{"id": "c468", "title": "Alternate-Method Verification of the Finite 529 Findings", "filename": "490d_C468_Alternate_Method_Source_Arithmetic_and_Closure_Verification_20260925.md", "role": "Research action", "step": 468, "sha256": "56304c7686b3ece15219b32a62805318fa01d7f6f73c27f14d400a97f4ef3f56", "bytes": 3726, "origins": ["C01–C479/packets/C468/490d_C468_Alternate_Method_Source_Arithmetic_and_Closure_Verification_20260925.md"], "download": "/sources/56304c7686b3ece15219b32a62805318fa01d7f6f73c27f14d400a97f4ef3f56.md", "format": "md", "derived": false, "tags": ["Regular", "Cumulative", "Calendar Keys", "Mirror / 529"], "excerpt": "490d C468 — Alternate-Method Verification of the Finite 529 Findings\n\n25 September 2026 UTC. Step 24 of 25, C445–C469.\n\nA second implementation passes51 checks and reproduces528 source labels,373 coordinates,330 complete reflection compositions,15 complete two-E paths,60 direct529 pairs,522 mixed reachable pairs with n", "content": "# 490d C468 — Alternate-Method Verification of the Finite 529 Findings\n\n25 September 2026 UTC. Step 24 of 25, C445–C469.\n\nA second implementation passes51 checks and reproduces528 source labels,373 coordinates,330 complete reflection compositions,15 complete two-E paths,60 direct529 pairs,522 mixed reachable pairs with no529 gap, the63-pair shared-word closure with three edges, and all fixed-Mirror image counts. The23 predecessor packets and69 publications pass the sealed integrity audit.\n\nThis implementation reconstructs the528-record grid from normalized source bases and permitted source-state offsets. It derives E arrows by solving h=(25x−23y)/2 over existing endpoint pairs, rather than forwarding inputs through E. Reflection arrows come from endpoint sums.\n\nBitset transitive closure replaces the earlier breadth-first method for single-coordinate reachability. Residue buckets produce the529 inventory. A precomputed relation of6,122 shared-operator pair edges supplies a different fixed-point algorithm for interval closure. Reverse enumeration from cumulative records verifies the Mirror pair and anchor-qualified image counts.\n\nThe results agree exactly with the frozen earlier data. The only source-qualified nonzero529-gap two-E path remains2148→2020→1956 about effective3206. The shared-word pair closure retains the three admitted edges and no others. The source sensitivity checks also reproduce the unique companion dependence and unchanged coordinate support after LXX-OFF label removal.\n\nThe sealed audit verifies648 payloads,276 certificate bindings,349 frozen source entries,23 predecessor links and all23 evidence ZIPs. Every one of the69 prior publications succeeded with its expected filename and content hash.\n\nThis is a different implementation by the same root agent. It is not an independent-agent review or additional historical evidence. The final step will bring the entire authorized batch together and provide a compact, authenticated continuation packet.\n\n## Verification and scope\n\n51 calculation checks and 54 source/predecessor authentication checks passed. Main result files replay byte for byte. These are root-agent checks, not an independent-agent review or independent historical witnesses.\n\nThe alternate method tests the declared register and operator menu. Agreement validates the calculations and source handling, not historical intent or a broader chronology claim.\n\nMirror/529 focus: K=529, E=25/23, P=70/69; J=300/299 remains File02 gap conversion, not a calendar date operator or Residue Protocol. Regular Gears are Noah/Shem/Flood only. SP person companions are local to Noah/Shem; Flood close is an independent event boundary. Both500/100 and502/98 bindings remain valid; SP primary Noah death retains its inclusive/harmonic qualification. LXX native Cainan is ON; OFF is theoretical removal. Global paired Mirror January AD1; local junction January AD2; no civil year zero. No new source point, phase, fitted axis, upstream/cumulative Gear, primer reopening or canonical/graph edit. Capture now; canonize later. Coordinates, source labels, context aliases and derived comparisons remain distinct. Counts are not independent historical witnesses.\n\n## Best next bounded step\n\n**C469, proposed and unexecuted:** Synthesize C445–C469, state the positive interval ladder and finite exclusions with source limits, resolve any label-count ambiguities, and publish the complete checkpoint, reading index and recovery archives. LeaveC470 unexecuted.\n\nThe decisive finite results now agree under different enumeration and closure methods. The remaining authorized step is a synthesis that preserves these distinctions and makes all completed evidence recoverable.\n", "evidenceLinks": [{"id": "d-24203a4c3b282f9b", "title": "File 02"}]}