# C321 — NativeON counterpart of the600 rectangle: source review

24 September 2026. Separate source/method review of C321 only.

## Controlling distinctions

The left-side source field is cumulative LXX native CainanON: Shem p=−6350+i and Flood q=−5750+i, retaining the frozen eight annual members and their phase pairs. Relative to the comparisonOFF field, both signed coordinates move−460. This uses cumulative Cainan's lifespan contribution. It is not the regular130 insertion, and it does not restore an additional Cainan to a field already designated nativeON.

The right-side candidate is the existing regular register under the unchanged8993 translation. The regular contexts must be discovered and reported with their complete labels. A label such as MT CainanON/Terah60/full430 means a restored MT comparison state, not native MT textual Cainan. It is also not the same state as cumulative native LXXON merely because both carry an ON flag.

File_18 §0.1d rule12 and its Cainan boundary explanations distinguish regular130 and cumulative460. §1.1 opens the Terah60 variant. §3.1.4 fixes the same-Gear SP versus MT Flood650 difference and start/close roles. Its restored-MT example at lines826–829 explicitly supports Flood2646/2648/2650 with regular Cainan130 and Terah60. C286's frozen Noah records and File_18's Noah/Shem bindings supply the matched birth counterparts.

## Meaning of the common460 displacement

For a regular SP primary Noah/Flood biography, the candidate SP→MT comparison subtracts650 in positive BC numbers, then adds regular Cainan130 and Terah60. Thus its net reflected-coordinate displacement equals−460, matching the cumulative signed displacement. This is a composition of three separately typed source comparisons. It does not convert the regular Cainan operator into460 or establish a universal state-changing translation.

The same coordinate arithmetic can be evaluated for SP companion records, but those are exactly where source admission is decisive. MT has no imported SP Noah companion. A translated SP companion Flood close can remain an authentic MT Flood close while its translated Noah coordinate lacks the required MT birth record. Admission of one endpoint is not admission of the whole600 rectangle. These partial results must remain visible rather than being repaired by changing Gear, boundary, or ancestry.

LXXOFF regular aliases from C320 retain their own tradition provenance when compared with any MT result. Their coordinate equality with SP primary stations does not provide an extra source companion or independent attestation. The nativeON cumulative field and theoreticalOFF regular LXX field belong to different chronology methods and must not be conflated.

## Verification and interpretation limits

The complete finite census should keep three levels distinct: formal translated coordinates; individually source-admitted endpoints; and same-context source-admitted Noah/Flood pairs. Check exact phase equality and the complete context tuple for the third level. A600 difference follows algebraically from translating the two cumulative nodes equally, but a pair's source-role validity is a separate test.

This step can show a partial correspondence between already admitted whole biographies and identify the missing-companion boundary. It cannot show that every SP biography transports to MT, that both entire source fields are isomorphic, or that the source texts prescribe the8993 selection. It preserves C311's source-selector limitation and C319's conditional nature of the all-K criterion.

## Suggested final bounded diagnostic before synthesis

After C321, use only the completed census to form a single **joint support table**: directOFF600 rectangle, nativeON600 counterpart, C287 all-K rectangle, reversed500 partner, and full support at the reversed partner. State which intersections are source facts and which are consequences of prior selections. This would establish exactly how much of the proposed combined structure is jointly executable and prevent a final synthesis from conflating separately valid pieces. It should introduce no new endpoint or numerical search. No such later table or intersection calculation is performed here.