# 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.