{"id": "c681", "title": "C681 — Complete the conserved-center2940 corridor", "filename": "C681.md", "role": "Research action", "step": 681, "sha256": "82a32ce4c5ab653f0a169af3378718c03ee0a322fbfec0d5dbc2f7ec27d99bf4", "bytes": 1376, "origins": ["C480–C1634/Research_Cycles/C0632_C0731/journal.json#C681"], "download": "/sources/82a32ce4c5ab653f0a169af3378718c03ee0a322fbfec0d5dbc2f7ec27d99bf4.md", "format": "md", "derived": true, "tags": [], "excerpt": "What invariant joins all three source-selected outer endpoint pairs?", "content": "# C681 — Complete the conserved-center2940 corridor\n\n## Question\n\nWhat invariant joins all three source-selected outer endpoint pairs?\n\n## Inputs\n\n```json\n{\n  \"pairs\": [\n    [\n      4326,\n      1416\n    ],\n    [\n      4336,\n      1406\n    ],\n    [\n      4341,\n      1401\n    ]\n  ],\n  \"final_outward_displacement\": 5,\n  \"source_local_components\": [\n    2,\n    3\n  ]\n}\n```\n\n## Sources\n\n```json\n[\n  \"Supplement A §5.1\"\n]\n```\n\n## Opened utc\n\n2026-09-28T01:12:24.068500+00:00\n\n## Results\n\n```json\n{\n  \"endpoint_sums\": [\n    5742,\n    5742,\n    5742\n  ],\n  \"centers\": [\n    2871,\n    2871,\n    2871\n  ],\n  \"widths\": [\n    2910,\n    2930,\n    2940\n  ],\n  \"width_increments\": [\n    20,\n    10\n  ]\n}\n```\n\n## Finding\n\nOpposed endpoint changes preserve U+L=5742 while widening2910→2930→2940. The final five-year displacement is the source’s local2+3 construction; it supplies generated extremities4341/1401, not new canonical Creation/Conquest anchors or upstream Gear permission.\n\n## Reassessment\n\nExpress translation and symmetric opening in center/width coordinates.\n\n## Checks\n\n```json\n{\n  \"conservation\": true,\n  \"widths\": true,\n  \"increments\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T01:12:24.068917+00:00\n\n## Record provenance\n\nExact record hash: `d32d88df01582cdc941379c82608f496ef61a931430306f6dc332bed2584b4d9`\n\nSource journal: `Research_Cycles/C0632_C0731/journal.json`", "journalDownload": "/sources/f0643e934c6a7443706351fa40040684d915ed0ae25c0f9188a4c4dba12814ff.json"}