simpler native-pixel-center estimate as a diagnostic, but the quoted circle probabilities use the refined integral. In particular, the native-center estimate of 62.4% for 260807A is too crude; the refined result is 64.1%.

The maps are plotted in local sky-offset coordinates, with equal horizontal and vertical angular scales within each panel. Panel scales differ; each includes a 0.5-degree Moon disk. The blue region is nested within the orange 90% region. Whole threshold pixels are shown, whereas numerical areas interpolate within the last pixel.

## GCN cross-check and event status

The new archive contains 20 event-page text exports with **85 actual circular blocks**, plus a manifest recording URLs, HTTP status 200, and retrieval times on 2026-10-09. Circular identifiers mentioned in the text were distinguished from full circular blocks: for example, the repeatedly cited general announcement GCN 43419 is not itself a full included circular. All 20 requested event pages are present.

For all 20 events, the primary IceCube circular describes an offline-refined reconstruction. The FITS best-fit RA and Dec and all four asymmetric 90% RA/Dec bounds agree exactly with the values printed in those circulars: **120 numeric coordinate/error comparisons pass**. The circulars call the errors “90% PSF containment”; the FITS headers call their map regions highest-posterior-density credible regions. These descriptions and the GCN documentation are preserved rather than recast as Gaussian standard deviations.

Run/event IDs in the primary circular's AMON link match the FITS headers for **19 of 20 events**. The remaining circular, 260217A, does not supply that link and explicitly reports that the initial classical notice was not distributed. It is not an ID mismatch. Only the first two primary circulars contain explicit FITS URLs; both match the supplied manifest. The others refer to the map-distribution workflow without an explicit FITS URL in the supplied text, so their file identity is supported by coordinates and event metadata, not a matching binary checksum supplied by GCN.

Event dates agree. All printed event times are within **0.099 seconds** of DATE-OBS, but they are not all identical: five exceed 0.01 seconds (260315A: 0.040 s; 260504A: 0.058 s; 260807A: 0.023 s; 260916A: 0.039 s; 260930A: 0.099 s). 260425A differs by 0.010 s. These differences are retained in the audit, not silently called exact time matches or interpreted as localization revisions.

The supplied circulars do not independently provide the map-integrated 50% areas or the FITS contour-area metadata. The earlier density-integration versus FITS-header comparison therefore remains the relevant area check. Agreement of 90% coordinate bounds does not settle the normalization/contour-area discrepancies.

| IceCube event | Primary IceCube circular | Map RA/Dec and four 90% bounds | Status qualification |
|---|---|---|---|
| 260115A | [GCN 43421](https://gcn.nasa.gov/circulars/43421) | All six match | No withdrawal/reclassification identified in supplied page |
| 260125A | [GCN 43512](https://gcn.nasa.gov/circulars/43512) | All six match | No withdrawal/reclassification identified in supplied page |
| 260217A | [GCN 43768](https://gcn.nasa.gov/circulars/43768) | All six match | Preliminary notice errors documented; updated notice said unaffected |
| 260315A | [GCN 44017](https://gcn.nasa.gov/circulars/44017) | All six match | No withdrawal/reclassification identified in supplied page |
| 260425A | [GCN 44409](https://gcn.nasa.gov/circulars/44409) | All six match | No withdrawal/reclassification identified in supplied page |
| 260504A | [GCN 44464](https://gcn.nasa.gov/circulars/44464) | All six match | No withdrawal/reclassification identified in supplied page |
| 260610A | [GCN 44899](https://gcn.nasa.gov/circulars/44899) | All six match | No withdrawal/reclassification identified in supplied page |
| 260622A | [GCN 45018](https://gcn.nasa.gov/circulars/45018) | All six match | No withdrawal/reclassification identified in supplied page |
| 260704A | [GCN 45075](https://gcn.nasa.gov/circulars/45075) | All six match | No withdrawal/reclassification identified in supplied page |
| 260708A | [GCN 45120](https://gcn.nasa.gov/circulars/45120) | All six match | Cosmic-ray muon interpretation in GCN 45171; excluded |
| 260712A | [GCN 45141](https://gcn.nasa.gov/circulars/45141) | All six match | No withdrawal/reclassification identified in supplied page |
| 260722A | [GCN 45194](https://gcn.nasa.gov/circulars/45194) | All six match | No withdrawal/reclassification identified in supplied page |
| 260805A | [GCN 45294](https://gcn.nasa.gov/circulars/45294) | All six match | No withdrawal/reclassification identified in supplied page |
| 260807A | [GCN 45307](https://gcn.nasa.gov/circulars/45307) | All six match | No withdrawal/reclassification identified in supplied page |
| 260821A | [GCN 45412](https://gcn.nasa.gov/circulars/45412) | All six match | No withdrawal/reclassification identified in supplied page |
| 260825A | [GCN 45438](https://gcn.nasa.gov/circulars/45438) | All six match | No withdrawal/reclassification identified in supplied page |
| 260827A | [GCN 45455](https://gcn.nasa.gov/circulars/45455) | All six match | No withdrawal/reclassification identified in supplied page |
| 260916A | [GCN 45598](https://gcn.nasa.gov/circulars/45598) | All six match | No withdrawal/reclassification identified in supplied page |
| 260919A | [GCN 45645](https://gcn.nasa.gov/circulars/45645) | All six match | No withdrawal/reclassification identified in supplied page |
| 260930A | [GCN 45787](https://gcn.nasa.gov/circulars/45787) | All six match | No withdrawal/reclassification identified in supplied page |

