moira

Moira Validation Report - Astronomy

Version: 1.3 Date: 2026-04-05 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.

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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:

• IAU 2006 Fukushima-Williams precession (vs. older Swiss models)
• IAU 2000A nutation with 1358 luni-solar + 1056 planetary terms (2414 total), IAU 2006 corrections
• Direct SPK segment routing with correct NAIF chain selection
• Stephenson-Morrison-Hohenkerk (2016) historical Delta T model
• Separate NASA-canon Delta T path for eclipse-publication compatibility

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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 geography (where)	Swiss t.exp	pytest	Validated (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)
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 now treats occultation validation as two distinct programs:

• modern_future_occultation_path_validation primary authority: IOTA graze/limit path publications secondary authority: Swiss where validation mode: path and graze-boundary geometry parity

• ancient_occultation_validation primary authority: scholarly historical-astronomy record corpora secondary authority: later scholarly reductions and site chronologies validation mode: reconstructed local-event plausibility under explicit uncertainty

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:

• live IOTA graze/limit slices now sit within about 0.002° to 0.17° in graze-boundary latitude on the active corpus
• the enforced IOTA graze-boundary tolerance is <= 0.18°
• where a source file declares a nominal site altitude, that altitude is now used in the graze solve; the present ceiling is still set by profile-aware Spica north-limit geometry rather than by missing elevation

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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 - 104 passed

3.1 Greenwich Mean Sidereal Time

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

Max error: 0.000075 arcsec

Mean: 0.000017 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: 0.000075 arcsec

Mean: 0.000017 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: 0.000369 arcsec

Mean: 0.000084 arcsec

ALL PASS

3.5 Nutation in Obliquity (Delta epsilon)

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

Max error: 0.000168 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: 0.000168 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: 0.000349 arcsec

Mean: 0.000074 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:

• erfa.gst06a uses the equation-of-origins approach: GAST = ERA − equation of origins (derived from the full NPB matrix)
• Moira uses the equation-of-equinoxes approach: GAST = GMST + Δψ·cos(ε) + complementary terms

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:

• 1” of GAST error → 1” of RAMC → imperceptible house cusp displacement
• 1” of GAST error → < 0.001% perturbation to the Moon’s topocentric parallax
• 1” of GAST error → ≈ 0.07 s of time in rise/set computation

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: 0.000452 arcsec

Mean: 0.000142 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: 0.000667 arcsec

Mean: 0.000161 arcsec

ALL PASS

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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:

• Worst angular error: 0.577850” (Uranus, 1900-01-01)
• Worst distance error: 1684.977 km (Pluto, 1900-01-01)

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:

• Worst angular vector error: 0.762685” (Uranus, 1800-06-24)
• Worst absolute vector difference: 10201.934 km (Uranus, 1800-06-24)

The wider epoch span (1800-2150) introduces two additional sources of residual beyond the measured-era suite. First, Delta T uncertainty grows for pre-1900 dates where the historical rotation model diverges from any single polynomial approximation. Second, epochs beyond the current IERS measured window (post ~2026) are subject to the future Delta T divergence described in section 6: Horizons freezes near ~69 s while Moira’s hybrid model projects ~84 s by 2100, which alone can produce artificial disagreements of 3–20” on fast-moving bodies at 2100 depending on body and epoch. The 0.762685” worst case is consistent with these mechanisms and is not evidence of a geometry error.

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:

• HORIZONS vector tables are sampled around the next local heliocentric distance minimum and maximum.
• The external extrema are refined numerically from the sampled brackets.
• Moira’s distance_extremes_at(...) results are then compared directly against those vector-derived perihelion/aphelion events.

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):

• Worst perihelion date residual: 0.000387961511 d (Uranus)
• Worst aphelion date residual: 0.001369935926 d (Neptune)
• Worst perihelion distance residual: 0.000000000001 AU (Mars — floating-point floor)
• Worst aphelion distance residual: 0.000000000001 AU (Mars — floating-point floor)

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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:

• Earth: [0,3] + [3,399]
• Mercury: [0,1] + [1,199]
• Venus: [0,2] + [2,299]
• Moon: EMB-to-Moon branch with Earth removed

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

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6. Delta T Model

Moira uses three distinct Delta T paths selected via DeltaTPolicy:

Policy model	Function	Use
'hybrid' (default)	delta_t_hybrid() in delta_t_physical.py	General ephemeris work; physics-based
'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.

