# C195 — Expansion, symmetry and source admission are separate requirements

23 September 2026 · Step 40 of 50, continuing C155.

**C186–C195 establish three distinct checks for an expanded Mirror construction:** length arithmetic, anchor-compatible annual coordinates, and source-field membership.

The529 width ladder K→575→625 is exact. Nonzero δ in the present family introduces fractional expanded widths. Atδ=0, whole widths still do not make a4K-centered dilation land on annual source vertices. Centered dilation commutes with the8K complement, but the four exact square vertices fail its anchor congruence.

Two bounded annual contacts were recorded: Isaac death's460→500 complement window and q1403's1341/2891 generated pair. Neither supplies a sourced expanded biography, and neither remains annual after a second centered dilation. The2891 contact also has a native/full-430 frame distinction.

These results preserve the useful affine relations while specifying their chronological limits. The final ten steps return to the unexpanded source intervals, asking what their totals and centers reveal about the original868/190 offsets.

## Evidence and scope

K=529. Positive BC base B denotes (B+1)t/Bn BC; reflected AD base A denotes AD At/(A+1)n. Their same-season civil span is B+A, after the no-year-zero correction. AD source projections are not historical AD occurrences. Generated coordinates and interval midpoints do not acquire event identity from numerical coincidence.

Regular Gears remain confined to Noah/Shem/Flood. Creation and Conquest use fixed source-field members; no fourth Gear is admitted. File_18/File_09 and the C127 graph are unchanged. C133–C155 source corrections remain controlling, with the C10 ancestry of the next-Flood-Gear rule now explicit. No historical campaign is rerun, no quarantined primer is reopened, and no N01/N03 expansion or missing Shem join is repaired. Original Reports 01–10 remain previously verified; interrupted original Reports 11–25 remain unestablished.

Sources: controlling File_18 §§2–3, 6A–6D; File_09 paired Mirror rules; selectively retained C05, C08, C10, C123, C128 and C133–C155 evidence. Specific dependencies are named in the body/certificate. **21 assertions passed**; see `RESULTS.json` and `CERTIFICATE.json`. Assertions, selected field combinations and inherited identities are not independent historical witness counts.