{"id": "c1063", "title": "C1063 — Allocation identity versus available source cuts", "filename": "C1063.md", "role": "Research action", "step": 1063, "sha256": "7165c4e23b10dc51ef3d6c5d720d5e88608d5c2002357468802aedaefd8c6404", "bytes": 1382, "origins": ["C480–C1634/Research_Cycles/C0932_C1131/journal.json#C1063"], "download": "/sources/7165c4e23b10dc51ef3d6c5d720d5e88608d5c2002357468802aedaefd8c6404.md", "format": "md", "derived": true, "tags": [], "excerpt": "Can the1/6 or1/26 allocation be made from whole components of the completed paths?", "content": "# C1063 — Allocation identity versus available source cuts\n\n## Question\n\nCan the1/6 or1/26 allocation be made from whole components of the completed paths?\n\n## Inputs\n\n```json\n{\n  \"duration\": 14720,\n  \"fractions\": [\n    \"1/6\",\n    \"1/26\"\n  ]\n}\n```\n\n## Sources\n\n```json\n[\n  \"C991\",\n  \"C1058–C1062\"\n]\n```\n\n## Opened utc\n\n2026-09-28T04:10:00.880635+00:00\n\n## Results\n\n```json\n{\n  \"required_selected_amounts\": [\n    \"7360/3\",\n    \"7360/13\"\n  ],\n  \"whole_component_realization\": false,\n  \"proof\": \"All original components and their one-pass values are integers; any sum of whole components is integral, while both required amounts are nonintegral.\",\n  \"scope\": \"does not refute source allocations on other paths; a new fractional cut would need source support\"\n}\n```\n\n## Finding\n\nThe factor identities transfer algebraically, but neither allocation can select whole components of these four paths. A named subdivision is additional source information.\n\n## Reassessment\n\nUse paired endpoint gaps to test common-pivot integrality without searching pivots.\n\n## Checks\n\n```json\n{\n  \"noninteger_amounts\": true,\n  \"values\": true,\n  \"integer_source_components\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T04:10:00.881122+00:00\n\n## Record provenance\n\nExact record hash: `33639af14c299054b0ed518aa9468c255e77b29e480910f4478353b18ef28553`\n\nSource journal: `Research_Cycles/C0932_C1131/journal.json`", "journalDownload": "/sources/f6bdc7aaaaa4fd40f1151b367204ddee7f0f9b77a9c43ae8764831b52d862670.json"}