{"id": "c757", "title": "C757 — Transfer the residual field to SP", "filename": "C757.md", "role": "Research action", "step": 757, "sha256": "109fb255fd8cc20bb9f2ffa24e9fd18f59cfd75d8b2d8aa0e9b29309358dcfd0", "bytes": 1142, "origins": ["C480–C1634/Research_Cycles/C0732_C0831/journal.json#C757"], "download": "/sources/109fb255fd8cc20bb9f2ffa24e9fd18f59cfd75d8b2d8aa0e9b29309358dcfd0.md", "format": "md", "derived": true, "tags": ["Cumulative", "Rounded"], "excerpt": "Why does SP gain three at the cumulative head?", "content": "# C757 — Transfer the residual field to SP\n\n## Question\n\nWhy does SP gain three at the cumulative head?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"File18 SP inclusive lifespan ledger; C756\"\n]\n```\n\n## Opened utc\n\n2026-09-28T01:55:12.782893+00:00\n\n## Results\n\n```json\n{\n  \"row_support\": {\n    \"Methuselah\": -1,\n    \"Lamech\": 4\n  },\n  \"boundary_differences\": {\n    \"Adam\": 3,\n    \"Seth\": 3,\n    \"Enosh\": 3,\n    \"Kenan\": 3,\n    \"Mahalalel\": 3,\n    \"Jared\": 3,\n    \"Enoch\": 3,\n    \"Methuselah\": 3,\n    \"Lamech\": 4\n  },\n  \"head_actual_rounded\": [\n    13398,\n    13401\n  ]\n}\n```\n\n## Finding\n\nSP rounding changes the cumulative head by+3, entirely from Methuselah−1 and Lamech+4 relative to MT residuals. The inclusive ledger remains the input type.\n\n## Reassessment\n\nDetermine cross-tradition interval families preserved by rounding.\n\n## Checks\n\n```json\n{\n  \"support\": true,\n  \"head\": true,\n  \"downstream\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T01:55:12.783236+00:00\n\n## Record provenance\n\nExact record hash: `9436f33d7f8f2a9ea18288d69d28a0cb181026754919387530d91ba1dfb5af12`\n\nSource journal: `Research_Cycles/C0732_C0831/journal.json`", "journalDownload": "/sources/8ea2b882289fbcea5cf11177923617f0c1d1ad7e6eaa3bffb174c6f89699d97d.json", "evidenceLinks": [{"id": "d-68301ab760bfbe2e", "title": "File 18"}]}