moira

Moira Validation Report - Astronomy

Version: 1.3 Date: 2026-07-19 Runtime target: Python 3.14 Validation kernel: JPL DE441 (engine is kernel-agnostic; see note below) Validation philosophy: external-reference first, regression-enforced second

Kernel note. All numerical results in this document were obtained with JPL DE441 installed. Moira is kernel-agnostic: it accepts de430, de440, or de441, and the validation numbers below would be expected to reproduce within the same tolerance envelopes on de440 or de430 for epochs within their coverage window (1550 BCE – 2650 CE). DE441 was used here because it covers the full historical epoch range exercised by the test corpora.

1. Executive Statement

This document covers the pure-physics layer of Moira: IAU-standard celestial mechanics, JPL ephemeris geometry, time-scale handling, and observational phenomena that have no astrological convention component.

The validation standard here is strict: every result must be compared against an authoritative external oracle (ERFA, JPL Horizons, NASA catalogs, published historical tables) and the comparison must be enforced continuously in pytest.

Moira’s astronomy layer is materially more precise than Swiss Ephemeris in several respects:

2. Validation Surface

Domain Oracle Enforcement Status
GMST, ERA, obliquity, nutation, GAST ERFA / SOFA pytest Validated
Precession matrix, P x N matrix ERFA pmat06, pnm06a pytest Validated
Apparent geocentric planetary positions JPL Horizons pytest Validated
Wide-range vector geometry (DE441 corpus) JPL Horizons pytest Validated
Topocentric sky positions JPL Horizons pytest Validated
Heliocentric orbital elements JPL Horizons ELEMENTS pytest Validated
Heliocentric distance extrema JPL Horizons VECTORS pytest Validated
Eclipse classification and search Swiss t.exp + NASA Five Millennium pytest Validated
Solar eclipse greatest and polar central-path geography NASA/GSFC 2015 WGS 84 path pytest Validated (named implemented slice)
Solar partial-visibility footprint contacts, boundary anchors, and topology NASA/GSFC 2003/2006 total-eclipse penumbral Table 2 products + geometric invariants pytest Validated (named implemented slice)
Lunar eclipse individual contact instants NASA/GSFC 2023/2024/2025/2027 detailed figures pytest Validated (named implemented slice)
Local lunar occultations Swiss setest/t.exp pytest Validated
Occultation path geometry (where) Swiss t.exp + live IOTA graze/limit text paths (El Nath, Spica N/S, epsilon Ari, Alcyone, Merope, Asellus Borealis, Regulus) pytest Validated (implemented slice)
Polar-crossing lunar-occultation path topology JPL Horizons North-Pole contacts + independent spherical invariants pytest Validated (named contact/invariant slice)
Topographic lunar-graze contact chronology IOTA 2024 Spica reductions at two observing sites + official USGS LOLA RDR assets Frozen fixtures + network source/STAC identity checks + DE441/LE441 solve Externally characterized and regression-admitted (named two-site slice; no authority-supplied model tolerance)
Sothic heliacal rising Censorinus 139 AD historical record + latitude trend pytest Validated
Generalized heliacal / visibility surfaces Published modern planetary apparition windows; Censorinus 139 AD Sirius slice (delegated stellar corpus); Yallop 1997 lunar class law pytest Validated (implemented slice)
Rise / set / transit times JPL Horizons offline fixture; USNO published tables (supplemental) pytest Validated
Delta T model divergence envelope IERS measured table Documented Documented

Occultation Validation Tracks

Moira treats modern/future path validation and ancient-event reconstruction as two distinct programs. The observed/topographic contact surface described below is a third, product-specific evidence track rather than an extension of either path program:

The active pytest occultation path suite belongs to the first track only. Ancient occultations are intentionally deferred to a separate historical reduction program and should not be represented as if they were validated by the modern/future path corpus.

Current modern/future occultation path envelope:

The first-class polar-safe topology is a distinct nominal product inside the modern/future program. It admits only a spherical mean lunar limb and one connected two-sided band. Its left and right identities are intrinsic to increasing-UT1 centerline motion, not aliases for geographic north and south; they remain continuous when latitude ordering reverses across a pole. Finite planetary targets use JPL Solar System Dynamics equatorial solid-body radii, fixed stars remain point sources, and Saturn’s rings are excluded. The Sun is excluded because the cited JPL planetary table does not govern its radius and solar occultation belongs to the eclipse product. The topocentric observer geometry is WGS 84 geodetic, while reported half-widths and total width are explicitly great-circle distances on the 6378.137 km sphere.

