{"id": "c963", "title": "C963 — Aggregate cap identification", "filename": "C963.md", "role": "Research action", "step": 963, "sha256": "fc994279654f6630bde2e729130cfdc3ff0f7e1164dfa0aef12d8a61701a0c45", "bytes": 984, "origins": ["C480–C1634/Research_Cycles/C0932_C1131/journal.json#C963"], "download": "/sources/fc994279654f6630bde2e729130cfdc3ff0f7e1164dfa0aef12d8a61701a0c45.md", "format": "md", "derived": true, "tags": ["Regular", "Cumulative"], "excerpt": "Can the complete lifespan sum identify k after support is fixed?", "content": "# C963 — Aggregate cap identification\n\n## Question\n\nCan the complete lifespan sum identify k after support is fixed?\n\n## Inputs\n\n```json\n{\n  \"source_total\": 7137,\n  \"active\": [\n    5,\n    7,\n    8\n  ]\n}\n```\n\n## Sources\n\n```json\n[\n  \"C953\",\n  \"C954\",\n  \"C962\"\n]\n```\n\n## Opened utc\n\n2026-09-28T03:47:49.292737+00:00\n\n## Results\n\n```json\n{\n  \"sum_equation\": \"total = 5334 + 3k\",\n  \"intercept\": 5334,\n  \"recovered_k\": 601\n}\n```\n\n## Finding\n\nWithin the fixed support region, the sum7137 identifies601. It is an alternative coordinate for the same data, retaining support and order assumptions.\n\n## Reassessment\n\nRecover the changed begetting inputs from the individual cap equations.\n\n## Checks\n\n```json\n{\n  \"intercept\": true,\n  \"k\": true,\n  \"support_valid\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T03:47:49.293122+00:00\n\n## Record provenance\n\nExact record hash: `edc906fe880f6d55bfe19b73556dbd967e635409f1c642e40e45512690f8acfc`\n\nSource journal: `Research_Cycles/C0932_C1131/journal.json`", "journalDownload": "/sources/f6bdc7aaaaa4fd40f1151b367204ddee7f0f9b77a9c43ae8764831b52d862670.json"}