# C314 — Source and interpretation review

24 September 2026. Separate source/method review of the proposed five-case reversal after C313. This review does not perform a new endpoint census or a future numbered step.

## Source basis

C313 fixes the five SP Shem-life cases j=3,…,7 in the regular Cainan OFF / Terah0 / full430 state after the documented +155 normalization. File_18 §1.1, lines541–551, supplies the regular variant fork. File_18 §3.2.1, lines1573–1594, supplies the SP primary/companion station rows, their locality, matched Noah/Shem500 and Shem-life600, and qualified endpoint comparison permission. The rows are source-controlled derived stations, not six independently attested source states. The regular +155 normalization must not propagate to cumulative chronology.

File_09 §0.5, lines279–283, keeps cumulative and regular node classes distinct unless a conversion and dependency are stated. Its working-state register at lines101–111 and Appendix A retain the January AD1 global Mirror axis and distinguish paired components from single-date states. Its same-side reciprocity classification at line141 is a useful precedent for naming local geometry without promoting it to the global Mirror operator.

## What the candidate reversal means

The C313 formulas are q_j=−5290+j, n(q)=q+8993, s(q)=−q−2077, and d(q)=s(q)−600. The forced cross-index condition i+j=10 gives:

R(q)=−10570−q, with R(R(q))=q.

Calling this a **local affine involution on the specified signed cumulative coordinate field** is mathematically legitimate. Its center is the coordinate q=−5285, the j5 station. It maps the five selected centers into themselves, reversing their order. The phase-resolved version R(q+ε)=R(q)−ε explicitly reverses the two cumulative ancestry components. Consequently the candidate comparison is n(R(q+ε))=s(q+ε)+500, and the corresponding death comparison is n(R(q+ε))=d(q+ε)+1100. These are forced algebraic relations; endpoint and source-label admission must still be checked by the C314 finite verifier.

The operation preserves absolute coordinate differences and phase-pair width, and is involutive. It reverses signed differences and temporal ordering. Only the center j5 is a fixed center; its individual quarter-year components are exchanged, not fixed. When properly admitted, the mapped Noah endpoint and the original Shem endpoint share source Gear and rail. That does **not** mean R preserves the Gear label of Noah_j as it sends it to Noah_i. It is a correspondence between two differently typed endpoint families.

The five-center field is closed under this map. The original eight-center j0…7 field is not: the proposed formula sends that whole field to indices3…10. No endpoint extension, extra cumulative year, new source role, or global Mirror axis follows. The scalar−5285 is an algebraically derived local center, not a newly authorized historical or calendrical anchor. Nor does the relation settle C311's missing source prescription for C310's MT→SP selector.

## C287 boundary distinctions

The frozen C287 data have complete four-node rows only at i2,3,4,5. On the present j3…7 subset, original same-index four-node support is therefore j3,4,5. Under i=10−j, the mapped Noah-side row has four-node support at j5,6,7 (i5,4,3). At j3/4 the direct Noah endpoints i7/6 remain source-admitted but do not complete the inherited C287 four-node configuration; its needed cumulative ON Shem index is outside the frozen field. If a stronger claim requires **both** original-j and mapped-i full C287 configurations, only the central j5 meets it. These three domains must have distinct labels and counts.

This is not a defect in the direct500-year source biography or the finite reversal. It limits extension of that correspondence to the entire previously retained all-K structure.

## Suggested subsequent bounded question

After C314, ask whether the phase-resolved finite correspondence commutes with the already active25/23 expansion when the operator's declared fixed anchors and endpoint roles are retained. Test the existing five pairs only and keep scaled genealogy spans separate from literal source ages. This would connect the reversal to the Key-of-23 mechanism rather than merely repeating its index symmetry. No calculation of that future question is performed here.

Review conclusion: the local-involution wording is sound with these domain, phase, typing and global-axis qualifications. Arithmetic verification and source admissibility remain distinct from a source-prescribed selector or a claim of historical design.