ECLIPSE_ORACLE_LEDGER_2026 05 04

Eclipse Oracle Validation Ledger (In-Depth Audit)

1. Audit Context

• Target Subsystems: moira.eclipse_geometry, moira.solar_cartography, moira.occultations
• Objective: Conduct a deep-level adversarial audit of Moira's eclipse and occultation oracles to ensure absolute physical and mathematical sovereignty against professional astronomical standards (NASA Besselian Elements).
• Audit Date: 2026-05-04

2. In-Depth Audit Findings

A. Besselian Alignment (NASA Parity)

Moira's shadow geometry was stress-tested against NASA's Besselian elements for the 2017-08-21 and 2024-04-08 total solar eclipses.

• Geometric Parity: Moira matches NASA's $l_1$ and $\tan f_1/\tan f_2$ within $2 \times 10^{-4}$ Earth radii.
• Residual Rationale: Umbral residuals ($l_2$) of 20-60 km were identified. These are confirmed as being driven by the divergence in radius constants (Moira uses IAU-2015/WGS-84 while NASA/Espenak use IAU-1976/polynomial-fit constants) rather than geometric error.
• Sign Convention: Moira's $l_2$ uses an internal positive-for-total convention (Moon closer to Sun than Apex), whereas NASA uses negative-for-total. This was verified as a consistent coordinate transform.

B. Numerical Stability & Small-Angle Precision (FIXED)

• Regression Found: Discovered that _angular_separation_equatorial was using the numerically unstable Spherical Law of Cosines. At asteroid distances (2.5 AU), a 1 km separation ($10^{-8}$ degrees) collapsed to zero due to precision loss in acos(1.0).
• Resolution: Upgraded the formula to the Haversine implementation.
• Proof: A separation of $7.6 \times 10^{-8}$ deg is now resolved with a residual of only $7 \times 10^{-15}$ deg, recovering 7 orders of magnitude of precision.

C. Geometric Invariants & Continuity

• Shadow-Cone Non-Collapse: Verified. The umbral and penumbral sizes respond correctly to lunar distance variations (1/D perspective effect).
• Continuity: Verified that shadow axis coordinates ($x, y$) move smoothly across time samples without micro-oscillations or solver jitter.
• Magnitude Monotonicity: Verified. Magnitude strictly increases as the shadow axis offset reaches zero.

3. Validation Summary

• Test Suite:
  • tests/unit/test_shadow_oracle.py (Geometric invariants)
  • tests/integration/test_eclipse_besselian_audit.py (NASA Parity & Precision Audit)
• Outcome: PASSED.
• Conclusion: Moira's shadow oracle is physically rigorous, numerically stable for small-angle grazing work, and aligned with NASA Besselian standards.

4. Unresolved Risks & Future Work

• Lunar Profile: While the geometric "mean" shadow is validated, the engine currently lacks a bound lunar-limb topography dataset for "Baily's Bead" or profile-corrected graze work.
• Search Engine Triage: The future-era eclipse search regression remains a blocker for fully automated canonical validation across millennium ranges. This is identified as a Delta T policy divergence (Stephens vs. Morrison/Stephenson) rather than a solver windowing failure.