VALIDATION_ASTRONOMY - TheDaniel166/moira GitHub Wiki

Astronomy Validation: Methods, Results, and Limits

Version: 2.0

Date: 2026-08-13

Engine: Moira 6.1.0

Calculation baseline: 68544ae1403009e3b25c30554992acb48790487c

Validation runtime: Python 3.14.3

Planetary kernel: JPL DE441

Overall status: partially validated; every result below is product-specific

Abstract

Moira does not have one universal astronomy-accuracy number. Its astronomy layer contains different products—reference-frame transformations, planetary places, event searches, eclipse circumstances, occultation paths, rise/set times, and visibility models—and each product has its own authority, frame, time scale, correction regime, corpus, and acceptance envelope.

The strongest current numerical results are:

  • 120 apparent geocentric major-body comparisons against JPL Horizons pass a 0.35 arcsecond angular and 0.1 km distance gate. The recorded maxima are 0.277781 arcsecond and 0.066846 km.
  • 80 geometric ICRF vector comparisons against JPL Horizons pass a 0.001 arcsecond angular and 0.01 km vector-difference gate. The recorded maxima are 0.000021829 arcsecond and 0.002937 km.
  • IAU 2006/2000A frame and Earth-rotation functions agree with their matching ERFA functions within 0.001 arcsecond across the declared test epochs.
  • Lunar orientation matches five JPL Horizons geocentric/topocentric cases at the declared 0.001 degree surface and 0.002 degree axis gates (0.02 degree for Horizons' rounded bright-limb angle), while three rounded NASA SVS holdouts pass 0.01 degree after applying SVS's distinct J2000-north convention.
  • NASA/GSFC, JPL Horizons, IOTA, USNO, and source-specific visibility corpora validate named eclipse, occultation, rise/set, and visibility slices. They do not establish universal event accuracy outside those slices.

The two planetary suites now enforce exact target identity and exact ephemeris-epoch identity. Older planetary residuals that mixed planet centers with system barycenters or sent a different time basis to Horizons are retired and are not evidence about Moira's accuracy.

1. How to read this paper

The word validated means only that a named product satisfied a named gate over a named corpus. It does not mean every body, epoch, observer, kernel, or public API route has the same error bound.

Every quantitative claim should answer these questions:

  1. What object was compared?
  2. Which authority or independent evidence governed that object?
  3. What body identity, origin, frame, time scale, and correction regime were used?
  4. How many cases were exercised?
  5. What units and acceptance threshold were enforced?
  6. What remains outside the claim?

If one of those answers is absent, the statement is not a complete accuracy claim.

1.1 Evidence classes

Evidence class What it establishes What it does not establish
Authority validation Agreement with a product-relevant primary standard or publication under matched semantics Accuracy outside the named corpus or the authority's own model
Cross-model comparison A bounded difference between two explicitly different models Same-model parity or a physical uncertainty estimate
Cross-engine corroboration Agreement with another implementation Primary scientific authority
Physical or structural invariant Required geometry, ordering, continuity, conservation, or topology External numerical accuracy by itself
Regression evidence A result remains stable after it has been admitted Independent truth
Native/Python differential Two implementations of the same admitted computation agree A second scientific oracle
Release-artifact evidence A named artifact installs and reproduces its declared checks Publication, deployment, or downstream adoption

An acceptance threshold is a test gate, not automatically an uncertainty bar. Catalog rounding, model-basis differences, source resolution, numerical search tolerances, atmosphere variability, and observational uncertainty remain separate quantities.

2. System under test and reproducibility

The results in this revision were reviewed against Moira 6.1.0 at calculation baseline 68544ae, using Python 3.14.3 and the discovered DE441 resource with downloads disabled. The repository's tests/KNOWN_ISSUES.yml contained no active entries at review time.

The two major-body maxima quoted in the abstract and Section 5 are dated receipts from the isolated live Horizons run on 2026-08-13. The acceptance thresholds and comparison contracts are executable tests; the observed maxima are not promoted to frozen golden truth and should be refreshed with a later live-oracle run rather than copied forward unexamined.

DE441 is the kernel used for the numerical results in this paper. Moira can open other compatible SPK kernels, but this paper does not transfer the DE441 residuals to DE430, DE440, or any other kernel without a separate run.

The test environment distinguishes three kinds of evidence:

  • Live external comparisons query an authority such as JPL Horizons and require the explicit external_network test boundary.
  • Frozen authority fixtures retain source URLs, query semantics, retrieval dates, units, and tolerances so the admitted comparison can run offline.
  • Internal invariants and regressions require no external network and are never relabelled as external truth.

The calculation path under test is the Python-governed engine with its required native computational substrate. Native/Python agreement is reported only where a dedicated differential exists; it is not assumed for every product.

