{"id": "c1009", "title": "C1009 — Joint Esau reconstruction", "filename": "C1009.md", "role": "Research action", "step": 1009, "sha256": "a8b3f8ca591eeb8241f26244c624948b759054ad5646c0783bc894ea2ba7fdd8", "bytes": 1101, "origins": ["C480–C1634/Research_Cycles/C0932_C1131/journal.json#C1009"], "download": "/sources/a8b3f8ca591eeb8241f26244c624948b759054ad5646c0783bc894ea2ba7fdd8.md", "format": "md", "derived": true, "tags": [], "excerpt": "Do combined source registers recover all nine original counts?", "content": "# C1009 — Joint Esau reconstruction\n\n## Question\n\nDo combined source registers recover all nine original counts?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"C1008\",\n  \"File58 §13\"\n]\n```\n\n## Opened utc\n\n2026-09-28T03:57:22.081645+00:00\n\n## Results\n\n```json\n{\n  \"measurement_field\": {\n    \"path\": \"model/esau_joint_measurements.json\",\n    \"sha256\": \"77a91c74e28f7c20eb73c4696dd716bf02c5dd479498c60cd93f15f7cde55c1c\",\n    \"bytes\": 1374\n  },\n  \"rank\": 9,\n  \"recovered\": [\n    200,\n    20,\n    200,\n    20,\n    40,\n    10,\n    30,\n    20,\n    10\n  ]\n}\n```\n\n## Finding\n\nThe two ordered registers plus grand total recover every supplied count. This extends the separate-register analysis to the whole list.\n\n## Reassessment\n\nRemove the grand total to identify its exact information contribution.\n\n## Checks\n\n```json\n{\n  \"full_rank\": true,\n  \"complete_reconstruction\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T03:57:22.087796+00:00\n\n## Record provenance\n\nExact record hash: `a5d9dfdf1f3a063c81f43ffd9f4207ddc565c537d972d58c5d2947cb93d82763`\n\nSource journal: `Research_Cycles/C0932_C1131/journal.json`", "journalDownload": "/sources/f6bdc7aaaaa4fd40f1151b367204ddee7f0f9b77a9c43ae8764831b52d862670.json", "evidenceLinks": [{"id": "d-77a91c74e28f7c20", "title": "model/esau_joint_measurements.json"}, {"id": "d-924db415dff003d2", "title": "File 58"}]}