Test files:

• tests/unit/test_julian_delta_t.py — 10 passed (IERS table, NASA canon, decimal-year ancillaries)
• tests/unit/test_delta_t_policy.py — 15 passed (DeltaTPolicy construction, ut_to_tt/tt_to_ut integration)
• tests/unit/test_delta_t_physical.py — 46 passed, 3 skipped (physical model unit tests; skipped = no-data fallbacks not applicable because data files are present)
• tests/integration/test_delta_t_hybrid.py — 36 passed (IERS comparison, era boundaries, uncertainty model, data-file presence)

Total: 107 passed, 3 skipped across the Delta T test corpus.

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6.1 Hybrid Model Architecture

delta_t_hybrid is a physics-based model that routes by era:

Era	Source
Pre-1840	Stephenson-Morrison-Hohenkerk (2016) table lookup (_smh2016_lookup)
1840–1962.4	Secular trend + historical bridge term + optional historical core angular momentum
1962.4–2026	Secular trend + fluid low-frequency term + modern bridge + core (IERS EOP) + cryosphere (GRACE J2) + residual spline
Post-2026 (future)	Secular trend only

Secular trend model:

• Tidal deceleration: +31.0 s/cy²
• Glacial isostatic adjustment (GIA): −3.0 s/cy²
• Net: +28.0 s/cy²
• Reference anchor: REFERENCE_YEAR = 2026.0, REFERENCE_LOD = 69.114742 s

The historical bridge and modern bridge terms enforce continuity at era boundaries with zero first-derivative constraints at the reference anchor.

Optional data files (both present on this machine, activated in the test run):

• grace_lod_contribution.txt — GRACE/GRACE-FO J2 cryosphere series
• core_angular_momentum.txt — IERS EOP core angular momentum series

When these files are absent the model degrades gracefully to SMH2016 + secular trend only, which the no-data unit tests enforce.

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6.2 Modern Era Validation vs IERS Table

Oracle: IERS 5-year mean Delta T table, 13 epochs 1962.5–2020.5 Threshold (enforced): max error < 2.0 s, RMS < 1.5 s

Live residuals (hybrid model vs IERS 5-yr table):

• Max error: 1.2467 s (at 1962.5 — era boundary, fluid term onset)
• RMS error: 0.6573 s

Residual spline fit quality (internal model self-consistency):

• In-sample RMS: 0.2666 s
• Cross-validation RMS: 0.4265 s (threshold enforced: < 0.5 s)

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6.3 Future Projection

The hybrid model uses secular trend only beyond 2026. This is an extrapolation, not a guarantee. The model also carries a propagated uncertainty estimate:

Year	Projected ΔT	1σ uncertainty
2026	69.10 s	±0.30 s
2050	70.70 s	±0.43 s
2075	75.77 s	±0.46 s
2100	84.34 s	±0.53 s
2150	111.98 s	±0.92 s

Divergence from Horizons beyond the IERS window: Horizons freezes Delta T near ~69 s after the measured window; Moira’s hybrid model projects secular growth reaching ~84 s by 2100. This ~15 s divergence propagates to artificial positional disagreements of approximately 3–20 arcseconds on fast-moving bodies at 2100 — a model-basis difference, not an engine error. (The previous figure of ~203 s by 2100 was from an earlier, superseded approximation model.)

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6.4 Uncertainty Model

delta_t_hybrid_uncertainty(year) returns a 1σ propagated uncertainty in seconds, combining:

• Reference anchor uncertainty
• Secular trend coefficient uncertainty (quadrature)
• Future extrapolation growth

Enforced properties (tests passing):

• σ < 1.0 s at reference year (2026)
• σ < 5.0 s at 2100
• Monotonically non-decreasing from 2026 through 2100

7. Eclipse Validation

Oracle: Swiss setest/t.exp + NASA Five Millennium solar and lunar catalogs
Test files:

• tests/integration/test_eclipse_external_reference.py
• tests/integration/test_eclipse_nasa_reference.py

Current representative accuracy:

Case	Residual	Note
Ancient lunar total (~1801 BCE)	49.65 s	Stable across light-time refactor
Ancient solar hybrid (~1797 BCE)	80.06 s	Shifted from 43.17 s; see below
Future lunar penumbral	20.76 s	Stable
Future solar total	20.75 s	Shifted from 14.68 s; small, within noise

Residual history and root cause (ancient solar hybrid):

The ancient hybrid solar residual changed from 43.17 s (measured 2026-03-24) to 80.06 s (measured 2026-04-05). This shift is entirely in TT space — it is not a Delta T conversion issue.