3. Results at a glance

Product Evidence and corpus Enforced gate Claim status
IAU frames and Earth rotation Official SOFA C 2023-10-11 frame fixture plus secondary ERFA parity Matrix-specific binary64 gates Authority-validated on the named epochs and declared frame-router boundaries
Apparent geocentric major bodies JPL Horizons; 10 targets × 12 epochs = 120 <= 0.35 arcsecond, <= 0.1 km Cross-model angle; same-target/same-epoch distance
Geometric geocentric major-body vectors JPL Horizons; 10 targets × 8 epochs = 80 <= 0.001 arcsecond, <= 0.01 km Authority comparison of matched ICRF vector geometry
Topocentric apparent RA/Dec JPL Horizons; 18 cases Per-case RA 15–30 arcseconds, Dec 4–12 arcseconds Authority-validated on the named sites/epochs; not an azimuth/altitude claim
Osculating orbital elements Frozen exact-JDTDB JPL Horizons VECTORS and ELEMENTS; 4 calibration, 7 planet holdout, 6 current-catalog holdout cases Exact-kernel gates from 2e-14 to 5e-10 degree; sampled-catalog product gates from 1e-5 AU to 0.05 degree Strict core authority-validated; current asteroid/comet releases admitted on six holdouts; live drift 17/17; full 11,720-body runtime inventory passed
Heliocentric distance extrema JPL Horizons vectors; 8 bodies <= 1 day, <= 3e-4 AU Authority-validated for the next local extrema in each case
Asteroid apparent ecliptic positions Frozen JPL Horizons fixture; 203 cases, 61 bodies 0.5 arcsecond default; four named TNO exceptions at 1.5 or 5.0 arcseconds Product-specific authority fixture; not the planetary threshold
Delta T policies Source-priority, continuity, policy, and compatibility tests Product-specific invariants and source envelopes Documented/partially validated; no universal Delta-T accuracy claim
Lunar orientation and libration Native/SPICE matrices, JPL Horizons quantities 14-17, NASA SVS 2026 hourly data Matrix <= 3e-12; Horizons surface <= 0.001 degree, axis <= 0.002 degree, rounded bright-limb <= 0.02 degree; SVS <= 0.01 degree Authority-validated on two calibration and six disjoint holdout cases, including one topocentric site
Solar and lunar eclipses NASA/GSFC catalogs, detailed products, and geometric invariants Product-specific classification, time, coordinate, and topology gates Authority-validated only for named catalog/product slices
Lunar occultations JPL Horizons, IOTA, LOLA, cached Swiss cases, and invariants Product-specific time/path/topography gates Mixed authority, corroboration, and invariant evidence
Rise, set, and transit Four frozen JPL Horizons cases plus USNO checks <= 2 seconds on the Horizons corpus Authority-validated on the named bodies/sites/windows
Yallop lunar criterion Yallop 1997 Table 4; 295 rows q- and boundary-family gates Criterion validation, not guaranteed human sighting
Physical point-source visibility Independent equations, libRadtran holdouts, external event goldens, invariants 16-cell release matrix; 12 timed cells within 60 seconds Admitted only inside the declared clear-sky model and data-pack domain

4. Reference frames, Earth rotation, and time

4.1 ERFA/SOFA-aligned functions

tests/integration/test_erfa_validation.py compares Moira with the matching ERFA functions for:

  • Gregorian/Julian calendar identity at two BCE anchors;
  • Greenwich Mean Sidereal Time (erfa.gmst06);
  • Earth Rotation Angle (erfa.era00);
  • IAU 2006 mean obliquity (erfa.obl06);
  • IAU 2000A nutation with IAU 2006 adjustment (erfa.nut06a);
  • IAU 2006 precession (erfa.pmat06);
  • the combined precession-nutation matrix (erfa.pnm06a);
  • true obliquity; and
  • Greenwich Apparent Sidereal Time.

Most comparisons use 12 epochs from 500 BCE through 2100 CE and enforce < 0.001 arcsecond. Full erfa.gst06a GAST parity is separately enforced at eight modern epochs from J1500 through J2100.

Before J1000, Moira's equation-of-equinoxes construction and ERFA's equation-of-origins construction can differ by about 1.1 arcseconds. That is a declared model-basis difference. It is not described as ERFA parity, and it is not dismissed merely because historical Delta T may be larger.

4.2 Time-scale boundaries

Moira keeps civil or caller-facing time separate from ephemeris time. Tests bind astronomy calculations to the reader that supplies the relevant ephemeris clock, and external comparisons send the resulting epoch with an explicit Horizons time type.

Orbital Core Stage 1 makes the SPK boundary explicit: public reader methods accept TT, convert exactly once with the official NAIF naif0012.tls implicit TDB-minus-TT equation, and pass only TDB to raw segment evaluation. The frozen time fixture records the NAIF source URL, 5,257-byte artifact and SHA-256 678e32bdb5a744117a467cd9601cd6b373f0e9bc9bbde1371d5eee39600a039b. Round trips are bounded to one binary64 ULP and strict orbital results expose both numerical epochs and the conversion receipt.

