Lunar Direction and Sahl Burnt-Path Validation — 2026-07-15

Scope

This record validates the Phase 3 computational boundaries for Western electional issues 2, 3, 4, and 7:

• the source-neutral lunar ecliptic direction and exact node-crossing witness;
• Dorotheus V.6 southern descent;
• Dorotheus V.6 solar disengagement in longitude or latitude;
• Dorotheus V.7 northward latitude motion;
• Sahl section 22d burnt-path policy selection and endpoints.

The astronomical witness is a measurable product. The Dorothean and Sahl clauses are historical-doctrine interpretations of that product. Passing these tests is not empirical validation of astrological claims.

Authorities and source boundary

The Dorotheus authority is Carmen Astrologicum, Umar al-Tabari translation, 2nd edition, Benjamin Dykes translator/editor, V.6.7, V.6.10, note 15, and V.7.1-3, printed pp. 234 and 238. V.6 identifies the ecliptic and names disengagement in longitude or latitude, but supplies neither a before/after crossing interval nor a longitude/latitude combination law.

The secondary transmission witness is Hephaistion of Thebes, Apotelesmatics III.7.10, translated by Benjamin Dykes. It describes the Moon as advancing in latitude toward the north, and the translator's note identifies north/south as ecliptic latitude. It likewise supplies no numerical crossing region. This corroborates direction; it does not authorize a node orb.

The Sahl authority is On Elections section 22d in Benjamin Dykes, Choices & Inceptions, printed p. 100. The text says only the end of Libra and the beginning of Scorpio. The same edition's glossary distinguishes the fall-degree and later Via Combusta conventions, but neither is silently relabeled as Sahl's missing numeric endpoints.

Governing astronomical object

LunarEclipticDirectionWitness is governed by the Moon's apparent geocentric ecliptic latitude of date, beta(t):

1. hemisphere derives from the sign of beta at the query instant;
2. northward/southward motion derives independently from a centered latitude rate;
3. a node crossing is a sign-changing root beta(t) = 0;
4. the sign of the latitude rate at the root determines ascending or descending direction;
5. fixed scanning brackets and deterministic bisection locate the previous and next exact roots;
6. the returned numerical tolerances are root policy, not historical doctrine.

The result exposes UT1 event times, root longitude, residual latitude, latitude rate, hours from query, nearest-root relation, frame, timescale, provenance, and the explicit scope astronomical_witness_only_no_doctrinal_region.

Doctrine decisions

• Dorotheus V.6 southern descent consumes the exact witness but remains NOT_EVALUABLE: no source-owned interval around the descending root exists.
• Dorotheus V.7 northward crossing consumes the same geometry under a separate policy and remains NOT_EVALUABLE for the same missing interval.
• V.6 solar disengagement exposes instantaneous signed conjunction motion and independent latitude evidence. It remains NOT_EVALUABLE because the source does not define whether either branch is sufficient or give either interval.
• Sahl public moment and scan calls require an explicit burnt-path policy. The source-faithful selection performs no interval test. The Dykes glossary/fall degree interpretation is [199, 213) and the later fifteen-degree convention is [195, 225), both in tropical longitude with inclusive start and exclusive end.

Evidence classes

• Invariant testing: synthetic periodic latitude verifies adjacent root order, sign-changing direction, exact-query classification, deterministic bisection, and immutable result semantics.
• Substrate integration: DE441 verifies that returned prior and next events bracket the query and that direct planet_at latitude changes sign across each returned root with sub-nanodegree residual.
• Doctrine regression: Dorotheus witnesses preserve the measured geometry while retaining indeterminate states; Sahl endpoint tests exercise both half-open boundaries exactly.
• Public-contract validation: root exports, facade delegation, REST request requirements, response serialization, registered route, and OpenAPI schemas are tested together.

Known limits

No test establishes a historical duration around a node crossing, a physical visibility threshold for Dorotheus's solar disengagement wording, or a numeric Sahl endpoint absent from section 22d. Those omissions are preserved as source boundaries rather than filled by modern convention.