{"id": "c958", "title": "C958 — Greatest feasible lifespan field", "filename": "C958.md", "role": "Research action", "step": 958, "sha256": "76d3766c6bc90703a86525d69c3c8b0436af0aa957994416c95b198610c36484", "bytes": 1297, "origins": ["C480–C1634/Research_Cycles/C0932_C1131/journal.json#C958"], "download": "/sources/76d3766c6bc90703a86525d69c3c8b0436af0aa957994416c95b198610c36484.md", "format": "md", "derived": true, "tags": ["Cumulative"], "excerpt": "Why does the minimum represent shortening only as required?", "content": "# C958 — Greatest feasible lifespan field\n\n## Question\n\nWhy does the minimum represent shortening only as required?\n\n## Inputs\n\n```json\n{\n  \"constraints\": [\n    \"x_i≤baseline_i\",\n    \"x_i≤capacity_i\"\n  ],\n  \"objective\": \"maximize sum(x_i)\"\n}\n```\n\n## Sources\n\n```json\n[\n  \"C956\",\n  \"C957\"\n]\n```\n\n## Opened utc\n\n2026-09-28T03:46:48.269850+00:00\n\n## Results\n\n```json\n{\n  \"coordinate_bound\": \"Every feasible x_i is at most min(L_i,C_i).\",\n  \"feasibility\": \"The coordinatewise minimum satisfies both upper bounds.\",\n  \"uniqueness\": \"If any coordinate is smaller, the sum is smaller because no other coordinate can exceed its bound.\",\n  \"qualification\": \"Conditional on the two upper bounds and fixed row meanings.\"\n}\n```\n\n## Finding\n\nThe cap is the unique coordinatewise greatest feasible vector and uniquely minimizes total reduction. This states the model’s mechanism without inventing an optimization history.\n\n## Reassessment\n\nRecover death labels with each branch’s own counting convention.\n\n## Checks\n\n```json\n{\n  \"upper_bound_logic\": true,\n  \"no_increase\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T03:46:48.270093+00:00\n\n## Record provenance\n\nExact record hash: `8d9ff13e69ac57e12fe216c71f7c1cdb31fab566310d7957925835a63d4d7329`\n\nSource journal: `Research_Cycles/C0932_C1131/journal.json`", "journalDownload": "/sources/f6bdc7aaaaa4fd40f1151b367204ddee7f0f9b77a9c43ae8764831b52d862670.json"}