The range-search admission policy is 0 < step_days <= 0.25, at most 400 days, and no more than 4096 coarse cells. Boundary cells are candidates even when their endpoints are outside, preventing a positive event peak near a requested range boundary from being skipped. Pole contacts use a separate fixed internal lattice rather than the presentation sample count. The summary duration is solved at the fixed greatest site; the global footprint interval only governs the track’s temporal extent. A constrained optimum at, or within max(4e-8 d, 8 binary64 ULP) of, a global request boundary is not emitted as an unconstrained greatest event. Raw maxima are grouped by overlapping open positive-clearance support, not by an enlarged epoch tolerance; tangent-only contact therefore remains separate. Because connected support does not imply a unimodal time profile, component greatest uses a private at-most-30-minute lattice, refinement of every resolved local maximum plus edge cells and raw witnesses, and a 128-cell fail-closed budget. A synthetic two-hump case proves that a stronger greatest outside the request suppresses a smaller interior hump, while an in-range case selects the stronger hump. The greatest tangent uses history-independent witnesses refined from the same center anchor. Synthetic coverage limits the width difference between two equivalent greatest witnesses 0.160973 s apart to 0.02 km. The parallax-envelope invariant separately covers observers outside and inside a body’s geocentric radius: asin(R/d) for R < d, and a conservative 180 degree bound when R >= d.

The 0.25 d ceiling gives about 109 coarse samples across JPL’s descriptive 27.322-day mean lunar period. That mean-elements table explicitly is not an ephemeris source; Moira uses it only to make the bounded operational cadence legible, while DE441 governs the actual event geometry. The cadence is not claimed as a proof for arbitrary ephemerides or unbounded intervals.

The bounded primary-authority case is the 2026-10-05 lunar occultation of Mars at the geographic North Pole:

Horizons reported DE441 for the Moon and Earth, mar099 for Mars, and the predictive eop.260717.p261013 Earth-orientation file when the fixture was retrieved on 2026-07-18. The fixture is frozen evidence, not a claim that those predicted EOP values are final, and its refresh policy requires a post-event replacement when measured data become available. The 0.5 s bracket and 2 s comparison gate are respectively source resolution and a cross-model regression envelope, not uncertainty estimates or exact-model parity.

This Horizons slice validates pole containment and the two pole-contact instants only. The complete left/right tracks, zero-clearance boundary points, branch continuity, and scalar width are enforced by independent spherical invariants: center and boundary epochs share one ordered lattice, boundary clearance is numerically zero, each half-width reproduces its center-to-limit great-circle distance, and the two greatest half-widths reproduce the public total width. No external dense polar limit-track or width parity is claimed. The live IOTA ordinary-graze path and limit-line corpus remains separate because those prediction products do not govern this nominal mean-limb topology or an observed contact chronology.

Topographic Lunar-Contact Validation Boundary

The direct-import moira.lunar_occultation_contacts module owns a separate engine-only product: an immutable, strictly ordered sequence of disappearance, reappearance, and admitted limiting-tangency contacts at one terrestrial site. Its signed clearance is evaluated against an already prepared, finite-resolution lunar-limb profile. Half-open-bin maxima are represented at bin centres and reconstructed linearly; the product makes no exact sub-bin topography claim. It does not mutate or replace LunarOccultation, the nominal mean-limb path topology, or the existing graze limit products. It is not exposed through the Moira facade or FastAPI.

The Moira-derived LOLA RDR profile path separates translation from orientation. The caller’s content-identified DE441/LE441 reader owns the physical Moon-to-observer reception light cone. Observer-motion aberration is excluded from that surface-intersection ray. The NAIF moon_pa_de440_200625.bpc and moon_de440_250416.tf resources own only the retarded-emission-epoch rotation into MOON_ME_DE440_ME421. Official USGS Astrogeology LOLA point-cloud assets from the lunar_orbiter_laser_altimeter STAC collection supply IAU 2015 Moon-centred Cartesian radii relative to the 1737.4 km sphere. The immutable profile records content hashes and byte lengths for those resources as well as the distinct translation and orientation models. Its finite-distance tangent circle and perspective-equivalent profile radii retain the actual observer-centre/observer-surface angular separation. Missing coverage, excessive interpolation gaps, ambiguous reader identity, and unavailable no-download resources fail explicitly.

The stellar target is a frozen, named sovereign-registry vessel: its ICRS barycentric direction is proper-motion propagated to an explicit TT epoch inside the event window. A positive catalog parallax is converted to finite distance and translated by the complete reception-epoch observer SSB vector, so annual and diurnal parallax share one origin. A contact-private Klioner equation-70 light-deflection path binds DE441 Sun, Jupiter, and Saturn position/velocity states, closest-passage backtracking, declared SOFA Ldn limiters, and the exact finite-star deflector-to-source direction before bending the incoming stellar ray. The Moon light cone remains the retarded geometric location of the blocking surface, not the apparent direction of lunar image photons; curvature over the final Earth-Moon segment is not modeled. Observer-motion aberration and atmospheric refraction are excluded from contact admission: they may change apparent coordinates or observing circumstances, but they do not change whether the incoming stellar photon ray intersects the lunar surface. The contact search stays in UT1 and converts a result to UTC once for civil representation.

tests/fixtures/iota_spica_2024_observed_contacts.json is primary-authority evidence for the observed 2024-11-27 Spica chronology at the Dunham1 and Dunham2 sites. It preserves the published disappearance/reappearance order, GPS-referenced UTC realization, site and height provenance, source timing-error semantics, and identities of the IOTA reduction PDF and event page. The network-marked check verifies that those authority documents still match their frozen lengths and SHA-256 digests. These are observed IOTA events, not Moira predictions; the source timing errors are not model tolerances.

