# C233 — Integral expanded square vertices do not preserve ordinary Creation

23 September 2026 · Step 28 of 60, continuing C205.

The exact C204 square has vertices p−12K, p−10K, p+5K and p+7K. Its first two macro images are integral because K becomes 575 and 625. Ordinary Creation and ordinary MT Flood additionally contain the −190 profile term, whose scaled images are fractional.

Integral square vertices therefore do not imply an integral expanded ordinary Creation/Flood configuration. The alternate-MT vertex remains a generated image under this map; its integrality does not preserve the profile relation as a held 190-year source shift. This supplies a direct source-domain explanation of the anchor obstruction.

## Evidence and scope

K=529 and r=25/23. BC base B means (B+1)t/Bn BC; reflected AD base A means AD At/(A+1)n. Their civil span is B+A in both seasonal components, with no year zero. Signed paired centers are −B and +A; the center model uses components ±1/4 and restores this separation after dilation. An interval center is geometry, not an event or a proposed universal Mirror axis.

Regular Gears are restricted to Noah/Shem/Flood. Creation and Conquest retain fixed source-field members; no fourth Gear is admitted. Generated coordinates, source-field membership and stored graph incidence are distinct. File_18/File_09 and the frozen C127 graph are unchanged. Earlier N01/N03 qualifications, the missing Shem join, closed primers and unestablished original Reports 11–25 remain unchanged. This packet selectively uses prior evidence; it does not rerun completed campaigns. Assertions and alternative placements are not independent historical witness counts.

**12 step-specific checks and 19 frozen-input checks passed.** Exact inputs, results and predecessor hashes are in the accompanying JSON records; calculation code is in the evidence archive. Source dependencies are identified in the body and frozen in `sources/`.