{"id": "c306", "title": "Admitted selector alternatives and exact phases", "filename": "490d_C306_Selector_Alternatives_and_Exact_Phases_20260924.md", "role": "Research action", "step": 306, "sha256": "93c03a6941b072db66a30a59609b7a1e793eb010da45ce43d9ffb14493887f8f", "bytes": 2890, "origins": ["C01–C479/packets/C306/490d_C306_Selector_Alternatives_and_Exact_Phases_20260924.md"], "download": "/sources/93c03a6941b072db66a30a59609b7a1e793eb010da45ce43d9ffb14493887f8f.md", "format": "md", "derived": false, "tags": ["Cumulative", "Rounded", "Mirror / 529"], "excerpt": "C306 — Admitted selector alternatives and exact phases\n\n24 September 2026. Existing Gear1 source choices only; fixed whole-pair interface equations.\n\n Result\n\nNeither phase selection within the two jointly bound source pairs nor substitution among the admitted Gear1 selectors produces600 while preserving both fixed int", "content": "# C306 — Admitted selector alternatives and exact phases\n\n24 September 2026. Existing Gear1 source choices only; fixed whole-pair interface equations.\n\n## Result\n\nNeither phase selection within the two jointly bound source pairs nor substitution among the admitted Gear1 selectors produces600 while preserving both fixed interface bindings. **Four admitted center600 alternatives exist, but each changes one fixed equation by one year.**\n\nThis closes the local compatibility question raised by C305. It does not remove any source endpoint or invalidate the separately qualified600-year intervals.\n\n## Finite selector audit\n\nFor each of cumulative C=5288 and5287, the existing SP Gear1 register has Noah companion3705/primary3706 and Flood close3105/start3106. The MT Flood counterpart is P−650 with the same Gear and boundary. These give eight combinations. Define residuals\n\n    r17 = C+N−8993\n    r2832 = C−B−2832.\n\n| C | Admitted600-year pair N→P | r17 | r2832 |\n|---:|---|---:|---:|\n| 5288 | 3705 companion→3105 close | 0 | +1 |\n| 5288 | 3706 primary→3106 start | +1 | 0 |\n| 5287 | 3705 companion→3105 close | −1 | 0 |\n| 5287 | 3706 primary→3106 start | 0 | −1 |\n\nAll four alternatives use real source records. The residuals show exactly what changes; they are not adopted as revised bridges or anchors. The two zero/zero combinations remain companion→start599 and primary→close601.\n\n## Exact seasonal components\n\nThe C271 source register supplies actual reflected components center±1/4. The checker uses these fractions directly, rather than rounded dates. Across the two jointly fixed center pairs, all eight component-to-component comparisons yield widths in\n\n    {598.5, 599, 599.5, 600.5, 601, 601.5}.\n\nNone is600. Across all eight selector combinations there are32 component comparisons; eight yield600, all belonging to the alternative center bindings in the table. Same-component comparisons of the matched selectors retain600; exchanging components changes a width by at most1/2.\n\nThe fixed interfaces are paired statements with retained seasonal ancestry. An arbitrary cross-selection of comparison-anchor seasons would change that statement and is not used to rescue a whole-pair relation. Translation and Mirror also remain distinct: Mirror reverses ancestry even when a paired set has the same image.\n\n## Evidence and next decision\n\nNineteen mathematical/domain checks and eight source authentication checks passed, with byte-identical replay. Inputs are C305, C286 and the exact C271 phase register. Author review only; original controls unchanged.\n\nC307 will reduce these results to a typed affine model, explicitly separating source transport, the fixed cross-bridge equality, context changes and phase behavior. This will make clear which attractive equalities follow from common premises and which impose an additional source restriction.\n"}