# C323 independent scientific synthesis review

Date: 2026-09-24. This review audits the completed C314–C322 DATA records and their scientific dependencies. It does not rerun a new endpoint search, change source states, review ZIP integrity, or execute C324. The portable audit passes29 named checks across the nine completed predecessor steps.

**Verdict:** the batch establishes a stronger, finite correspondence between cumulative LXX comparison fields and complete regular SP/MT Noah–Shem–Flood biographies. It also isolates the remaining source-selection question. The positive source coherence and the unresolved selector must both be retained in the synthesis.

The broadest completed OFF census contains six coordinate rectangles, carrying nine compatible source-pair labels: six SP cases and three LXX primary aliases. Those aliases add source labels without adding coordinates. The native cumulative ON census yields three MT cases, with Cainan ON, Terah+60 and full430. The context was found by searching the frozen register, not imposed before matching. The resulting SP/MT primary correspondences extend through all five checked source roles—Noah birth, Shem birth, Flood start, Noah death, Shem death—by the same−460 displacement. All fifteen endpoint and thirty exact-phase residuals are zero. This is a meaningful extension beyond fitting two rectangle corners.

The complete source biographies preserve spans500,100,350,150. The initial suggestion that same-Gear MT should require502 was corrected by the actual register. Same-Gear harmonic500 remains distinct from the cross-Gear Noah G2→Shem G1 binding502. File_18's two modal bindings must both remain visible. Neither is a correction of the other, and no MT companion or wrong-Gear endpoint was inserted to force the successful correspondence.

The finite coverage sets are:

| Completed comparison | Admitted annual indices i |
|---|---|
| OFF/SP600-year rectangle | 2,3,4,5,6,7 |
| Native ON/MT600-year rectangle | 3,5,7 |
| Reversed SP500 correspondence | 3,4,5,6,7 |
| C287 full form at i | 2,3,4,5 |
| C287 full form at reversed j | 5,6,7 |
| First four conditions together | 3,5 |
| All five conditions together | 5 |

The final intersectioni=j5 is conditional on those five questions. It must not be elevated into a source-prescribed choice or an identification of differently typed events. The excluded SP G1 companion casei2 is still a valid source biography and17K/600 rectangle; only its reversed Shem ancestryj8 is outside the retained field. At the other end, i6/7 support the reversed-Shem comparison but not the C287 full form. Domain failures remain part of the result.

The ancestry work also has a precise limit. C314's500 relation needs`i+j=10` and opposite cumulative phase offsets. The finite index map fixes5, but the full phase map swaps the two components even there; it has no fixed exact component. C315's original same-ancestry8993/8395 paths retain598 rather than600 and miss the selected same-Gear Flood by2. C316 gives a valid alternative8395 route through`h=i−2`, but its source is cumulative Flood, while C271's actual Flood ancestry is cumulative Shem at i. Their equality factors as`598+8395=8993`. It does not repair the same ancestry or merge the two source roles.

The paired458 change has source-qualified ingredients: cumulative`−460+2`, and regular`−650+130+60+2`. Those are distinct operations; cumulative annual movement is not a cumulative Gear, and regular Cainan130 is not cumulative Cainan460. The completed paths exist only at three of the five original cases; the others would need cumulative indices8/9 and regular Gear4, which remain absent.

The strongest control is C319. Equal17K bridges do **not** require the paired22 selection. Choice00 preserves equal17K in all five original source cases, with1060-year sides. Choice22 produces1058=2K sides and the all-K matrix, with three source-admitted cases. The mixed choices fail the equal-bridge condition. Thus all-K selects22 inside the declared four-choice menu, while equal17K alone permits00 and22. A source reason to require22 remains unestablished.

Rank wording should be exact. The two parallel17K equations have rank2. Adding one600-year side raises the rank to3; the other side follows. All six four-node durations still have rank3, with a common-translation freedom. The displayed equivalent equalities, phase repetitions, and matching aliases must not be counted as independent observations. Likewise the side identity`600+(460−2)=1058=2×529` is the already audited paired-shift consequence, not a second independent occurrence discovered by rewriting it.

The strongest retained conclusion is therefore a **source-qualified family of finite correspondences**, with full primary biographies and explicit phase ancestry, rather than a newly prescribed chronology or global action. C311's absence of a located rule selecting C310's MT→SP switch is not overturned by these numerical correspondences. Canonical files, the fixed graph, the Mirror axis and the restriction of regular Gears to Noah/Shem/Flood remain unchanged.

Reproduction: `C323_Independent_Synthesis_Audit.py --sources DIR --out DIR`, with `C314_DATA.json` through `C322_DATA.json`. The output records29 scientific claim checks, consolidated counts, exact domain sets, dependency ranks and the500/502 correction. These29 are verification checks of completed work, not29 new discoveries.

Best next bounded question after the ten-step batch: seek a source-based reason to couple the cumulative+2 annual selection with the regular one-Gear advance, independently of the desire to obtain K-multiples. Restrict that audit to the relevant existing Gear/cumulative source passages and preserve the demonstrated00 control. This is a proposal only; C324 remains unexecuted.