The principal Delta-T policies are:

Policy Intended use
hybrid Default source-priority table/scenario policy
physical Explicit source-priority/scenario surface with uncertainty and accounting vessels
nasa_canon Compatibility with NASA eclipse-publication conventions
fixed Controlled sensitivity and reproducibility experiments

4.3 Lunar orientation and libration

tests/integration/test_lunar_orientation_spice_oracle.py compares the native binary-PCK type-2 evaluator and the composed J2000 -> MOON_ME_DE440_ME421 matrix with spiceypy.pxform. The five epochs include the PCK coverage endpoints and the shared segment boundary. The maximum permitted matrix-element residual is 3e-12; SPICE is test-only and is not part of the production computation.

tests/integration/test_lunar_orientation_authority.py separates calibration from holdout evidence. The two-case Horizons calibration contains an Earth geocentre query and a WGS-84 New York observer query. Three disjoint geocentric dates are retained as Horizons holdouts. Quantities 14 through 17 govern sub-observer and subsolar longitude/latitude, apparent subsolar-point position angle (the bright limb), and apparent north-pole position angle. Surface coordinates must agree within 0.001 degree; the north-pole angle uses a 0.002 degree gate, which covers the measured true-of-date reduction difference. Horizons rounds the bright-limb value to 0.01 degree, so its gate is 0.02 degree.

Three further hourly cases come from NASA SVS's 2026 Moon Phase and Libration JSON. Surface coordinates and the converted axis angle must agree within 0.01 degree. SVS defines posangle against J2000 celestial north, whereas Moira's public value and Horizons quantity 17 use true-of-date north. The test therefore derives a J2000-basis diagnostic from the same lunar pole; it does not compare unlike angle conventions directly.

All fixtures retain source URLs, query quantities or source-asset identity, retrieval time, byte length, SHA-256, and explicit longitude/position-angle conventions. The separate acquisition script is scripts/build_lunar_orientation_authority_fixtures.py. These results cover the named 2026 cases and admitted DE440/DE441 resource identities; they are not a universal error bound for every epoch in the PCK coverage interval.

tests/integration/test_delta_t_hybrid.py and tests/integration/test_delta_t_model_comparison.py enforce policy routing, source-priority identity, continuity, finite extrapolation behavior, and the distinction between the canonical and physical paths. Those tests do not use a fabricated Horizons or IERS fixture and do not claim one universal historical Delta-T error.

For ancient eclipse comparisons, NASA catalog TT and Moira TT retain their own declared Delta-T bases. The 360-second ancient gate is a cross-authority regression envelope, not an estimate of ancient timing uncertainty.

5. Planetary and small-body validation

5.1 Target identity is part of the result

The DE441 routes exposed by Moira do not all terminate at planet centers. The Horizons target must match the final SPK target exactly:

Moira body Horizons target used in the major-body suites
Sun 10 — Sun center
Moon 301 — Moon center
Mercury 199 — Mercury center
Venus 299 — Venus center
Mars 4 — Mars system barycenter
Jupiter 5 — Jupiter system barycenter
Saturn 6 — Saturn system barycenter
Uranus 7 — Uranus system barycenter
Neptune 8 — Neptune system barycenter
Pluto 9 — Pluto system barycenter

Both major-body test files contain an executable identity assertion against NAIF_ROUTES. A comparison to 499, 599, or another planet center would be a different product and cannot be mixed into these residuals.

5.2 Apparent geocentric positions

Test: tests/integration/test_horizons_planet_apparent.py

Corpus: 10 bodies × 12 epochs from 1900-01-01 through 2025-09-01

Origin: geocentric

Moira reduction: ICRF geometry reduced with IAU 2006 precession and IAU 2000A nutation

Horizons product: Earth-based apparent RA/Dec, quantity 2

Epoch contract: reader-bound ephemeris JD sent as discrete TLIST with TIME_TYPE=TT

All 120 cases pass:

  • angular separation <= 0.35 arcsecond;
  • distance difference <= 0.1 km;
  • recorded maximum angular separation 0.277781 arcsecond for the Saturn system barycenter at the 1900 epoch; and
  • recorded maximum distance difference 0.066846 km for Mercury at the 1933 epoch.

The angle is a cross-reduction-model comparison. Moira uses IAU 2006/2000A true-of-date reduction, while the Horizons manual describes apparent quantity 2 using its EOP-corrected IAU 1976/1980 true equator and equinox of date. The distance comparison is same-target and same-epoch.

5.3 Geometric ICRF vectors

Test: tests/integration/test_horizons_planet_vectors_wide.py

Corpus: 10 bodies × 8 epochs from 1800-06-24 through 2150-01-01

Product: geometric, uncorrected geocentric ICRF vectors

Horizons correction: VEC_CORR=NONE

Epoch contract: the same numeric ephemeris JD sent as discrete TLIST with TIME_TYPE=TDB

All 80 cases pass:

  • angular vector difference <= 0.001 arcsecond;
  • absolute vector difference <= 0.01 km;
  • recorded maximum angular difference 0.000021829 arcsecond for the Moon at J2000; and
  • recorded maximum vector difference 0.002937 km for Mercury at J2000.

This isolates target and vector geometry. Orbital Core Stage 1 separately locks the public-TT/private-TDB conversion and compares strict orbital states at an identical frozen JDTDB instant; the older vector corpus is no longer used as evidence for the clock boundary.

5.4 Retired planetary results

Earlier versions of this report published apparent residuals of 0.577850 arcsecond / 1684.977 km and vector residuals of 0.762685 arcsecond / 10201.934 km. Those comparisons mixed Moira system-barycenter routes with Horizons planet centers and did not hold the ephemeris epoch contract constant. They are comparator-contract defects, not measurements of DE441 or Moira, and must not be reused.