The separate model fixture tests/fixtures/iota_spica_2024_moira_lola_model.json admits a named predicted-versus-observed slice. Its model uses content-identified DE441/LE441, the sovereign Spica ICRS record with catalog parallax, a maximum 15 s profile cadence, 0.002 degree half-open PA bins with no missing-bin interpolation, and sixteen official USGS LOLA RDR COPC assets admitted by exact URL, byte length, and SHA-256. The network-marked executable test refreshes the official STAC mapping before the pinned COPC bytes are decoded.

All ten Dunham1 contacts and all eight Dunham2 contacts have a unique optimum under the declared chronological same-kind matcher. Their mean absolute timing residuals are 0.137143 s and 0.156497 s; their maxima are 0.381008 s and 0.337355 s. Both pass the Moira-owned 0.5 s cross-model regression and topology envelope. That bound is neither source uncertainty nor an absolute accuracy tolerance. Dunham1 has no model-only contacts. Dunham2 retains and requires a leading model-only disappearance/reappearance pair about 1.529 ms wide because it exceeds the declared 1 ms scan feature guarantee.

GRAZPREP is not used as a hidden runtime or treated as an equivalent oracle. IOTA/ES documents that it consumes a derived, precomputed LUNLIMB profile set recalculated from LRO/LOLA source data, but the current reconstruction and interpolation doctrine are not public. A future product-to-product comparison would require exact-site GRAZPREP contact tables and identified LUNLIMB inputs. The admitted IOTA timing comparison therefore does not establish GRAZPREP/LUNLIMB equivalence.

3. Core Celestial Mechanics (ERFA Suite)

Oracle: ERFA / SOFA (IAU standard routines)
Threshold: 0.001 arcsecond (1 milliarcsecond)
Epoch corpus: 12 canonical epochs, 500 BCE to 2100 CE
Test file: tests/integration/test_erfa_validation.py - 106 passed

The BCE anchors are proleptic-Gregorian 1 January in astronomical year numbering: 500 BCE is year -499, JD 1538803.5; 200 BCE is year -199, JD 1648376.5. The test independently derives both JDs through ERFA cal2jd and Moira julian_day, then enforces the Moira calendar round trip. This identity guard was added on 2026-07-14 after the previous numeric literals were found to identify positive-CE dates rather than their labels.

3.1 Greenwich Mean Sidereal Time

Model: IAU 2006 ERA-based (Capitaine et al. 2003)
ERFA ref: erfa.gmst06

Max error: 0.000089 arcsec Mean: 0.000019 arcsec ALL PASS

3.2 Earth Rotation Angle

Model: IAU 2000 linear model (IERS Conventions 2010 §5.4.2) ERFA ref: erfa.era00 Moira surface: julian.earth_rotation_angle()

Max error: 0.000089 arcsec Mean: 0.000019 arcsec ALL PASS

3.3 Mean Obliquity

Model: IAU 2006 P03 full 6-term polynomial ERFA ref: erfa.obl06

Max error: 1.28 × 10⁻¹¹ arcsec (floating-point floor) ALL PASS

3.4 Nutation in Longitude (Delta psi)

Model: IAU 2000A, 1358 luni-solar + 1056 planetary terms (2414 total), IAU 2006 corrections ERFA ref: erfa.nut06a

Max error: 0.000526 arcsec Mean: 0.000108 arcsec ALL PASS

3.5 Nutation in Obliquity (Delta epsilon)

Model: IAU 2000A (same series as 3.4) ERFA ref: erfa.nut06a

Max error: 0.000149 arcsec Mean: 0.000029 arcsec ALL PASS

3.6 True Obliquity

Model: mean obliquity (3.3) + Δε (3.5) ERFA ref: erfa.obl06 + erfa.nut06a

Max error: 0.000149 arcsec ALL PASS

3.7 Greenwich Apparent Sidereal Time — Approximation Cross-Check

Model: Equation of equinoxes, IAU 1982 form: GAST = GMST + Δψ·cos(ε_true). Both sides of the comparison use the same approximation, so this validates the internal consistency of GMST, nutation, and obliquity — not the full GAST model. ERFA ref: erfa.gmst06 + erfa.nut06a + erfa.obl06 (not erfa.gst06a) Test: test_gast_approximation_matches_erfa

Max error: 0.000392 arcsec Mean: 0.000090 arcsec ALL PASS (12 epochs)

3.7.1 Full GAST — Oracle Comparison Against erfa.gst06a

Oracle: erfa.gst06a — IAU 2000/2006 full GAST including equation-of-origins path Moira surface: apparent_sidereal_time_at() — equation-of-equinoxes path with complementary terms Test: test_full_gast_matches_erfa_gst06a

Modern epoch agreement (J1500–J2100, 8 epochs):

Epoch Residual
J1500.0 0.000492”
J1800.0 0.000091”
J2000.0 0.000256”
J2100.0 0.000352”
Max error J1500–J2100: < 0.001 arcsec ALL PASS

Ancient epoch behaviour (documented, not enforced):

For pre-J1000 epochs the residual grows: 0.009” at J1000, 0.528” at 200 BCE, 1.111” at 1 CE. This is a model-basis difference, not an algorithm defect:

These two formulations are numerically equivalent near J2000 but diverge for epochs far from it, because the complementary-terms series was not designed for accuracy across millennia.

