# C225 — Admission boundary for the local expansion maps

23 September 2026 · Step 20 of 60, continuing C205.

C216–C225 establish a finite source domain for the two local maps. The three endpoint stages are sourced; the first right-endpoint midpoint is sourced; its image is generated; and the next endpoint iterate is nonannual. Affine equalities survive outside this domain without extending it.

The translated rectangle, midpoint carrier and seasonal check all reach the same limit through different questions. They do not supply additional historical witnesses. The next block compares these local maps with C04’s already documented cumulative 17-fold expansion, using interval centers to expose the different fixed anchors.

## 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/`.