# C224 — Center dilation and seasonal-pair restoration

23 September 2026 · Step 19 of 60, continuing C205.

The declared expansion acts on paired centers and then restores the standard ±1/4 seasonal display. Applying 25/23 directly to each ±1/4 component would instead enlarge their separation from 1/2 to 25/46, shifting them by −1/46 and +1/46 relative to the restored pair.

Those two operations must remain distinct. The source 6877 interval is 6877 in both civil components, and all annual endpoint identifications use the restored-pair convention. A fractional phase artifact cannot supply a missing annual event or remove the two-year difference later encountered between 6875 and 6877.

## 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.

**8 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/`.