{"id": "c1185", "title": "C1185 — Compare complete row recovery with two head differences", "filename": "C1185.md", "role": "Research action", "step": 1185, "sha256": "5e490f2f85097ce3fad5ff139701e2296df69d7fe9a68925fba94125e0204c88", "bytes": 1191, "origins": ["C480–C1634/Research_Cycles/C1132_C1431_Recovered/journal.json#C1185"], "download": "/sources/5e490f2f85097ce3fad5ff139701e2296df69d7fe9a68925fba94125e0204c88.md", "format": "md", "derived": true, "tags": ["Regular", "Cumulative"], "excerpt": "Can regular and cumulative totals distinguish the same five coefficients?", "content": "# C1185 — Compare complete row recovery with two head differences\n\n## Question\n\nCan regular and cumulative totals distinguish the same five coefficients?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"C1182\"\n]\n```\n\n## Opened utc\n\n2026-09-28T05:21:06.762307+00:00\n\n## Results\n\n```json\n{\n  \"head_information\": {\n    \"path\": \"model/whole_genealogy_head_information.json\",\n    \"sha256\": \"855645f2d27bb371e76a02f8b5dcc6b46e64ebdaa303b4c33eb8bf74b49071c6\",\n    \"bytes\": 487\n  },\n  \"head_differences\": [\n    1250,\n    430\n  ],\n  \"rank\": 2,\n  \"lost_dimensions\": 3\n}\n```\n\n## Finding\n\nThe two heads see12.5u and3u+lambda+2a+e+n. Their values1250 and430 leave three coefficient directions invisible, even though all local row changes are recoverable from five named observations.\n\n## Reassessment\n\nCheck whether the four-amplitude restriction restores that missing information.\n\n## Checks\n\n```json\n{\n  \"expected_heads\": true,\n  \"rank2\": true,\n  \"kernel3\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T05:21:06.763813+00:00\n\n## Record provenance\n\nExact record hash: `6a67cf88a2e9cc4663e984eccabf03a1a65a3b9aa0c8ac3871d288c473e99c5a`\n\nSource journal: `Research_Cycles/C1132_C1431_Recovered/journal.json`", "journalDownload": "/sources/6adb632ce171623c2bce60d7ed58ae319ccb379cf76b751c0a477c1742fd348c.json", "evidenceLinks": [{"id": "d-855645f2d27bb371", "title": "model/whole_genealogy_head_information.json"}]}