Task 264: EP03 Distance Inconsistency Resolution

Status: DONE

Priority: HIGH

Problem

EP03 analysis used Saturn-Uranus minimum distance (9.62 AU, phase angle ≈ 0°) for brachistochrone calculation, but the previous epoch (2241-12-09) placed the planets at 135.5° phase angle (distance 26.82 AU). This was a data integrity issue flagged in Task 263.

Resolution

Added findOptimalEpoch() to timeline-analysis.ts which searches for the epoch where Saturn-Uranus conjunction aligns with the EP03 departure in the timeline chain.

Optimal epoch found: 2214-10-27 (EP01 departure)

The timeline chain (Mars-Jupiter opposition → +72h → +3d stay → +87d transit → +2d stay) naturally lands EP03 departure at 2215-01-30, when Saturn-Uranus are near conjunction:

Phase angle: -11.1° (near conjunction)
Saturn-Uranus distance: 9.36 AU (consistent with EP03's 9.62 AU assumption)
Mars-Jupiter distance at EP01: 3.54 AU

Changes

timeline-analysis.ts: Added findOptimalEpoch() function with TDD tests
cross-episode-analysis.ts: Uses optimal epoch instead of hardcoded 2240
orbital-3d-analysis.ts: Uses optimal epoch timeline dates
update-diagram-angles.ts: Uses optimal epoch for angle computation
Episode reports (ep01-05.md): Updated epochAnnotation dates and orbital diagram angles
cross-episode.md: Updated timeline dates, Saturn-Uranus distance (26.82→9.36 AU), removed inconsistency note, updated 3D Z-height table
3d_orbital_analysis.json: Regenerated with new epoch
Tests: Updated timeline-constraints, episode-summary-consistency, update-diagram-angles tests

Verification

2033 TS unit tests pass
377 Rust tests pass
TypeScript type check passes
Build succeeds