### Substantive follow-up findings

**260708A — background interpretation.** The initial [GCN 45120](https://gcn.nasa.gov/circulars/45120) reports computational anomalies in the primary offline reconstruction and uses an alternative offline algorithm for the quoted direction. The later IceCube [GCN 45171](https://gcn.nasa.gov/circulars/45171), dated 2026-07-15, states: “the observed signatures are unlikely to be produced by a high-energy neutrino but instead indicate an origin in multiple muons produced in a cosmic-ray air shower.” This is a substantive rejection of the neutrino interpretation despite the absence of the word “retraction.” The record does not establish a machine-readable Kafka alert_type=retraction; the report therefore labels the physical interpretation precisely rather than asserting a formal notice status. Its 1.03-Moon 50% and 3.55-Moon 90% maps remain historical numerical products, not evidence for the direction of a confirmed neutrino.

**260217A — preliminary notice correction.** [GCN 43768](https://gcn.nasa.gov/circulars/43768) reports a roughly 30-minute Kafka delay and errors in the initial schema: ra_dec_error and far were strings; record_number was sent as 1 but should have been 0; and p_astro was transmitted as a percentage, 30.722, rather than a fraction, with the circular giving 0.31 as the correct value. It explicitly says these problems did not affect the updated reconstruction notice sent with the circular. Thus record_number alone cannot reliably distinguish its initial and updated messages without examining the payload. The supplied map matches the circular's refined position and uncertainty bounds.

**260825A — duplicate follow-up, not a localization revision.** [GCN 45461](https://gcn.nasa.gov/circulars/45461) and [GCN 45462](https://gcn.nasa.gov/circulars/45462), posted 32 seconds apart, contain identical additional-neutrino-search bodies. They do not give a replacement sky localization. Multiple circulars for one event must not be counted as multiple map revisions.

**Counterpart rejection is separate from alert rejection.** The optical candidate for 260722A was classified as a Type Ia supernova and described as unrelated to the neutrino in [GCN 45217](https://gcn.nasa.gov/circulars/45217). That rejects the proposed counterpart, not the underlying alert. Likewise, follow-up “no candidate,” upper-limit, or non-significant additional-neutrino results do not retract the original event. These events remain in the 19-candidate summary.

### Provenance and remaining limits

The earlier event-record ZIP SHA-256 is `54fef5167e1e3835a56e65321672a3890a9e0d57e33e9e3b98cd6407f36e8ee1`. The subsequently supplied `gcn-provenance-complete.zip` has SHA-256 `17fc6ab3d689776e4728cd3063cbf208e3708b11c1e8d092a540910035d9f5b0` and contains 20 HTML files, 20 text exports, and a representation manifest.