5.5 Topocentric sky positions

tests/integration/test_horizons_sky.py contains 18 live Horizons cases for the Sun, Moon, Mercury, Venus, Mars, Jupiter, Saturn, and Pluto at Greenwich and New York epochs. It compares topocentric apparent right ascension and declination. Per-case gates range from 15–30 arcseconds in right ascension and 4–12 arcseconds in declination.

The current test does not assert its stored azimuth and altitude tolerances. Therefore this section makes no azimuth/altitude parity claim from that file.

5.6 Osculating elements and distance extrema

Orbital Core Stage 1 uses three disjoint, frozen JPL Horizons corpora generated with exact TLIST JDTDB and explicit TIME_TYPE=TDB for both uncorrected ICRF VECTORS and J2000-ecliptic ELEMENTS:

  • four calibration cases: Mercury, Earth, Jupiter, and Earth-centered Moon;
  • seven planet holdouts: Venus, EMB, Mars, Saturn, Uranus, Neptune, and Pluto;
  • six catalog holdouts: Ceres, Hektor, Atira, Apophis, 1P/Halley, and 2P/Encke.

tests/integration/test_orbital_elements_kernels.py proves raw state, TT-wrapper, element, gravity, time, frame, and source-receipt parity against the installed kernel subset. Planet state coordinates are gated at 1e-5 km; tight field-specific element gates range from 2e-14 for eccentricity to 5e-10 degree for angles. tests/integration/test_horizons_orbits.py retains an isolated live-primary drift audit and never rewrites accepted fixtures.

Orbital Core Stage 2 replaces the older sampled-distance comparison with a frozen official JPL Horizons passage corpus and an isolated live-primary drift audit. Horizons requests use geometric uncorrected ICRF VECTORS, exact TDB epochs, and radial velocity dot(r, v) / |r|; sign crossings are refined and confirmed by distances on both sides. The frozen planet gates are 1e-4 day for event time and 1e-9 AU for distance. The disjoint calibration/holdout set covers Mercury through the Pluto system, Earth versus the Earth-Moon barycenter, Eros, Chiron, 1P/Halley in 2061, 2P/Encke, Sedna near its 2076 pericenter, and Eris near its 2257 pericenter.

Deterministic synthetic tests separately cover forward/reverse and exact-start inclusion, explicit windows, flat radius, initially hyperbolic motion, fixed evaluation budget, route gaps, an admitted continuous seam with an extremum on the seam, and a rejected discontinuous seam. Real DE441 checks prove TT in legacy DistanceExtremes, verified inverse UT1 in PhenomenonEvent, the Earth-centered Moon rule, and the immutable route/evaluation receipt.

The ten installed DE441 planet/system cases pass those gates. At the September 28 checkpoint, the catalog releases did not carry a reviewed Stage 2 apsidal-passage accuracy admission, so their six passage-time authority comparisons were NOT RUN, not silently accepted under wider gates. This is a separate event-search validation frontier from the orbital-element and geometric-node release admission below. A runnable Eros search proves catalog routing without substituting that smoke test for passage-time authority parity. The September 28 follow-up refreshed Encke from JPL#K273/14 to JPL#K273/17 and isolated the comet defect: the installed 30-day/5-node release misses Halley's perihelion by 8985.653 seconds, Encke's perihelion by 16862.339 seconds, and Encke's aphelion by 43.564 seconds. Reconstructing the same Type-13 products with the asteroid catalog's 10-day/7-node base policy plus exact daily, nonuniform nodes around every radial extremum reduces those timing residuals to 0.000322, 0.008570, and 0.005713 seconds without widening the existing 8.64-second / 1e-9 AU gates. The candidate also bounds each Horizons refinement query to 32 Julian years; a centuries-wide TLIST was shown to add measurable long-span propagation drift even after interpolation was repaired. The source-receipted probe is tests/artifacts/oracle/comet_apsidal_sampling_probe_2026-09-28.json. The refreshed authority corpus is retained separately as tests/fixtures/horizons_apsidal_passages_reference_2026_09_28.json; the September 15 predecessor remains byte-identical to its historical release receipt.

The 10-day/7-node baseline by itself still fails the strict passage-distance gate for the high-curvature comet cases, so the daily extremum nodes are an additional event-accuracy requirement rather than a substitute for catalog parity. This diagnoses and repairs the catalog builder, not the apsidal root solver. That September probe was not release admission: the complete 497-comet catalog still needed a new sealed release and release-bound validation. The immutable 2026.07.28.1 release was not rewritten. The published replacement and its current-solution evidence are recorded below.

The same question was then closed exhaustively for the asteroid release rather than inferred from Icarus alone. The governed audit in tests/artifacts/oracle/asteroid_type13_apsidal_sampling_audit_2026-09-28.json partitions all 11,223 admitted identities. For all 126 bodies whose current JPL SBDB perihelion distance is below 1.3 AU, it compares the existing 10-day/7-node Type-13 representation with a same-start/stop 5-day Horizons VECTORS series at every off-grid witness adjacent to every radial-velocity sign crossing across the body's catalog coverage. All paired replies agree exactly at their shared epochs, so the measured residuals are interpolation error rather than different Horizons integrations. Fifty-nine bodies fail the unchanged 1e-9 AU (0.1495978707 km) radial-distance gate, occupying 40 of the 449 release shards. The other 11,097 admitted bound bodies are covered by a worst-case elliptic Type-13 invariant at the 1.3 AU boundary: eccentricity 0.0000 through 0.9999 and every 0.1-day grid phase produce a worst radial residual of 0.000173152 km, an 863.97x margin inside the gate.