Use-case assessment — not a practical concern for Moira:

GAST is consumed in Moira for local sidereal time (house cusps), topocentric parallax hour-angle, and rise/set timing — none of which are sensitive to sub-arcsecond GAST errors:

More importantly, at ancient epochs the dominant uncertainty is Delta T, which reaches tens of arcseconds for pre-medieval dates. A 1.1” GAST model-basis difference at 1 CE is entirely within that noise floor. Implementing the equation-of-origins path would not meaningfully improve any astrological product Moira produces for historical charts.

3.8 Precession Matrix

Model: Fukushima-Williams four-angle parameterization (IAU 2006) ERFA ref: erfa.pmat06 Moira surface: precession_matrix()

Max error: 0.000532 arcsec Mean: 0.000163 arcsec ALL PASS

3.9 Combined Precession-Nutation Matrix

Model: P×N = nutation_matrix_equatorial × precession_matrix_equatorial ERFA ref: erfa.pnm06a Moira surface: mat_mul(nutation_matrix_equatorial(), precession_matrix_equatorial())

Max error: 0.000938 arcsec Mean: 0.000195 arcsec ALL PASS

4. Planetary Positions (JPL Horizons Suite)

4.1 Apparent Geocentric Positions

Oracle: JPL Horizons
Bodies: 10 major bodies
Epochs: 12 measured-era epochs, 1900-01-01 to 2025-09-01
Thresholds: angular separation <= 0.75”, distance error <= 1750 km
Test file: tests/integration/test_horizons_planet_apparent.py - 120 passed

Recorded envelope:

These figures do not reflect a planetary kernel accuracy limit. The kernel itself is accurate to well under 1 milliarcsecond for the major planets in the measured era. The dominant contributor to the residual is Delta T convention disagreement between Moira and JPL Horizons. Moira uses the Stephenson-Morrison-Hohenkerk (2016) historical rotation model; Horizons uses its own internal Delta T. Even a 1-second difference in Delta T propagates to roughly 0.5” on fast-moving bodies such as the Moon or Mercury at historical epochs. The worst-case 0.577850” is consistent with this mechanism and is not evidence of a defect in the geometry or the reduction pipeline. If both systems were forced to use identical Delta T, the residual would collapse to well under 0.01”.

4.2 Wide-Range Vector Geometry (DE441 corpus)

Oracle: JPL Horizons
Bodies: 10 major bodies
Epochs: 8 wider-span epochs, 1800-06-24 to 2150-01-01
Thresholds: angular vector error <= 1.0”, vector difference <= 15000 km
Test file: tests/integration/test_horizons_planet_vectors_wide.py - 80 passed

Recorded envelope:

The wider epoch span (1800-2150) introduces Delta-T model-basis sensitivity in addition to geometric and reduction residuals. Before 1900, historical rotation uncertainty is significant; after 2026, Moira uses the explicit scenario in section 6 (83.294360 s at 2100 under the current boundary aggregate). A Horizons comparison is interpretable only when the fixture records the comparator’s actual time-scale and Delta-T settings; this document no longer assumes that Horizons simply freezes Delta T. The recorded 0.762685” envelope is regression evidence for the named fixture, not a term-by-term attribution of its residual.

4.3 Topocentric Sky Positions

Oracle: JPL Horizons
Test file: tests/integration/test_horizons_sky.py - 18/18 passed

4.4 Heliocentric Orbital Elements

Oracle: JPL Horizons EPHEM_TYPE=ELEMENTS
Bodies: Mercury through Pluto
Epochs: 3 validation epochs spanning J2000.0 through 2025-09-01
Thresholds: semi-major axis <= 1e-5 AU, eccentricity <= 1e-5, inclination/node <= 0.001 deg, argument of perihelion and mean anomaly <= 0.05 deg, perihelion/aphelion distances <= 1e-5 AU
Test file: tests/integration/test_horizons_orbits.py - 27 passed (9 bodies × 3 epochs)

All cases pass against live HORIZONS osculating elements. Outer-planet validation uses the corresponding HORIZONS barycenter commands (5 through 9) because the DE-series routing for those long-period systems is barycenter-based.

