# C317 — Same17K rectangles: source and dependency review

24 September 2026. Separate source/method review. No later numbered test is executed.

## What the inherited records establish

The C271 register explicitly pairs cumulative LXX_OFF Flood_i with regular SP Noah birth and cumulative LXX_OFF Shem_i with regular SP Flood start/close. Its comparison-status field calls these derived T8993 comparisons between admitted endpoint records, without asserting a new stored path. The cumulative entries have regular_Gear=null. The SP endpoints retain their source Gear, Noah primary/companion rail, and Flood event start/close role.

For each selected i3…7, write p_i=−5890+i, q_i=−5290+i, f_i=p_i+8993, and n_i=q_i+8993. The cumulative difference is q_i−p_i=600 and the reflected regular difference is n_i−f_i=600. File_18 §3.2.1 authenticates the Noah/Shem source stations and matched regular biographies; §3.1.4 authenticates the Flood event boundaries. A primary Noah binds here to Flood start and a companion Noah to Flood close. The close is not a Flood companion produced by the SP person operation.

The cumulative Shem coordinate is a cumulative node, not a substituted regular Shem birth or death. File_09 §0.1 and §0.5 guard that distinction. File_18 §6D directly supplies native LXX cumulative Flood, while the inherited derived OFF table and supplemental ReportIII provide the full OFF Shem/Flood provenance. Do not imply that File_18 prints a native OFF Shem row that it does not contain.

The SP station labels are source-controlled derived states, not six independent ancient witnesses. Exact phase checks should bind the C271 cumulative_coordinate and reflected_coordinate entries directly, retaining the intermediate translation/reflection information as provenance. Center equalities alone cannot replace those checks.

## Independent conditions versus repeated consequences

The rectangle has four displayed edge equalities but only three independent linear constraints on its four coordinates. Once q−p=600 and the two parallel translations n−q=f−p=8993 are imposed, n−f=600 is algebraically forced. A zero rectangle closure is therefore a consistency check, not a fourth independent numerical witness. Checking the regular source endpoint, Gear, rail/boundary and phase admission is nevertheless informative: a formally closed rectangle can fail to land on an admitted source station.

The present contribution is recovery and explicit verification of a coherent source-labelled529 comparison already implicit in C271. It does not independently rediscover17K, prove literary design, establish C311's missing context selector, or turn every span into a multiple of529. In particular600 is not an integral K edge.

## Comparison with the stronger C287 object

At the same index the C287 lower pair is S=−6348+i and R=2645+i, each458 below the direct rectangle's p and f. C287 keeps the upper pair q,n, so its same-side separation is1058=600+458=2K. Its cross-widths are consequently15K,17K,19K. These differences must not erase the source change: S is LXX_ON cumulative Shem at indexi+2, whereas R is a regular MT Flood endpoint in Cainan ON / Terah+60 / full430.

The direct SP600 rectangle succeeds across the five held indices; source validity of the stronger C287 lower pair is separately bounded. On this subset C287 remains admitted only i3,4,5. At i6,7 the source field needed for S and the regular endpoint needed for R are outside the inherited support. Success of the direct rectangle cannot license those extensions. Two differently typed objects sharing an upper edge and equal17K diagonal are not interchangeable chronologies.

## Best subsequent bounded question

After C317, a useful next question is whether the458 replacement has an explicit composition of already admitted **typed** changes on both sides. The candidate cumulative route is CainanOFF→ON with the stated+2 annual reindexing; the candidate regular route is SP→MT normalization, regular Cainan insertion, Terah+60, and one permitted Gear move. A future finite test should verify the actual source states, order/dependencies, exact phase action and the i6/7 boundaries. Scalar agreement alone does not show that these roles are interchangeable. This prospective source-action audit is not executed here.