This is an exhaustive catalog partition for apsidal sampling, not a general all-epoch close-encounter position audit. It did not itself admit the September asteroid release for apsidal passages: the exact 59-body/40-shard repair roster still required rebuilding and release-bound validation. That work is now complete for the published replacement, without rewriting the historical audit.

October 12, 2026 rebuilt-catalog closure

Both catalogs 2026.10.10.1 are published and active. The asteroid release rebuilds 40 shards for the 59 audited bodies and reuses 409 byte-identical shards after full server-hash verification. All 497 comet trajectories use certified adaptive sampling. The ten-day/seven-node base remains; local refinement starts at one day and is halved as needed, with policy floors of 1.5 hours for the repaired asteroids and 11.25 minutes for comets. Those floors are limits, not uniform sampling intervals.

Final sealed-release integration checks all 11,720 bodies for native state/element, identity, coverage and provenance invariants, plus four frozen asteroid element holdouts, six anchored asteroid apsidal events and three current-solution comet events. The latter bind Halley JPL#75 and Encke JPL#K273/22; their largest measured timing residual is 0.000603497 seconds. The independent-event gates remain 8.64 seconds and 1e-9 AU. The final comet freshness census checked all 497 solutions; 38 bodies were refreshed and 459 trajectory segments remained byte-identical.

This closes the rebuild/publication work, not every possible small-body accuracy question. Internal convergence and all-body structural checks are not an independent all-body/all-epoch event oracle. Comet distant-apparition and upstream solution limitations remain. Public manifest identities and release-bound evidence are listed in the release closure.

Historical September 28 element/node admission

The packaged 25-asteroid wheel remains a fallback implementation check. The September 28 element/node admission binds the independently refreshed exact-JDTDB catalog holdout to [email protected] (manifest SHA-256 1956b613f072a0dbd78c45d74552dbadb169fafc64fe4d28f02261752e3b667e) and [email protected] (manifest SHA-256 31fbbedbb3ea7ba276fa9d49d52211ae41d90f76c74fb49ec0a6bafb014f07a1). It uses the pre-existing live-product gates from test_orbital_elements_match_horizons: 1e-5 AU for semi-major axis and apsidal distances, 1e-5 eccentricity, 0.001 degree inclination/node, and 0.05 degree argument/mean anomaly. These are intentionally distinct from the strict-core extraction gates because the release kernels are 10-day asteroid and 30-day comet sampled Type-13 products, not raw one-epoch Horizons replies.

All six authority cases in that historical admission pass those declared gates. The largest measured residual is Encke at 1.203e-6 AU in semi-major axis and 0.000107 degree in mean anomaly. The isolated live-primary drift audit passes all 17 calibration and holdout cases after Horizons advanced Encke from JPL#K273/14 to JPL#K273/17; the historical fixture and receipts remain unchanged. On the release host, all 11,223 asteroids and 497 periodic comets (11,720 bodies) pass the exhaustive orbital-element coverage, finiteness, identity, and manifest/shard receipt gate. The admission receipt is tests/artifacts/oracle/small_body_orbital_catalog_admission_2026-09-28.json.

5.7 Orbital Core Stage 3 geometric nodes

Stage 3 removes the independent state, gravity, frame, and conic pipeline from planetary_nodes.geometric_node. The public signature and OrbitalNode vessel remain unchanged, but every result now adapts one strict osculating_elements computation with a Sun center and TRUE_ECLIPTIC_OF_DATE. The perihelion field maps the projected pericenter vector longitude rather than the inclined-orbit dogleg Omega + omega.

Deterministic adapter tests prove exact field mapping, one core call, canonical identity, Boolean-input rejection, typed failure when a required legacy-vessel field is undefined, preservation of frame-range errors, and absence of the old duplicate pipeline. DE441 integration covers Mercury through Pluto including Earth; all nine results map exactly to their independently requested strict-core result. Requests on either side of JD(TT) 2415020.0--2488070.0 fail with OrbitalFrameUnavailableError.

The loaded representative checks map Ceres, Hektor, Atira, Apophis, 1P/Halley, and 2P/Encke exactly to the same true-date core and their receipted catalog routes. All six current frozen catalog-Horizons numeric cases now run and pass under the same release-bound product admission used by the direct orbital-element tests. The admission binds fixture SHA-256 1e0b5fa423a87087c084f00f4e4e2be377a96f30602c1b3ca8b2374871f33395, the exact two manifest hashes, and the established live-product gates; no catalog manifest or older historical receipt was rewritten.

