C218 — Expansion intertwines 598 and 650 translations

23 September 2026 · Step 13 of 60, continuing C205.

The exact relation is Pₐ(t+598)=Pₐ(t)+650. The 598 translation before expansion corresponds to a 650 translation afterward. This explains how successive source gains can be compatible with one affine map despite being unequal.

The relation is algebraic for every center t. Its event interpretation is narrower: C01 supplies the particular Flood→MT Noah→SP Noah endpoint chain. Translating another named coordinate by 598 does not by itself supply a new named endpoint. The evidence checks the relation on the retained endpoints and midpoint, while preserving their different source statuses.

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.

7 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/.