Worst-case residual per field (27 tests: 9 bodies × 3 epochs):

Field Worst residual Body Epoch
semi-major axis 3.11 × 10⁻⁶ AU Earth J2000
eccentricity 3.05 × 10⁻⁶ Earth J2000
inclination 3.10 × 10⁻⁸ deg Mars 2025-09-01
longitude of ascending node 1.07 × 10⁻⁵ deg Earth J2000
argument of perihelion 2.07 × 10⁻² deg Venus 2000-12-31
mean anomaly 2.07 × 10⁻² deg Venus 2000-12-31
perihelion distance 4.54 × 10⁻⁶ AU Earth 2025-09-01
aphelion distance 6.22 × 10⁻⁶ AU Earth J2000

All residuals are well within their respective thresholds.

4.5 Heliocentric Distance Extrema

Oracle: JPL Horizons EPHEM_TYPE=VECTORS Thresholds: event date <= 1.0 day, event distance <= 3e-4 AU Test file: tests/integration/test_horizons_orbits.py - 8 passed (3 inner + 5 outer planets)

All validated planets are now treated under one oracle standard:

This is the summit-grade oracle for this subsystem because it compares Moira against the external heliocentric distance curve itself rather than against a single epoch’s osculating event prediction.

Current observed residual envelope (8 planets: Venus through Pluto):

5. SPK Segment Selection

Moira iterates all matching SPK segments and selects the one whose date range covers the requested Julian day, falling back to nearest range only when no exact coverage exists. NAIF body chains are explicitly constructed:

This is validated implicitly by the Horizons suite across historical epochs where naive segment selection would return wrong results.

6. Delta T Model

Moira exposes four explicit Delta-T policies:

Policy model Function Use
'hybrid' (default) delta_t() in julian.py Source-priority table cascade and admitted future scenario
'physical' delta_t_hybrid() in delta_t_physical.py Bounded source-priority/scenario surface with uncertainty and accounting vessels
'nasa_canon' delta_t_nasa_canon() in julian.py Eclipse-publication compatibility
'fixed' caller-supplied constant Controlled sensitivity testing

The DeltaTPolicy object is accepted by ut_to_tt(), tt_to_ut(), and planet_at(), making the Delta T model an explicit, inspectable parameter rather than a hidden default.

6.1 Mean and domain architecture

Era Source
Before -2000 under the physical policy Explicit ValueError; no first-row clamp
-2000 until modern aggregates take priority Published HPIERS total through julian.delta_t()
Overlapping modern aggregates through representative epoch 2026.123287671233 Higher-priority julian.delta_t() monthly-source aggregate totals
After representative epoch 2026.123287671233 Boundary value + boundary slope + 28 s/cy² declared curvature scenario
After 2150 Computable scenario extrapolation, not an authority-validated forecast

The public core, cryo, fluid, and residual fields are compatibility fields and are zero. Their historical C04, GRACE, AAM, and OAM artifacts are quarantined because they do not establish independent causal contributions.

6.2 Evidence actually exercised

The Delta-T corpus separates:

Tests against Moira’s own julian.delta_t() are regression or routing parity, not an independent IERS oracle. Python/native agreement is also not external validation. No deterministic test validates the actual future rotation of Earth.

Relevant suites are:

6.3 Uncertainty posture

delta_t_hybrid_uncertainty(year) uses published HPIERS error values while HPIERS owns the admitted mean, then a 0.06 s modern policy floor through the final aggregate representative epoch (currently 2026.123287671233). For future years it adds, arithmetically rather than in quadrature, the floor, declared tidal-coefficient scale, GIA scale, and an integrated O-U LOD term with theta = 0.1/year and diffusion scale 0.2379 ms/day/sqrt(year). The small-horizon O-U expression uses its series limit to avoid cancellation. This is an explicitly uncalibrated policy scale: it has no asserted coverage probability, omits unquantified handoff-value and slope uncertainty, and does not combine the quarantined proxies as independent Gaussian causes. Forecast-policy validation is bounded through 2150; later values are mathematical continuation only.

DeltaTDistribution is a normal-approximation computational vessel. Its intervals are policy envelopes, not a claim that ancient or future Earth-rotation errors have measured Gaussian tails.

7. Eclipse Validation

Primary authority: NASA Five Millennium solar and lunar catalogs and named NASA/GSFC Besselian and path products

Secondary cross-engine corroboration: cached Swiss setest/t.exp rows

Test files:

Primary Besselian fixture: tests/fixtures/nasa_solar_besselian_reference.json

Primary polar central-path fixture: tests/fixtures/nasa_solar_polar_path_reference.json

Primary partial-visibility footprint fixture: tests/fixtures/nasa_solar_penumbral_footprint_reference.json

Primary lunar contact-instant fixture: tests/fixtures/nasa_lunar_contact_instants_reference.json

Executable representative TT comparison policy (DE441, current Delta-T policy):

For every search row, the NASA reference TT is the catalog UT1 plus that catalog row’s published Delta-T value. The Moira result TT is the searched event UT1 transformed with Moira’s default Delta-T policy. This preserves each product’s declared Earth-rotation basis while comparing the event search on a common dynamical scale.