The historical September 28 inventory-wide Stage 3 check passes all 11,223 bodies in the verified [email protected] release and all 497 bodies in [email protected]. All 11,720 sovereign bodies receive finite node checks, exact true-date mapping, canonical resolution, manifest/kernel receipt checks, and coverage checks. The packaged wheel is present as a fallback but is not substituted for either full-release gate.

5.8 Measured Stage 1 compatibility shifts

The Stage 1 compatibility harness replays the pre-change baseline 29dd164c80c2a6788aa598a832eff3d4fd8e727a and the implementation worktree against identical, path-free resource identities. All 19 required probes are green in both captures. The corpus covers raw reader routes, planet_at, native and Python all_planets_at, a packaged asteroid and comet, transit and fixed-star searches, eclipses, lunar geometry, phase and phenomena products, end-to-end Shadbala, and four protected frame-consumer families.

The reader-clock receipt proves, to 1e-12 in the recorded state units, that:

  • the old public result is reproduced by the candidate's explicit-TDB operation when given the old numeric argument;
  • every candidate public-TT adapter equals exactly one TT-to-TDB conversion;
  • a second conversion is observably different on every sampled raw route; and
  • admitted native and forced-Python planetary paths agree within 1e-9.

Across the heterogeneous reader-clock probes, 84 of 137 shared numeric fields move and the largest raw absolute delta is 0.0017674416303634644. These fields mix kilometres, kilometres per day, degrees, Julian days, and derived doctrine units, so that maximum is a change detector, not one physical error measure or accuracy threshold.

The frame receipt compares 188 shared fields, of which 121 move; its largest heterogeneous raw delta is 0.00237959623336792. The direct matrix probe is a frame-only comparison at fixed TT epochs. Planetary, eclipse, and lunar-geometry probes deliberately show the combined clock and frame correction; their clock component is separately accounted for in the reader-clock receipt. Frame truth itself remains governed by the frozen official IAU SOFA 2023-10-11 matrices.

The focused Stage 1 gate and isolated 52-case element audit pass on this worktree. The Stage 2 live exact-TDB event audit passes its Earth and Neptune sentinels, including Neptune's first perturbed local maximum that the retired period/100 sampled-distance validator skipped. At the Stage 1 checkpoint, release readiness was blocked by the then-unresolved full-asteroid prerequisite and by a repository-wide non-network command that terminated in pre-existing harness-import, hybrid-eclipse-topology, and asteroid fixture/resource failures reproduced on the untouched baseline. The Stage 3 release-host inventory gate later satisfied the full-asteroid prerequisite; the remaining live-primary, catalog-admission, and inherited repository gates stay explicit. The plan's exact changed-file Ruff command also reports the same 66 inherited findings on candidate and baseline; the new Stage 1 files are clean when checked separately. None of these conditions is represented as orbital validation.

5.9 SPK routing and kernel scope

Moira resolves each body's NAIF chain and selects a segment that covers the requested epoch. The planetary validation suites exercise those routes over historical and future epochs, but passing output comparisons do not replace the dedicated resource, segment-selection, cache-ownership, and provenance tests.

The numbers in this paper belong to DE441. Kernel compatibility is an API capability; numerical transfer to another kernel requires a new corpus run.

5.10 Asteroid positions use a separate acceptance policy

tests/integration/test_horizons_asteroid_apparent.py uses a frozen, provenance-bearing Horizons fixture containing 203 cases across 61 bodies. The default longitude/latitude gate is 0.5 arcsecond for 57 bodies. Four named distant TNOs have explicit kernel-solution allowances:

  • Varuna and Quaoar: 1.5 arcseconds;
  • Orcus and Ixion: 5.0 arcseconds.

These are asteroid-product thresholds. They do not inherit the current 0.35 arcsecond major-body apparent-position threshold, and agreement within a widened TNO gate must not be described as shared planetary-pipeline accuracy.

6. Eclipse validation

Eclipse validation is split by product. Classification, greatest-event time, Besselian elements, central-path geography, visibility footprints, and lunar contact instants are not interchangeable claims.

6.1 Catalog classification and search

tests/integration/test_eclipse_nasa_reference.py binds NASA/GSFC catalog time semantics explicitly:

  • 23 solar maxima across ancient, modern, and future eras are classified by event family;
  • 15 lunar maxima across eras are classified by event family;
  • all 229 NASA/GSFC lunar catalog rows from 1901–2000 are classified at their published TD/TT maxima, preserving the Danjon shadow convention;
  • four modern solar event classes are recovered against NASA's separately published UT labels within 1 second;
  • the 2049 hybrid event is recovered within a named 30-second cross-model gate; and
  • representative ancient and future searches use separate 360-second and 60-second cross-authority regression envelopes.

The ancient gate is not an ancient-eclipse accuracy claim. It keeps distinct Delta-T and ephemeris models visible while preventing silent regression.

6.2 Besselian elements and central paths

tests/integration/test_eclipse_besselian_nasa_reference.py compares four NASA events—partial, total, hybrid, and annular—at five time offsets. Each Besselian field has its own unit and tolerance; for example, x, y, l1, and l2 use 0.0001 Earth equatorial radii, while d and mu use separate angular gates.

tests/integration/test_eclipse_path_nasa_reference.py validates four named NASA path products. The gates include:

  • greatest latitude 0.25 degree;
  • greatest longitude 0.5 degree unless a fixture row names another limit;
  • central path width 2 km;
  • central duration 5 seconds;
  • magnitude 0.005; and
  • central-axis separation 0.001 degree.