Root cause: commit 931b87c (2026-03-25) replaced a 2-step Newton light-time approximation in corrections.apply_light_time with a proper iterative convergence loop (tolerance = 1 × 10⁻¹⁴ days ≈ 1 ns). The old code returned a geocentric direction vector computed at t − lt_initial while reporting a separately-refined lt_final, creating a subtle inconsistency. The new code keeps direction and light-time mutually consistent at convergence. This is a physics improvement.

For the ~1797 BCE hybrid eclipse, the corrected light-time shifts the computed TT eclipse minimum by ~37 s. The resulting 80 s residual against the NASA catalog remains squarely within the model-basis explanation: Delta T uncertainty at that epoch is hundreds of seconds, and the NASA and Moira native eclipse models are not answering the exact same geometric question (see §7 model-basis difference note and Appendix §11).

The test threshold in tests/integration/test_eclipse_nasa_reference.py was updated from 60 s to 90 s in the same session (2026-04-05) with full provenance recorded inline.

Ancient timing residuals are primarily a centering/gamma-minimum timing issue, not a shape failure. Eclipse geometry (gamma, magnitudes, contact durations) matches NASA published values closely.

Model-basis difference: Ancient timing differences relative to published catalogs remain visible for some eclipse search cases. For the representative -1801 lunar total case, the current native search remains inside a 60-second envelope and materially outperforms the nasa_compat catalog-facing path, so this is treated as a model-basis difference rather than a generic search failure or geometry defect.[1]

Focused diagnosis of that case now shows:

• native shadow-axis minimum with native Delta T and retarded Moon: about 49.5 s from the NASA reference
• switching only the Moon treatment from retarded to geometric inside the native branch shifts the result by about 35 s
• switching the same native shadow-axis objective from native Delta T to the NASA-canon Delta T branch shifts the result by about 387 s
• once Delta T branch and Moon treatment are aligned, the native shadow-axis objective and the canon gamma-minimum objective agree to within about 0.01 s

So the residual is not a pure “search bug”. It is mainly a model-basis issue for ancient greatest-eclipse timing, with Delta T branch choice as the largest single contributor and Moon treatment as the secondary contributor.

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7.1 Correction-Layer Validation

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

Stellar aberration:

• tests/integration/test_astrometric_corrections_external.py
• Oracle: ERFA ab
• Status: direct vector-level test added; executes when erfa is installed in the active environment

Light-time correction:

• tests/integration/test_astrometric_corrections_external.py
• Oracle: JPL Horizons VECTORS with VEC_CORR='LT'
• Status: validated against direct corrected-state reference cases

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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:

• tests/unit/test_sothic.py
• tests/integration/test_sothic_research.py

Validated properties:

• Egyptian civil calendar arithmetic (month/day/epagomenal boundaries)
• days_from_1_thoth wrapping and cycle arithmetic
• Predicted Sothic epoch year via 1460-year cycle
• Drift rate recovery from wrapped linear trend
• 139 AD Alexandria: Sirius rises within 2 days of 1 Thoth (drift <= 2.0 days); exact day is within the ~1-day historical uncertainty of the Censorinus datum
• 139 AD Memphis: rises in last days of Egyptian year (Epagomenal, drift 362–365 days); exact day not asserted due to same uncertainty envelope
• Latitude ordering: Elephantine < Thebes < Memphis < Alexandria
• Arcus visionis direction: harder visibility -> later rising
• Arctic exclusion: no rising at lat 80 deg
• BCE year handling without Python datetime

Status: Validated

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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:

• topocentric sky positions: JPL Horizons
• refraction-aware altitude handling through the admitted apparent-altitude path
• apparent magnitude surfaces for planets and the baseline integrated lunar model

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

• file: tests/unit/test_heliacal_visibility_policy.py
• enforced properties:
  • Bortle-derived limiting-magnitude mappings are explicit and monotonic
  • explicit limiting_magnitude overrides site-class derivation
  • local horizon altitude blocks geometry independently of brightness policy
  • refraction-on vs refraction-off changes apparent altitude but not doctrine