Case class Representative products Executable TT envelope
Ancient lunar total (~1801 BCE) and solar hybrid (~1797 BCE) 360 s
Post-2150 lunar penumbral (~2801) and solar total (~2799) 60 s

Raw UT1 residuals may be emitted as diagnostic evidence by the executable test, but they are not accepted timing tolerances because a raw comparison conflates the event-search result with the products’ different Delta-T policies. Exact residuals are computed at runtime and are deliberately not frozen in this document.

tests/integration/test_eclipse_nasa_reference.py therefore enforces two explicit TT gates:

The focused ancient lunar compatibility test applies the same rule to both admitted paths. The native result is converted with Moira’s default Delta-T policy, while the nasa_compat result is converted with an explicit catalog month-midpoint coordinate through ut_to_tt_nasa_canon(). Both are held inside the same 360 s cross-authority regression envelope. The test computes their exact residuals at runtime and does not rank the paths by raw UT1 residual because that ranking would compare unlike time policies.

The separate catalog-maximum tests continue to enforce solar and lunar eclipse classification across the ancient, modern, and future fixture rows. Search timing evidence and classification evidence remain distinct.

Individual lunar phase boundaries have a separately governed primary-authority slice. NASA/GSFC detailed figures for the 2023 penumbral, 2024 partial, 2025 total, and limiting 2027 penumbral eclipses publish all 14 applicable P1, U1, U2, U3, U4, and P4 instants in UT. The dedicated fixture preserves every figure URL and SHA-256 digest, the event’s adopted Delta T, and the printed VSOP87/ELP2000-85 and CdT (Danjon) model lineage. Those figure contacts are not reconstructed from the separately published rounded phase durations.

Each source contact is compared on TT after adding the figure’s own Delta T. Native contact UT1 crosses through the content-identified DE441 ephemeris clock; NASA-compatibility contacts use their stored TT fields.

The original individual-contact evidence exposed omitted apparent reduction as the dominant compatibility defect. The repaired default method is nasa_shadow_axis_apparent_sun_moon: both the Sun and Moon use reception light-time from the same reception-epoch Earth state, followed by annual aberration. Gravitational deflection, topocentric parallax, and atmospheric refraction are excluded. The former geometric and retarded method identifiers remain explicit comparison experiments. At the 2025 figure’s published greatest-eclipse TT, executable intermediate assertions compare the resulting apparent geocentric Sun and Moon right ascensions and declinations with the coordinates printed by NASA/GSFC. This independently verifies the reduction before contact-root agreement is considered.

Ordinary per-instant ceilings are 120 s for native DE441 and 10 s for the NASA-compatibility path. The 0.0014-magnitude 2027 event has separate 240 s native and 30 s compatibility endpoint ceilings and remains robustness-only; its independent P4-P1 duration gate is retained. NASA-compatible greatest eclipse is bounded at 10 s. The modern ten-row catalog comparison separately enforces 10 s greatest timing and 2e-4 Earth-radii signed gamma. These are cross-model regression envelopes, not the source’s one-second print precision, uncertainty estimates, UTC claims, or exact-model parity. The bounded remainder includes DE441/LE441 versus VSOP87/ELP2000-85, constants, and source-algorithm differences. Greatest eclipse is a separate timeline instant rather than a seventh contact.

The instantaneous DE441-native Besselian surface has a separate per-field authority gate. Four named NASA/GSFC solar products—partial, total, hybrid, and annular—are sampled at five TT/TDT epochs each over their published six-hour polynomial intervals. The executable comparison covers x, y, d, circular mu, l1, l2, tan_f1, and tan_f2 under these exact absolute envelopes:

Fields Absolute envelope Unit
x, y, l1, l2 1.0e-4 Earth equatorial radii
d 0.003 degrees
circular mu 0.007 degrees
tan_f1, tan_f2 3.0e-6 dimensionless

NASA’s published rows use VSOP87/ELP2000-82 and their stated k1/k2 lunar-radius convention. Moira retains its independently derived DE441/LE441 Earth-reception shadow geometry and physical mean-limb radii. These are bounded cross-model validation envelopes, not field uncertainties or a claim of exact NASA-model parity.

The 2015-03-20 total eclipse supplies the bounded primary-authority polar path slice. Its official NASA/GSFC path and Besselian pages use one declared DE405, Delta T = 67.6 s, WGS 84, 120-second-cadence, mean-limb product lineage. Moira retains DE441. The executable comparison enforces 1 s for searched greatest time, 3 km for the greatest point, five late-track central-line rows, and both axis/ellipsoid tangencies, 3 km for width at greatest, 3 s for local central duration, 0.005 for magnitude, and 3 km of cone clearance at each available published north/south limit. It does not claim per-row width parity, full-atlas coverage, or one-limit/terminator-closure width support; those one-limit epochs fail explicitly in the ordinary closed-footprint solver.

