# 490d Mirror checkpoint after C313

24 September 2026. Latest completed: **C313 — SP500-year binding to17K Noah endpoints.** C314 is proposed and unexecuted.

Read the C313 report and this checkpoint first; the frozen C312 checkpoint carries the inherited synthesis and supplemental intake. This packet includes C312 target data, C286/C287/C307 records, C271's exact Noah phase register, File_18/File_09, independent review and portable verification. Retrieve earlier dependencies selectively; do not repeat completed batches or follow archived next-step paragraphs.

## C313 result

Five admitted C312 SP Shem-life targets j3…7 change from OFF/Terah+60/minimum215 to OFF/Terah0/full430 by adding155=215−60 to both BC bases. All five normalized pairs remain source-admitted, with600-year lives and unchanged Gear/rail.

| j | Shem life, BC | Shem Gear/rail | Same-index17K Noah, BC | Noah Gear/rail | Birth gap |
| ---: | --- | --- | ---: | --- | ---: |
| 3 | 3210→2610 | G3 primary | 3706 | G1 primary | 496 |
| 4 | 3209→2609 | G3 companion | 3707 | G2 companion | 498 |
| 5 | 3208→2608 | G2 primary | 3708 | G2 primary | 500 |
| 6 | 3207→2607 | G2 companion | 3709 | G3 companion | 502 |
| 7 | 3206→2606 | G1 primary | 3710 | G3 primary | 504 |

Exactly j5 retains source500 with matching Gear/rail: Noah3708→Shem3208→Shem death2608,500+600=1100. The other four rows are failed comparisons of different source states, not changes to source ages. Each Shem pair still has its own valid source-matched Noah500 earlier.

For q=−5290+j, reflected endpoints satisfy n=q+8993, s=−q−2077 and d=s−600. Hence n−s=490+2j and500 forces j5. All five selected Noah endpoints support a direct17K leg. Only j3/4/5 also belong to the retained C287 complete four-node family; j6/7 would require additional cumulative ON Shem indices8/9 outside the source field.

## Crucial phase distinction

For the same cumulative component q+ε, ε=±1/4, the17K path carries+ε while reflected Shem birth/death carry−ε. The birth gap is490+2j+2ε. At j5 the inherited component gaps are499½/500½, not500. Shem life remains600 for both components.

The direct source biography is still exactly500 between matched physical phases. The unordered reflected Noah and Shem pairs translate by500 at j5. Matching those output phases through the inherited paths reverses cumulative component ancestry. Keep separate: one valid source biography/center match; one unordered pair-set match; zero500 relations preserving the same cumulative component. No phase repair has been adopted.

## Retained C311–C312 limits

C312's regular relation is B_SP=B_MT−5−r, r=0 primary/1 companion. It holds for all six same-Gear comparisons. Under C−B=2832, cumulative j=i−1+r gives four complete MT ON→LXX OFF transports; G1 primary has a valid target but absent MT index8 antecedent, and G1 companion lies outside both cumulative fields. Those boundaries remain.

C310's minimum context cover remains MT at LXX OFF j0/2 plus SP at j3…7, with j1 absent. C311's three-source audit did not locate a rule prescribing the context/event-role switch. Neither C312's translation nor C313's center match establishes that selector.

The main529 framework remains conditional and source-labelled:2K+15K=17K from598+460 and8395−460; C287 retains its finite membership restrictions and free common translation. Fixed-reflection and all-K configurations remain distinct. Earlier599/601 and600-interface failures are not repaired by the present500-year test.

## Standing scope and corrections

Mirror/529 focus; K=529, E=25/23, P=70/69. Global Mirror January AD1; local junction x=1, January AD2; no civil year zero. Regular Gears Noah/Shem/Flood only. SP−1 remains local to SP Noah/Shem. No cumulative/upstream Gear operation, extra endpoint or anchor, primer reopening, canonical/graph edit or global axis/z-law. Capture now; canonize later. Coordinate coincidence does not merge event identities or create independent witnesses.

Supplemental Engine Report III explicitly documents the derived LXX OFF Shem/Flood field. Engine Reports I–IV duplicate inherited archive copies; current File_18 corrections override older LXX182/777 and mixed Cainan headings. Sothic and rounded studies remain background.

Preserve the corrected LXX crossover supplement:5494 BC→AD2970 versus reflected Conquest1406 gives1564→1700;4534 BC→AD3930 versus reflected Exodus1446 gives2484→2700, using W8464 and E25/23. Creation-to-Jared960 versus MT460 gives offsets1380/880 and difference920→1000. AD3746/2300 is superseded. Awareness only.

C-series, original unprefixed Reports01–10, interrupted original Reports11–25, and Engine Reports I–IV remain distinct. The original AD1905–1911 proposal remains unexecuted.

## Verification and best next bounded step

C313 passed44 main assertions and16 input/predecessor checks, with byte-identical replay and separate mathematical/source reviews. The frozen inputs and standing controls remain unchanged; C127 retains208 nodes/382 duration edges.

**C314, proposed only:** test the forced candidate reversed index pairing i+j=10 with explicit opposite cumulative phase ancestry over these same five cases. Verify Gear/rail, complete Shem lives, exact phase correspondence and the boundary of the stronger C287 structure. This is a finite source-labelled correspondence test, not a new global Mirror or prescribed annual selector. High is sufficient. **C314 has not been executed.**