{"id": "c848", "title": "C848 — Transfer the projection model to the four-household ledger", "filename": "C848.md", "role": "Research action", "step": 848, "sha256": "18957979105c4f030eaf259f78bc0f4d393e690a464523f348dbf3b217c3f345", "bytes": 1418, "origins": ["C480–C1634/Research_Cycles/C0832_C0931/journal.json#C848"], "download": "/sources/18957979105c4f030eaf259f78bc0f4d393e690a464523f348dbf3b217c3f345.md", "format": "md", "derived": true, "tags": [], "excerpt": "Do equal regrouped totals recover the ordered household inputs?", "content": "# C848 — Transfer the projection model to the four-household ledger\n\n## Question\n\nDo equal regrouped totals recover the ordered household inputs?\n\n## Inputs\n\n```json\n{\n  \"source_vector\": [\n    33,\n    16,\n    14,\n    7\n  ]\n}\n```\n\n## Sources\n\n```json\n[\n  \"File58 §1.4 Genesis46 printed-household subtotal register\"\n]\n```\n\n## Opened utc\n\n2026-09-28T02:34:32.561601+00:00\n\n## Results\n\n```json\n{\n  \"source_pair\": [\n    49,\n    21\n  ],\n  \"source_bracket\": [\n    40,\n    30\n  ],\n  \"source_prefix\": [\n    33,\n    49,\n    63,\n    70\n  ],\n  \"invisible_regrouping_direction\": [\n    1,\n    -1,\n    1,\n    -1\n  ],\n  \"diagnostic_prefix\": [\n    34,\n    49,\n    64,\n    70\n  ],\n  \"scope\": \"printed source subtotals only; no person-count repair or chronology projection\"\n}\n```\n\n## Finding\n\nThe same four counts produce49/21 and40/30 through two declared partitions. Both partitions miss one direction of change that the ordered prefix register detects. Retaining order adds information beyond shared totals.\n\n## Reassessment\n\nState the precise extension of the path grammar established by the list holdout.\n\n## Checks\n\n```json\n{\n  \"pair_preserved\": true,\n  \"bracket_preserved\": true,\n  \"order_detects\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T02:34:32.561778+00:00\n\n## Record provenance\n\nExact record hash: `d05d03a756cecf42b923038bf767ceba8209676005158203955d98d09d4a2626`\n\nSource journal: `Research_Cycles/C0832_C0931/journal.json`", "journalDownload": "/sources/6a37be4e218f9f467cbde5e9db3723ce9c79dc78cc97d1a289422b96cb9971e0.json", "evidenceLinks": [{"id": "d-924db415dff003d2", "title": "File 58"}]}