{"id": "c263", "title": "C263 — A minimal dependency description of the coupled families", "filename": "490d_C263_529_Mirror_Bounded_Step_20260923.md", "role": "Research action", "step": 263, "sha256": "359325ece8e36da092617ecd05a6e1231447e139c730168b1595aba4c3c218d0", "bytes": 1975, "origins": ["C01–C479/reference/490d_C01_C265_Complete_Window_Archive_20260923.zip!/workspace/mirror_C206_C265_529_Expansion_Centers_20260923/C263/490d_C263_529_Mirror_Bounded_Step_20260923.md"], "download": "/sources/359325ece8e36da092617ecd05a6e1231447e139c730168b1595aba4c3c218d0.md", "format": "md", "derived": false, "tags": ["Regular", "Mirror / 529"], "excerpt": "C263 — A minimal dependency description of the coupled families\n\n23 September 2026 · Step 58 of 60, continuing C205.\n\nThe coupled result can be tracked with three scalar relations: 13×625=15K+190; 11×625=13K−2; and 17K=13×625+868. The relations 868+190=2K and 2×625=2K+190+2 follow from these.\n\nThe five displayed linear", "content": "# C263 — A minimal dependency description of the coupled families\n\n23 September 2026 · Step 58 of 60, continuing C205.\n\nThe coupled result can be tracked with three scalar relations: 13×625=15K+190; 11×625=13K−2; and 17K=13×625+868. The relations 868+190=2K and 2×625=2K+190+2 follow from these.\n\nThe five displayed linear relations have rank three in the declared five-variable bookkeeping model. This is an algebraic dependency count, not an empirical probability or historical evidence count. The endpoint selector remains essential: algebra alone does not determine which native Creation member, Flood state or Noah rail supplies a realization. The center ladder and δ=2 partition are consequences of those selected endpoints.\n\n## Evidence and scope\n\nK=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.\n\nRegular 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.\n\n**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/`.\n", "evidenceLinks": [{"id": "d-68301ab760bfbe2e", "title": "File 18"}, {"id": "d-45851004c5864229", "title": "File 09"}]}