The separate partial-visibility product sweeps Moira’s exact common-tangent, physical mean-limb penumbral cone from content-identified DE441/LE441 Earth-reception states across zero-elevation WGS 84. It reports P1/P4 and optional P2/P3, named north/south penumbral-envelope and geometric sunrise/sunset boundary components, strictly time-ordered segment identity for folded connected limits, and explicit one_limit_connected or two_limit_two_loop topology in UT1. Its default sample_count is 181, bounded to 9..721, and controls interior density rather than the solved component/segment graph. Every penumbral kind admitted by the topology is the single component component_id=0; any UT1 folds are emitted under contiguous segment_id values with shared refined fold endpoints and exactly two sunrise/sunset incidences. Refraction, observer elevation, lunar-limb topography, magnitude contours, and local apparent circumstances are outside this product.

The primary external slice is the NASA/GSFC Table 2 products for 2003-11-23 (one limit) and 2006-03-29 (two limits). Published contacts and named north/south anchors are compared on a common TT scale under independently pinned 5 s and 40 km ceilings. NASA declares DE200/LE200 and its published k1 convention; Moira retains DE441 and physical mean-limb radii. The ceilings are cross-model regression bounds, not uncertainty estimates. Both NASA rows are total solar eclipses whose penumbral footprints exercise the admitted topologies; they do not externally validate the footprint greatest point of a globally partial event. That partial-event greatest is invariant-backed. NASA does not publish dense numerical track coordinates for these products, so no dense-track or full-atlas parity is claimed. Unit and integration invariants separately enforce contact ordering, closure of each penumbral component through horizon incidences and shared folds, WGS 84 bounds, both topology classes, and partial-event greatest-point admission. DE441 regressions for the 1991 folded limit graph and the 1992 sub-minute polar reversal additionally enforce shared fold endpoints, graph identity at requested output counts 9, 99, 181, 257, and 721, continuous fixed-site maximum admission, and rejection of spatial splices.

7.1 Correction-Layer Validation

Direct correction-layer oracles now exist in addition to the broader apparent position suites.

Stellar aberration:

Light-time correction:

8. Sothic Heliacal Rising

Oracle: Censorinus (De Die Natali, 238 AD) - the 139 AD epoch record;
latitude-ordered site comparison against published Egyptological literature

Test files:

Validated properties:

Status: Validated

8.1 Generalized Heliacal / Visibility

Surface: moira.heliacal.visibility_assessment(...), moira.heliacal.visibility_event(...)

Validation is stratified exactly by doctrine layer:

Astronomical geometry validation

This subsystem does not carry an independent geometry oracle. It inherits the validated astronomical substrate already enforced elsewhere in this document:

So the generalized visibility layer is not being validated as if it owned the celestial mechanics. It is being validated as a doctrinal layer built on top of that already-validated substrate.

Criterion validation

Threshold-family policy checks

Yallop lunar criterion checks

Published Yallop corpus slice

Current criterion-family authority posture:

Event validation

Modern planetary apparition windows

Historical stellar slice

Generalized-surface parity

Tolerance doctrine

Current visibility tolerances are family-specific:

This is deliberate. Moira does not presently claim minute-grade observational visibility truth across all targets and criterion families.

Claim envelope

Current external authority posture:

What Moira can currently claim:

What Moira must not currently claim:

Status: Validated (implemented slice)

9. Rise / Set / Transit Oracle Posture

Rise, set, upper transit, and lower transit now have a real external-oracle path rather than self-consistency-only coverage.

Primary oracle:

Regression found and fixed during this validation session (2026-04-05):

Commit 4173706 (2026-03-25) added atmospheric refraction to sky_position_at (the refraction=True default). This changed rise_set._altitude’s return value from geometric altitude to apparent altitude, while the rise/set bisector’s horizon-altitude threshold (e.g. -0.8333° for the Sun) remained the geometric threshold — which already embeds the standard refraction correction by definition.

Effect: the bisector was finding when apparent altitude = -0.8333°, which corresponds to the body sitting ~0.8° below the standard rise position. Result: Rise was ~300 s too early, Set was ~300 s too late. Transit and Anti-transit were exact (they use a separate hour-angle route, unaffected).

Fix applied (2026-04-05) in moira/rise_set.py: _altitude now calls sky_position_at(..., refraction=False) to get geometric altitude. The horizon-altitude threshold already carries the refraction component. The pressure_mbar / temperature_c parameters in _altitude are retained for API compatibility but are now ignored since refraction=False.

Supplemental published-table checks:

Legacy regression support:

Window semantics are explicit in the oracle suite: every event is interpreted as the first matching event in the next 24 hours from jd_start.

