# C313 source and method review

24 September 2026. Separate source review of the bounded C313 question; no new endpoint census, no C314 execution, and no independent historical corroboration.

## Direct source warrant

File_18 §§1.1 and 3.2.1 support the proposed normalization and biography test. Exact locations in `project_sources/40-File_18.Chronological_Data_Tables-20260919-141048-.md`:

- Lines 541–551: the common variant fork and the named difference `215−60=155`.
- Lines 1573–1579: SP primary/companion locality, source-status qualification, and the G1–G3 Noah/Shem tables. These are source-controlled derived stations, not six independently attested source states.
- Line 1581: add215 for equalized dates; matched Noah/Shem births preserve500; matched Shem birth/death endpoints preserve600. The mixed companion/primary alternative is499 and must not be silently substituted for500.
- Lines 1589–1594: named Gear/rail bindings and qualified endpoint-comparison permission. They preserve endpoint roles and do not create an unrestricted selector.
- Line 1637: SP+60 is state-valid where opened, while SP cumulative Terah remains145. The regular normalization must not propagate to cumulative nodes.

For a C312 SP Shem pair `(b,d)` in OFF/Terah+60/minimum215, its already admitted OFF/Terah0/full430 equivalent is `(b+155,d+155)`. The source-matched Noah birth is `b+155+500`, with the same Gear and rail. This is a declared change of regular source settings, not a fitted anchor. Both birth and death must move together, preserving600.

C312 report lines11–23 define the source settings and local rail action. Lines43–54 identify five admitted cumulative targets (j3…7); the sixth regular case is outside that cumulative target field and remains excluded. Line68 fixes C313 to those five cases.

## Direct biography versus common cumulative ancestry

The arithmetic consequences below are method diagnostics, not a claim that a source prescribes a new selection rule.

The five normalized Shem births satisfy `s_j=3213−j`. The retained direct17K formula is `n_i=3703+i`, from `q_i=−5290+i` and `n=q+8993` (C307 report lines13–19). Therefore source500 binding requires `i+j=10`. Reusing the same cumulative index instead gives `n_j−s_j=490+2j`, which equals500 only atj5. Exact biography matches after pairing different indices do not show that the original same-index paths preserve the binding.

A further domain distinction matters: C286's stronger two-leg all-K census retained SP Noah3705–3708. C307's formal direct17K endpoint expression reaches3703–3710. File_18 authenticates the SP birth stations3705–3710, but3703/3704 are unavailable. A direct17K success at3709/3710 must not be described as a success of the stronger all-K chain; that upstream conjunction has separate source limits. The C307 `all_source_bindings` flag also tests several Flood roles beyond Noah and cannot be reused as a Noah-only admission test.

## Component and orientation guard

C307 report line37 expressly distinguishes center equality, unordered pair equality, and ancestry-preserving component correspondence. Its direct17K path sends `q+ε` to `n+ε`; the reflected bridge path has negative slope and carries `−ε`. Regular normalization by+155 does not change that slope.

Consequently a common cumulative source can give a center gap500 while corresponding components give `500+2ε`:499.5 and500.5 for ε=±1/4. This does not invalidate the source500 biography: like physical Noah/Shem components are exactly500 apart when compared directly. It limits the stronger claim that the two inherited paths preserve the same component ancestry. Reversing component labels can give set coincidence, but that reversal must be disclosed rather than counted as a translation preserving the original source label.

A finite index pairing `i=10−j` and any associated phase reversal should be reported as an inferred correspondence within the existing field, not a new global Mirror, universal operator, or source-prescribed annual selector. No source examined here resolves C311's selector question merely by licensing500,600, or the variant fork.

## Review conclusion

The bounded C313 test has direct source support and is distinct from the earlier600-year Noah/Flood test. Keep separate counts for source-matched regular biographies, same-index17K matches, inferred cross-index matches, and phase-preserving path matches. Record failures and retain all state, Gear, rail, event-role, and finite-domain labels. High is sufficient.