{"id": "c748", "title": "C748 — Identify the ordered reconstruction operator", "filename": "C748.md", "role": "Research action", "step": 748, "sha256": "587ce9d34cf1f7c2d8a7b988aeeafe669778ddb85700e9c6f3fadf0e87d91f58", "bytes": 1979, "origins": ["C480–C1634/Research_Cycles/C0732_C0831/journal.json#C748"], "download": "/sources/587ce9d34cf1f7c2d8a7b988aeeafe669778ddb85700e9c6f3fadf0e87d91f58.md", "format": "md", "derived": true, "tags": ["Cumulative", "Rounded"], "excerpt": "Does the complete boundary profile determine itslocalcontributionsuniquely once theterminal is fixed?", "content": "# C748 — Identify the ordered reconstruction operator\n\n## Question\n\nDoes the complete boundary profile determine itslocalcontributionsuniquely once theterminal is fixed?\n\n## Inputs\n\n```json\n{\n  \"local_vector\": [\n    27,\n    100,\n    100,\n    100,\n    100,\n    60,\n    60\n  ],\n  \"terminal\": 0,\n  \"operator\": \"uppertriangularsuffixsum\"\n}\n```\n\n## Sources\n\n```json\n[\n  \"C742,C747; Research Strategy §5F\"\n]\n```\n\n## Opened utc\n\n2026-09-28T01:47:14.611732+00:00\n\n## Results\n\n```json\n{\n  \"suffix_matrix\": [\n    [\n      1,\n      1,\n      1,\n      1,\n      1,\n      1,\n      1\n    ],\n    [\n      0,\n      1,\n      1,\n      1,\n      1,\n      1,\n      1\n    ],\n    [\n      0,\n      0,\n      1,\n      1,\n      1,\n      1,\n      1\n    ],\n    [\n      0,\n      0,\n      0,\n      1,\n      1,\n      1,\n      1\n    ],\n    [\n      0,\n      0,\n      0,\n      0,\n      1,\n      1,\n      1\n    ],\n    [\n      0,\n      0,\n      0,\n      0,\n      0,\n      1,\n      1\n    ],\n    [\n      0,\n      0,\n      0,\n      0,\n      0,\n      0,\n      1\n    ]\n  ],\n  \"profile\": [\n    547,\n    520,\n    420,\n    320,\n    220,\n    120,\n    60,\n    0\n  ],\n  \"recovered_rows\": [\n    27,\n    100,\n    100,\n    100,\n    100,\n    60,\n    60\n  ],\n  \"determinant\": 1,\n  \"rank\": 7\n}\n```\n\n## Finding\n\nThe suffix-sum matrix is triangular with unit diagonal. With terminal fixed, every ordered boundary determines exactly one local row vector, recovered by adjacent differences. This gives theStrategy a small linear mechanism for whole-family explanation, while total-only evaluation loses theordering.\n\n## Reassessment\n\nTest thewhole rounded-row family for compatibility between lifespan projection androunding.\n\n## Checks\n\n```json\n{\n  \"recovered\": true,\n  \"unit_diagonal\": true,\n  \"triangular\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T01:47:14.611940+00:00\n\n## Record provenance\n\nExact record hash: `9191777041d2fcdd61aa3efbe11747e1d8a05d5c7f42ed72e8c0218cefbdfd3d`\n\nSource journal: `Research_Cycles/C0732_C0831/journal.json`", "journalDownload": "/sources/8ea2b882289fbcea5cf11177923617f0c1d1ad7e6eaa3bffb174c6f89699d97d.json"}