C306 — Admitted selector alternatives and exact phases
24 September 2026. Existing Gear1 source choices only; fixed whole-pair interface equations.
Result
Neither 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.
This closes the local compatibility question raised by C305. It does not remove any source endpoint or invalidate the separately qualified600-year intervals.
Finite selector audit
For 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
r17 = C+N−8993
r2832 = C−B−2832.
| C | Admitted600-year pair N→P | r17 | r2832 |
|---|---|---|---|
| 5288 | 3705 companion→3105 close | 0 | +1 |
| 5288 | 3706 primary→3106 start | +1 | 0 |
| 5287 | 3705 companion→3105 close | −1 | 0 |
| 5287 | 3706 primary→3106 start | 0 | −1 |
All 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.
Exact seasonal components
The 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
{598.5, 599, 599.5, 600.5, 601, 601.5}.
None 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.
The 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.
Evidence and next decision
Nineteen 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.
C307 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.