C256 — The double-11 selector chooses same-Gear rather than next-Gear Flood
23 September 2026 · Step 51 of 60, continuing C205.
The new double-11 selection is F′=5K−190+s−2 for s=2,…,7. It chooses the same Noah/Flood Gear and aligned primary/start or companion/close state. The original exact 13-fold selector is F=F′+2 and requires the next Flood Gear.
| s | SP Noah Gear | Rail | New 6875 endpoint | Original 6877 endpoint | Original endpoint status |
|---|---|---|---|---|---|
| 2 | 1 | companion | 2455 | 2457 | sourced |
| 3 | 1 | primary | 2456 | 2458 | sourced |
| 4 | 2 | companion | 2457 | 2459 | sourced |
| 5 | 2 | primary | 2458 | 2460 | sourced |
| 6 | 3 | companion | 2459 | 2461 | absent |
| 7 | 3 | primary | 2460 | 2462 | absent |
This explains the six-versus-four source count without adding any Gear. The original next-Gear rule is inherited from C10. The present contribution is the connection of the same-Gear selection to the twice-expanded 11-fold family.
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.
17 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/.