**The representation ambiguity is resolved.** SHA-256 was recomputed directly over the unmodified bytes of each ZIP member:

| Verification | Result |
|---|---:|
| HTML bytes match the explicitly labeled HTML checksum | 20/20 |
| Text bytes match the explicitly labeled text checksum | 20/20 |
| Earlier manifest checksum equals the actual HTML checksum | 20/20 |
| New text export is byte-for-byte identical to the previously analyzed export | 20/20 |
| Source URL and retrieval timestamp match the earlier manifest | 20/20 |

The earlier hashes identify **HTML**, not plain text. Comparing them against the text exports compared different representations; it did not demonstrate corrupted files. The prior unresolved-provenance warning is withdrawn. The text used for the scientific audit is unchanged, so no area calculations, event classifications, or summary statistics require revision.

The new checksum table records both representations explicitly. The updated audit replaces the ambiguous `checksum_matches` field with `html_checksum_verified`, `text_checksum_verified`, `earlier_manifest_matches_html`, and `text_identical_to_earlier_archive`. These all pass for every event. This establishes byte integrity and continuity among the supplied archives and manifests. It is not independent live-server authentication, a demonstration of the text-extraction algorithm, or evidence that the event inventory or FITS versions are current. The earlier successful 20-of-20 compressed and decompressed FITS checksum checks remain unchanged.

No additional event withdrawal or neutrino-to-background reclassification was identified in the supplied page contents. This is a bounded statement about these exports, not proof of current active status. The archive does not contain the complete machine-readable notice stream, cryptographically tied FITS revisions, or a complete dated alert-directory listing. It cannot establish that the downloaded FITS files are the newest binaries, that no later retraction exists, or that the 20 events exhaust all public 2026 alerts. No new network access was attempted.

All 20 map files listed in the original map manifest are present, and all have corresponding event-page exports. This resolves the missing-event-page limitation for this sample. It does not resolve year-wide missing maps. Preliminary notices can legitimately have healpix_url=null according to the supplied GCN documentation.

The 260115A FITS header lacks ALERT-STREAM, but its primary circular identifies it as Bronze. The 77 repeated Bronze ALERT-STREAM cards in 260217A's FITS header agree with the circular's stream classification and do not by themselves establish a map revision or retraction.

The supplied GCN mission HTML document's SHA-256 remains `db82beea310f608d4e55eaf018c37c452c1b4e104fc75358b567ff5186c8fbdb`. Its definitions were read locally, not refreshed online.

## Detecting a particle versus identifying a source

IceCube observes Cherenkov light from charged particles produced after a neutrino interacts in or near the detector. A track event allows the incoming direction to be reconstructed, but finite light measurements, propagation through the ice, detector and reconstruction uncertainties, and interaction kinematics limit its precision. The maps quantify that directional uncertainty under the reconstruction model.

The 260708A follow-up provides a concrete caution: an initial high-energy track alert can later be interpreted as cosmic-ray muons rather than a neutrino. Detecting light, identifying the particle class, reconstructing a direction, and associating an astronomical source are distinct inferences.

An astronomical source is an additional inference. Several objects may lie in a localization region; the true source may be uncataloged or electromagnetically faint; and the event may have an atmospheric origin. A credible spatial and temporal counterpart, repeated neutrinos, and an assessment of chance coincidence can strengthen an association. A 90% directional region is not a 90% probability that a named galaxy or blazar is the source.

## Reproduction

The provenance-verified results CSV now joins the original numerical results to per-event GCN evidence and an explicit include_candidate_summary flag. The separate GCN audit CSV retains coordinate comparisons, time differences, primary and follow-up circular IDs, source URLs, retrieval timestamps, explicit HTML and text hashes, representation-specific checksum checks, and byte-identity checks against the earlier text exports.

The numerical columns retain normalized areas, unnormalized-threshold sensitivity, crossing-pixel brackets, untouched header areas, circular radii and areas, circle probability integrals, density normalizations, invalid-pixel counts, source URLs, and map checksums.

The accompanying Python script runs entirely offline with NumPy, pandas, Astropy, and astropy-healpix. Astropy 8.0.1 and astropy-healpix 2.0.1 were used here. Its calculations were executed against the supplied archive and reproduced all 20 normalized 50% and 90% areas and both circle integrals to numerical tolerance. It reproduces numerical results rather than the figure layout. The earlier numerical script does not parse this new GCN archive or apply the 260708A exclusion; its all-map output remains a historical inventory. Use the audited CSV's include_candidate_summary flag for the 19-candidate summary.

```sh
python icecube-localization-analysis.py icecube-2026-localization-maps.zip --output reproduced-results.csv
```