10. Astronomy Validation Status

Domain Current state Recommended oracle Priority
Ancient eclipse timing vs catalogs Explained model-basis difference; regression-covered NASA Five Millennium Medium
Stellar aberration Direct ERFA-backed test added and passing in the validation env ERFA ab function Closed
Rise/set ~300 s systematic error Fixed 2026-04-05. Commit 4173706 added refraction to sky_position_at but rise_set._altitude kept the geometric threshold. Fixed by passing refraction=False. All 5 Horizons/USNO cases now pass at ≤ 2 s. JPL Horizons fixture Closed
Ancient eclipse TT comparison gate Repaired 2026-07-17. NASA catalog TT and Moira TT retain their own declared Delta-T bases. Executable tests enforce a 360 s cross-authority regression envelope without freezing exact residual snapshots in prose. This closes the scale-conflation defect in the test; it is not an ancient timing-accuracy claim. NASA Five Millennium Closed (test semantics only)
Solar partial-visibility footprint Admitted 2026-07-18. First-class DE441 mean-limb WGS 84 footprint with explicit one-limit/two-limit topology; NASA/GSFC 2003/2006 total-eclipse penumbral Table 2 contacts and sparse boundary anchors are bounded at 5 s and 40 km. A globally partial event’s greatest point is invariant-backed, not externally anchored. Dense track parity remains unclaimed because NASA does not publish a numerical dense-track corpus for these products. NASA/GSFC Table 2 + geometric invariants Closed (named product slice)
Lunar individual contact instants Repaired 2026-07-18. All 14 applicable P1/U1/U2/U3/U4/P4 instants in four named modern NASA/GSFC figures are compared on common TT. The former compatibility default omitted the figure product’s apparent reduction; nasa_shadow_axis_apparent_sun_moon now applies reception light-time and annual aberration to both bodies and is independently checked against the 2025 printed apparent RA/Dec. Ordinary ceilings are 120 s native and 10 s compatibility; the magnitude-0.0014 limiting event uses separate 240 s native and 30 s compatibility gates and retains an independent duration gate. NASA/GSFC detailed lunar figures Closed (named product slice)
Polar-crossing lunar-occultation path topology Admitted 2026-07-18. The 2026-10-05 Mars event supplies primary JPL Horizons airless North-Pole containment and two 0.5 s outer-contact brackets; Moira’s DE441 contacts use a separate 2 s cross-model gate. Horizons EOP was predictive at retrieval and must be refreshed after the event. Full left/right tracks and width are independently invariant-backed, not externally published parity. JPL Horizons pole contacts + spherical invariants Closed (named contact/invariant slice)
GAST ancient-epoch model-basis difference Documented 2026-04-05. Full GAST (erfa.gst06a oracle) diverges up to ~1.1″ before ~J1000. Cause: equation-of-equinoxes (Moira) vs equation-of-origins (ERFA). Modern epochs (J1500–J2100) all pass < 0.001″. Ancient divergence is beneath the Delta T noise floor for Moira’s use cases. No code change required. See §3.7.1. ERFA gst06a Closed
Chiron and Pholus vector accuracy Pre-existing open. 6 cases in test_horizons_vectors.py failing at ~7–8 arcsec vs 1.0 arcsec tolerance. Centaur orbits are chaotic; accuracy degrades outside JPL fit windows. Root cause not yet diagnosed — may require looser tolerance or SPK routing investigation for small bodies. JPL Horizons VECTORS Medium
Sothic 139 AD calendar accuracy Fixed 2026-04-05. Two changes applied. (1) moira/stars.py heliacal horizon threshold corrected from geometric 0° to −0.5667° (apparent horizon: standard refraction lifts the horizon by ~34′). With 0.0, Memphis crossed the Egyptian New Year boundary into Thoth 1, breaking the modular drift ordering. With −0.5667°, Memphis stays in Epagomenal, all three sites sit on the same side of the New Year, and the drift ordering is coherent. (2) Test assertions replaced exact-day claims with uncertainty-window checks: arcus_visionis=10° (Schoch’s traditional value) is retained; the Censorinus datum is verified to within 2 days of 1 Thoth (drift ≤ 2.0), consistent with the ~1-day historical uncertainty in site identification and atmospheric conditions. Asserting day == 1 exactly would be chasing uncertainty noise. All 3 previously failing tests now pass. Censorinus / published sites Closed
Sidereal fixture coverage gap Pre-existing open. 4 newly added ayanamsa systems (Babylonian (Britton), Aryabhata 522, True Mula, Galactic Equator (IAU 1958)) have no Swiss swetest reference data in the current fixture. Fix: extend the swetest fixture with oracle data for the new systems. Swiss swetest Low

11. Appendix - Model-Basis Difference

In this document, model-basis difference means that Moira and the comparison catalog are not necessarily answering the exact same mathematical question, even when both are internally consistent. In the eclipse context, contributors can include:

For the modern NASA lunar compatibility product, executable coordinate and contact diagnostics did isolate omitted apparent reduction as the dominant former defect; that defect is now repaired. DE441/LE441 versus VSOP87/ELP2000-85, constants, and source-algorithm differences form the bounded modern remainder. The broader NASA-reference tests do not claim the same term-by-term isolation for ancient products. They compare each product in TT using its declared Delta-T basis and classify the remaining ancient difference only as a bounded cross-authority regression residual.

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