{"id": "c303", "title": "Overlap with the retained8395 and17K correspondences", "filename": "490d_C303_Cross_Bridge_8395_17K_Intersection_20260924.md", "role": "Research action", "step": 303, "sha256": "7574a85edf0812b7a25f42956fadd0ba630dd1d9baa15cf57a3675587070c09e", "bytes": 2816, "origins": ["C01–C479/packets/C303/490d_C303_Cross_Bridge_8395_17K_Intersection_20260924.md"], "download": "/sources/7574a85edf0812b7a25f42956fadd0ba630dd1d9baa15cf57a3675587070c09e.md", "format": "md", "derived": false, "tags": ["Regular", "Cumulative", "Mirror / 529"], "excerpt": "C303 — Overlap with the retained8395 and17K correspondences\n\n24 September 2026. Continuation after C302. K=529; finite retained domains only.\n\n Result\n\nOf the six numerical cumulative-Flood/regular-MT-Flood comparisons admitted by C298, four also meet the retained8395 relation to regular SP Flood, and two meet17K to re", "content": "# C303 — Overlap with the retained8395 and17K correspondences\n\n24 September 2026. Continuation after C302. K=529; finite retained domains only.\n\n## Result\n\nOf the six numerical cumulative-Flood/regular-MT-Flood comparisons admitted by C298, **four also meet the retained8395 relation to regular SP Flood, and two meet17K to regular SP Noah**. The two17K cases are cumulative LXX_OFF Flood indices2 and3. They also belong to the complete four-node family of C287.\n\nThe fixed cross-bridge condition is C−B=2832, where C is the cumulative BC base and B is the regular MT Flood BC base. The additional source conditions use reflected SP endpoints: C+P=8395 for Flood and C+N=8993=17K for Noah. These are separate endpoint bindings, not alternative names for the MT endpoint.\n\n| Cumulative C | MT Flood B | SP Flood required by8395 | SP Noah required by17K |\n|---:|---:|---|---|\n| 5287 | 2455, Gear1 close | 3108, Gear2 start | 3706, Gear1 primary |\n| 5288 | 2456, Gear1 start | 3107, Gear2 close | 3705, Gear1 companion |\n| 5289 | 2457, Gear2 close | 3106, Gear1 start | 3704 absent |\n| 5290 | 2458, Gear2 start | 3105, Gear1 close | 3703 absent |\n| 5291 | 2459, Gear3 close | 3104 absent | 3702 absent |\n| 5292 | 2460, Gear3 start | 3103 absent | 3701 absent |\n\nAll SP records in this table retain Cainan OFF, Terah0 and full430. Cumulative MT_ON/LXX_OFF aliases at5289 and5290 are preserved as labels in the evidence; the six rows here count coordinates once.\n\n## What the overlap establishes\n\nAt5287 and5288, the SP Noah endpoint is598 years above the SP Flood endpoint selected by8395. This follows both from the source register and from8993−8395=598. These SP Flood endpoints belong to Gear2, while the selected SP Noah endpoints belong to Gear1. The earlier cross-index character of598 therefore remains visible.\n\nThe MT Flood endpoint selected by the cross-bridge comparison is a third endpoint. Moving it into its same-Gear SP frame by+650 does not select the SP Flood endpoint in the8395 column. Sharing the cumulative endpoint alone does not make all these routes one biography.\n\nThis narrows the useful provenance question: is either of the two17K overlaps already represented by an established source path, and if so with which interior nodes?\n\n## Evidence and next decision\n\nEight mathematical/domain checks and eight input authentication checks passed; two readouts are byte identical. Inputs are the C298 comparison ledger, C286 regular register and C287 four-node family. No graph edit, new Gear or historical identity is inferred.\n\nC304 will inspect the retained original Report09 interfaces and C127 graph selectively for the5287/3706 and5288/3705 comparisons. The aim is to distinguish an established path from a valid endpoint comparison whose interior route is not stored. Author review only.\n"}