comparative-twelfth-parts-1.0.0 is a deterministic TypeScript calculation over saved tropical longitudes. It does not call the ephemeris again, alter the immutable natal facts, or infer a preferred ancient variant.

Source comparison

Manilius gives an explicit twelvefold multiplication and distribution from the containing sign. The Antiochus/Porphyry excerpts preserve twelfth-part treatment for the Moon, Sun, and Hour-Marker. Rhetorius reports three transmitted approaches: Paulus multiplies by thirteen, Dorotheus by twelve, and Ptolemy distributes successive two-and-a-half-degree divisions. Rhetorius treats the Dorothean and Ptolemaic approaches as sign-equivalent while noting the Paulus result can differ.

Exact algorithm

• Normalize the natal longitude to [0, 360).
• Set signStart to floor(longitude ÷ 30) × 30.
• Set withinSign to longitude − signStart.
• Dorothean longitude = normalize(signStart + 12 × withinSign).
• Paulus longitude = normalize(signStart + 13 × withinSign).
• Derive sign, natal-frame Whole Sign place, and traditional domicile ruler from each result.

Input and output contract

The calculator requires exactly one finite longitude for each of the Sun, Moon, Mercury, Venus, Mars, Jupiter, and Saturn plus a finite natal Ascendant longitude. Duplicate, missing, unknown, or non-finite planet records fail closed. Each output preserves natal longitude, natal sign, natal place, named method, formula, derived longitude, derived sign, derived natal-frame place, sign ruler, and rules version.

Regression fixtures

• At 2°30′ Aries, Dorothean resolves to 0° Taurus and Paulus to 2°30′ Taurus.
• The frozen Dallas Sun resolves to 214.2482671608° under Dorothean and 239.6022894242° under Paulus.
• The Dallas result contains exactly seven rows and fourteen separately named projections.
• Removing or duplicating one traditional planet is rejected.
• The workbench preserves selected-profile links and never substitutes a derived angle, Lot, sect, or chart.

Interpretive exclusion

The historical sources establish calculations and uses, but they do not justify an automated modern synthesis across every natal factor. Stelliums therefore publishes the derived evidence, formula provenance, and source disagreement while leaving judgment to the ordered natal workflow.