# C320 — Held-domain rectangle census: source and method review

24 September 2026. Separate review of C320 only; no later test executed.

## Census scope

The eight cumulative LXX_OFF Shem/Flood annual pairs and the frozen528 regular records define a finite, reviewable comparison domain. Source admission must use the complete context tuple: tradition, Gear, Cainan state, Terah60 setting, full430 setting, and endpoint role. Numerical co-location alone is not a valid pair join. For SP Noah, the primary/companion label determines the biography comparison with Flood start/close; Flood itself has rail=null. Other traditions must use their own recorded Noah/Flood bindings and receive no SP companion operation.

The regular register already includes generated context variants and source-controlled derived stations. A census of those entries is not a census of independent manuscript witnesses or independent historical attestations. Likewise, repeated same17K rectangles with one common annual parameter are one structured family, not numerous independent discoveries.

## The omitted SP boundary

The C271 register explicitly contains SP G1 companion Noah3705 with cumulative Flood index2 and G1 Flood close3105 with cumulative Shem index2. Those endpoints are source-admitted. File_18's matched births provide the associated G1 companion Shem3205 in the same ordinary comparison frame. The prior five-case reversed500 construction, however, needed the Shem comparison indexj=10−i. For i2 this would requirej8, beyond the original retained j0…7 cumulative field and beyond C312's admitted five-target subsetj3…7.

This boundary distinguishes absence from a particular inherited path from absence of the regular source biography. The regular G1 companion500 and600 spans are valid; the proposed reversed cross-bridge ancestor is unavailable. No new annual member may be created to join them. C287's existing i2 full configuration remains separately admitted and must be retained in the completed coverage table.

## LXX coincidences and state typing

C286 explicitly constructs regular LXX Noah/Shem through the declared MT comparison+780 at native CainanON, and allows the held theoreticalOFF removal under its context register. File_18's Flood table supplies nativeON boundaries; their comparisonOFF forms use the regular130 removal, not cumulative460. Wherever LXXOFF coordinates coincide with SP primary coordinates, they remain different source traditions with different native-state provenance. This does not create an LXX companion and does not collapse SP primary states into LXX states.

LXX Noah/Flood labels must be joined by the LXX Gear and start/close source rule, not by borrowing the SP primary/companion label. Report numerical coordinate rectangles separately from tradition-labelled realizations. Retaining aliases is useful provenance; summing them as independent evidence would inflate the result.

## Exhaustiveness and limits

The completed result can claim exhaustive coverage of the frozen eight-pair /528-record domain under the specified same17K rule and join criteria. It cannot claim an exhaustive search of all chronologies, all endpoint roles, alternative constants, or unregistered states. The input sources and context construction remain premises. Exact quarter-year checks should use inherited phase records for SP and the established source/reflection convention for any other admitted tradition, stating where phases are derived rather than directly recorded in C271.

The census is particularly valuable for separating three predicates: direct600 rectangle; stronger C287 all-K configuration; and reversed500 cross-bridge compatibility. None should be substituted for another merely because some rows satisfy all three.

## Best subsequent bounded question

After C320, construct a minimal typed dependency description of the complete admitted family: identify which scalar equalities are independent premises, which follow by subtraction, and which additional **source admission and discrete selection conditions** distinguish the600 rectangle, all-K rectangle, and reversed500 path. Use the completed census as the fixed domain; do not open a new endpoint search or repeat C307's original five-variable rank test unchanged. The purpose would be an honest compact grammar for final synthesis, with the unresolved selector visible. No such subsequent analysis is executed here.