Those tests do not claim dense ingress-to-egress track parity where NASA does not publish a matching numerical product.

6.3 Solar partial-visibility footprints

tests/integration/test_eclipse_footprint_nasa_reference.py validates two NASA/GSFC total-eclipse penumbral products, including the one-limit/two-limit topology, contact order, sparse boundary anchors, and WGS 84 surface invariants. The external-comparison ceilings are 5 seconds for anchor time and 40 km for surface position. They cover a named DE200/LE200-to-DE441/LE441 comparison and source rounding; they are not NASA uncertainty estimates.

6.4 Lunar contact instants

tests/integration/test_eclipse_lunar_contacts_nasa_reference.py compares the 14 applicable P1/U1/U2/U3/U4/P4 instants in four modern NASA/GSFC detailed figures on a common TT basis. Ordinary native and NASA-compatibility gates are 120 seconds and 10 seconds. A magnitude-0.0014 limiting event has separate 240-second and 30-second gates and an independent duration check.

These are named mean-limb/shadow-model comparisons. They do not validate site-specific observed lunar-limb contacts.

7. Occultation validation

Moira keeps three occultation evidence tracks separate.

7.1 Local event corroboration

tests/integration/test_occultations_external_reference.py compares local Venus and Regulus lunar-occultation midtimes with cached Swiss t.exp rows at the fixture's sites and altitudes, using a 180-second gate. This is cross-engine corroboration, not primary authority validation.

7.2 Modern/future nominal path geometry

tests/integration/test_eclipse_occultation_where_reference.py exercises named live IOTA graze/limit slices for El Nath, Spica north and south, epsilon Ari, Alcyone, Merope, Asellus Borealis, and Regulus. The admitted graze-boundary latitude gate is 0.18 degree. Site altitude is used when the source declares it.

The polar-safe topology has a separate primary-authority case: the 2026-10-05 lunar occultation of Mars at the geographic North Pole. tests/fixtures/jpl_horizons_polar_occultation_reference.json preserves airless JPL Horizons rows with two 0.5-second contact brackets. Moira's DE441 contacts must fall no more than 2 seconds outside each bracket.

That fixture validates pole containment and the two pole-boundary contacts. It does not externally validate the complete left/right tracks or total path width; those are covered by spherical zero-clearance, continuity, ordering, and great-circle invariants. The frozen Horizons Earth-orientation prediction must be refreshed after the 2026-10-05 event when measured EOP data are available.

7.3 Topographic lunar contacts

The topographic contact product is a distinct observed/profile-conditioned surface. Its named two-site Spica slice combines IOTA reductions with official USGS LOLA assets and finite-resolution lunar-limb reconstruction. That evidence characterizes the admitted sites and profile resolution; it is not a universal topographic-contact accuracy statement. Release-specific details remain in wiki/03_validation/RELEASE_VALIDATION_5_1_TO_5_2.md.

Ancient occultation reconstruction is a separate historical-reduction program and is not validated by the modern IOTA or polar-path corpus.

8. Rise, set, transit, and visibility

8.1 Rise, set, upper transit, and lower transit

tests/fixtures/horizons_rise_set_reference.json contains four frozen JPL Horizons cases:

  • the Sun in New York at the March equinox;
  • the Moon in New York;
  • Venus in Sydney; and
  • the Sun in Tromso at midsummer, including explicit no-rise/no-set behavior.

The source tables were sampled at one-minute cadence and crossings were interpolated. Every expected event is the first matching event in the next 24 hours from jd_start. tests/integration/test_horizons_rise_set_reference.py enforces 2 seconds for the four cases. Published USNO tables provide supplemental fixed-star checks; cached Swiss rows remain secondary corroboration.

The 2-second result belongs to these bodies, sites, dates, altitude thresholds, and window semantics. It is not a universal rise/set bound.

8.2 Historical Sothic evidence

The Sirius/Sothic slice uses Censorinus's 139 CE record and declared latitude-order expectations. It is a bounded historical corroboration under an explicit visibility doctrine and calendar uncertainty, not an exact observed timestamp oracle.

8.3 Yallop lunar-crescent criterion

tests/integration/test_visibility_validation.py uses the 295 rows extracted from Yallop 1997 Table 4. The admitted audit reports:

  • 293/295 rows within ±0.03 in q;
  • 295/295 within ±0.05;
  • 289/295 exact class matches; and
  • all six class mismatches are boundary-sensitive adjacent-class cases.

Non-boundary rows use a ±0.035 q gate with exact class agreement; boundary-sensitive rows use ±0.03 without a false exact-class promise. Criterion agreement does not guarantee a human observation under arbitrary weather, terrain, optical aid, or observer conditions.

8.4 Opt-in physical point-source visibility

The current authority for the opt-in clear_sky_naked_eye_point_source_v1 model is Physical Heliacal-Visibility Validation and Admission. The model combines primary equation checks, independent libRadtran holdouts, a bounded Tousey-Koomen comparison, property/invariant tests, external event goldens, native/Python differential evidence, and offline artifact checks.