Yallop lunar criterion checks

• file: tests/unit/test_heliacal_visibility_policy.py
• enforced properties:
  • class thresholds A through F follow the declared q boundaries
  • observability depends on observing aid exactly as admitted in code
  • non-lunar use of YALLOP_LUNAR_CRESCENT is rejected
  • morning-event misuse of the Yallop family is rejected

Published Yallop corpus slice

• files:
  • tests/integration/test_visibility_validation.py
  • tests/fixtures/yallop_table4_reference.json
• authority: Yallop 1997, Table 4
• data-semantics note: column 6 of Table 4 is the Julian Date of the astronomical new moon (JD − 2,400,000), not the observation JD. The observation date is recorded in columns 2–4 (year, month, day). These are distinct quantities and must not be conflated when reconstructing the observation epoch from the fixture.
• current admitted corpus:
  • full published Table 4 extraction: 295 cases
  • both evening and morning criterion rows are represented
  • classes represented: A, B, C, D, E, F
  • split into:
    • non-boundary exact-tolerance rows
    • boundary-sensitive rows for near-threshold q validation
• tolerance doctrine:
  • non-boundary exact family:
    • q agreement within ±0.035
    • exact class agreement
  • boundary-sensitive family:
    • q agreement within ±0.03
    • no false exact-class claim when the published row sits on or very near a threshold
  • current full-corpus audit envelope (verified by direct audit, 2026-04-05):
    • 293 / 295 rows within ±0.03
    • 295 / 295 rows within ±0.05
    • 295 / 295 rows within ±0.10
    • 289 / 295 exact class matches (the 6 mismatches are all boundary-sensitive rows where the adjacent-class divergence is within doctrine)
    • mean residual across all 295 rows: 0.0077
    • max residual across all 295 rows: 0.0315
  • fixture correction applied (2026-04-05): five rows in the fixture had their UTC observation dates stored in place of local observation dates. For US western-hemisphere sites, local evening begins after UTC midnight, so the local date is one calendar day before the UTC date recorded. The affected rows were 165, 193, 244, 245, 285 (longitudes ranging from −70.7° to −121.6°). The dates were corrected by subtracting one calendar day each:
    • row 165: 1980-07-14 → 1980-07-13
    • row 193: 1987-05-29 → 1987-05-28
    • row 244: 1989-07-05 → 1989-07-04
    • row 245: 1989-10-03 → 1989-10-02
    • row 285: 1991-05-16 → 1991-05-15 No engine changes were made. After correction, all five rows compute within ±0.020 of the published q value and are fully absorbed into the standard tolerance family.

Current criterion-family authority posture:

• LIMITING_MAGNITUDE_THRESHOLD is an admitted engine threshold doctrine
• YALLOP_LUNAR_CRESCENT is admitted under Yallop’s published lunar first-sighting classification law
• morning and evening Yallop rows are now admitted as criterion-validation cases, but the current public event-search surface remains evening-scoped for this family

Event validation

Modern planetary apparition windows

• files:
  • tests/unit/test_planet_heliacal.py
  • tests/integration/test_visibility_validation.py
• coverage:
  • Venus heliacal rising 2020
  • Jupiter heliacal rising 2023
  • Venus acronychal rising 2021
  • Venus heliacal setting 2021
• tolerance doctrine:
  • wide date windows in Julian Day, intentionally measured in days rather than minutes
  • this is observational-visibility validation, not a claim of exact published event-time parity

Historical stellar slice

• primary file: tests/integration/test_sothic_research.py
• generalized-surface anchor: tests/integration/test_visibility_validation.py
• authority: Censorinus 139 AD epoch record plus published latitude-order trend across Egyptian sites
• status:
  • the star subsystem itself is externally anchored through the Sirius/Sothic corpus
  • generalized star visibility now has an explicit delegated-anchor test against the default stellar heliacal doctrine, plus a measured doctrinal offset to the 10° Sirius/Sothic slice
  • this is important because the generalized star surface currently delegates the default star-heliacal arcus policy, while the Sothic research slice is intentionally anchored to an explicit 10° Sirius visibility doctrine

Generalized-surface parity

• file: tests/unit/test_heliacal_visibility_policy.py
• enforced properties:
  • generalized planetary search matches the legacy admitted planetary wrappers
  • generalized stellar and cosmic event branches return typed event vessels
  • generalized lunar event search carries structured crescent details

