C207 — Half-width gains of 299 and 325

23 September 2026 · Step 2 of 60, continuing C205.

Holding Creation fixed halves each right-endpoint gain: 598 becomes 299 and 650 becomes 325. Consequently the interval centers themselves follow Pₐ, and 299×25/23=325. This is an affine midpoint identity, not an additional historical span.

For N02 the centers are −1961/2, −1363/2 and −713/2; N04 translates every center by +2. The center sequence is geometrically useful because it records exactly how the 13-fold interval grows while keeping its source origin fixed. Its dependency is C01’s endpoint ladder, not a second chronology.

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.

6 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/.