Its Phase 7 release matrix has 16 cells: 12 independently reconstructed event times and four explicit no-event/domain regressions. All 12 timed cells pass a fixed 60-second external-grid limit; the largest recorded engine/oracle difference is 5.8789461851119995 seconds.

That is numerical event-geometry evidence inside the exact clear-sky, point-source, target-profile, observer-protocol, and data-pack domain. It is not second-level human-visibility truth. Clouds, live weather, optical aids, extended objects, generic stellar inference, global site transfer, and observer-population probability remain excluded.

9. Limits and non-claims

This paper deliberately does not claim:

  1. one universal Moira accuracy figure;
  2. that passing cases prove all supported bodies, epochs, observers, or kernels;
  3. that DE441 residuals transfer unchanged to DE430 or DE440;
  4. that cross-model residuals are uncertainty estimates;
  5. that the apparent Horizons suite is same-model frame parity;
  6. that the geometric vector suite independently validates TT-to-TDB;
  7. that the topocentric RA/Dec suite validates azimuth and altitude;
  8. minute- or second-level observational visibility truth outside each named model and corpus;
  9. dense eclipse or occultation track parity where no matching external numerical product exists;
  10. universal topographic lunar-contact accuracy from two sites;
  11. precise ancient event timing beyond the admitted Delta-T/model envelope;
  12. that regression snapshots, benchmarks, native/Python agreement, or a clean artifact install are independent scientific authorities; or
  13. that an engine result has been published, deployed, or adopted merely because its local validation passed.

The absence of one of these broad claims is not a hidden failure. It is the boundary that keeps a narrower result scientifically meaningful.

10. Reproducing the admitted checks

Use the repository's project environment and disable downloads. On Windows:

$env:MOIRA_NO_DOWNLOAD = "1"
$env:MOIRA_TEST_MODE = "1"
$env:MOIRA_STRICT_KNOWN_ISSUES = "1"

Small offline examples:

.\.venv\Scripts\python.exe -m pytest tests\integration\test_erfa_validation.py -q
.\.venv\Scripts\python.exe -m pytest tests\integration\test_horizons_rise_set_reference.py -q
.\.venv\Scripts\python.exe -m pytest tests\integration\test_eclipse_nasa_reference.py -q
.\.venv\Scripts\python.exe -m pytest tests\integration\test_occultation_polar_topology_horizons_reference.py -q
.\.venv\Scripts\python.exe -m pytest tests\integration\test_lunar_orientation_authority.py -q

Live Horizons validation must be isolated to explicitly selected external tests:

.\.venv\Scripts\python.exe -m pytest `
  tests\integration\test_horizons_planet_apparent.py `
  tests\integration\test_horizons_planet_vectors_wide.py `
  -m external_network --run-external-network -q

The live suite depends on the current Horizons service and should record its date, target identities, query semantics, and result envelope. A later run can legitimately differ if the authority data, EOP inputs, or service behavior changes.

Documentation and publication guards:

.\.venv\Scripts\python.exe scripts\check_doc_consistency.py
.\.venv\Scripts\python.exe scripts\build_website_docs_bundle.py --check
.\.venv\Scripts\python.exe scripts\sync_git_wiki.py --check

These documentation checks verify consistency and generated mirrors. They do not rerun the scientific oracles.

11. Authorities and evidence records

Primary or product-relevant authorities used by the named suites include:

Repository evidence records with more detail include:

  • wiki/03_validation/RELEASE_VALIDATION_5_1_TO_5_2.md;
  • wiki/03_validation/PHYSICAL_HELIACAL_VISIBILITY_VALIDATION_2026-08-05.md;
  • wiki/03_validation/PHYSICAL_HELIACAL_VISIBILITY_CAPABILITY_MATRIX.generated.md;
  • wiki/03_validation/PHYSICAL_HELIACAL_VISIBILITY_API_INVENTORY.generated.md;
  • tests/fixtures/eclipse_nasa_reference.json;
  • tests/fixtures/eclipse_nasa_lunar_1901_2000.json;
  • tests/fixtures/nasa_solar_besselian_reference.json;
  • tests/fixtures/nasa_solar_penumbral_footprint_reference.json;
  • tests/fixtures/nasa_lunar_contact_instants_reference.json;
  • tests/fixtures/jpl_horizons_polar_occultation_reference.json;
  • tests/fixtures/lunar_orientation_horizons_calibration.json;
  • tests/fixtures/lunar_orientation_horizons_holdout.json;
  • tests/fixtures/lunar_orientation_svs_2026_holdout.json;
  • tests/fixtures/horizons_rise_set_reference.json; and
  • tests/fixtures/physical_visibility_phase7_evidence_registry.json.

12. Current status

This revision replaces the former mixed bug ledger with a current, product-owned validation account. Historical defects are retained only where they change how a published number must be interpreted—most importantly, the retired planetary target/time mismatches. Open work belongs in the roadmap or a dedicated dated evidence record, not in the current-results table.

The overall report remains partial because its component products have different evidence maturity and because no finite corpus can prove every supported astronomical condition. That status is a truthful boundary, not a failure of the validated slices above.