Tolerance doctrine

Current visibility tolerances are family-specific:

• modern planetary event validation: bounded Julian-day windows, typically on the order of weeks
• historical stellar validation: civil-calendar day and latitude-order envelopes, not minute-level claims
• Yallop lunar family: criterion-law validation, a multi-case published Table 4 corpus slice, and structured evening-event semantics

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:

• Yallop 1997 is the admitted authority for the current lunar first-sighting class law and its q partitions.
• U.S. Naval Observatory guidance is the admitted caution authority for the broader problem statement: lunar crescent visibility depends strongly on sky conditions, location, and observer quality, and cannot be predicted with certainty from age alone.
• The modern review literature — in particular Schaefer (1988, QJRAS 29:511–523) and Odeh (2006, Astronomical & Astrophysical Transactions 25(5–6):523–535) — confirms that large observational corpora exist and that contradiction-rate analysis remains the correct language for criterion assessment rather than false absolute-precision claims. Odeh’s 2006 criterion was calibrated against a 737-observation corpus and represents the most prominent published challenger to the Yallop q-law; it is a deferred authority target for Moira’s validation program.

What Moira can currently claim:

• The astronomical substrate used by the generalized visibility layer is backed by stronger external astronomy oracles elsewhere in this document.
• LIMITING_MAGNITUDE_THRESHOLD is implemented as a declared threshold doctrine with validated policy precedence and geometric/brightness separation.
• YALLOP_LUNAR_CRESCENT is implemented as a declared lunar criterion family with validated q thresholds, admitted aid-dependent class semantics, and a published Table 4 corpus split into exact-class and boundary-sensitive validation families.
• The generalized planetary event surface is validated against published modern apparition windows.
• The generalized stellar event surface is validated as a delegated surface over the default star-heliacal doctrine, with its policy offset from the Sirius/Sothic 10° slice measured explicitly.

What Moira must not currently claim:

• minute-level or second-level truth for observational visibility events
• universal first-sighting correctness across all observing environments
• that the current generalized stellar surface reproduces the explicit Sirius Sothic doctrine unless that 10° visibility policy is chosen deliberately
• that the current lunar implementation has been validated against a broad published first-sighting corpus comparable to the larger modern databases
• that the current public lunar event surface is morning-generalized under the Yallop family; morning rows are presently admitted only as criterion validation

Status: Validated (implemented slice)

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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:

• tests/integration/test_horizons_rise_set_reference.py
• Fixture: tests/fixtures/horizons_rise_set_reference.json
• Builder: scripts/build_rise_set_horizons_fixture.py
• Source: JPL Horizons observer tables sampled at 1-minute cadence using topocentric apparent azimuth/elevation plus local apparent hour angle (QUANTITIES=4,42)
• Coverage: Sun, Moon, Venus, multiple latitudes and longitude signs, plus a high-latitude no-rise/no-set Sun case
• Threshold policy: strict per-case timing thresholds in seconds; the current curated corpus is enforced at 2 seconds or better
• All 5 cases passing as of 2026-04-05 (4 Horizons cases + 1 USNO)

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:

• tests/integration/test_rise_set_published_reference.py
• Source: U.S. Naval Observatory published rise/set/transit tables
• Purpose: spot-check fixed-star behavior where Horizons event tables are not the practical source in this repo

Legacy regression support:

• tests/integration/test_rise_set_external_reference.py
• Fixture: tests/fixtures/swe_t.exp
• Status: retained as Swiss cross-check / sanity coverage, not the authority for this validation domain

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.

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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 hybrid solar eclipse threshold	Updated 2026-04-05. Iterative light-time (commit 931b87c) is more correct physics but shifted the TT eclipse minimum by ~37 s. Residual is 80 s (was 43 s). Documented in-test; threshold updated 60 → 90 s.	NASA Five Millennium	Closed
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

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11. Appendix - Model-Basis Difference

[1] 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, the main contributors are:

• Delta T branch choice
• retarded-vs-geometric Moon treatment
• the exact definition of “greatest eclipse” being optimized

When those assumptions are aligned, the native shadow-axis minimum and the canon gamma-minimum objective collapse to essentially the same instant. The remaining catalog offset therefore reflects differing model assumptions, not an unlocated defect in the search machinery.

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