{"id": "c504", "title": "C504 — Cross-tradition range of the tenfold529 placement", "filename": "C504.md", "role": "Research action", "step": 504, "sha256": "aea54d5b0253c2883c926e8cb907bf57d388b6b789bbd3adc79419f2ba11f2a4", "bytes": 1550, "origins": ["C480–C1634/Research_Cycles/C0482_C0531/journal.json#C504"], "download": "/sources/aea54d5b0253c2883c926e8cb907bf57d388b6b789bbd3adc79419f2ba11f2a4.md", "format": "md", "derived": true, "tags": ["Rounded", "Mirror / 529"], "excerpt": "Does12026=1446+10(Creation−NoahG1) transfer to the declared comparison states?", "content": "# C504 — Cross-tradition range of the tenfold529 placement\n\n## Question\n\nDoes12026=1446+10(Creation−NoahG1) transfer to the declared comparison states?\n\n## Inputs\n\n```json\n{\n  \"MT\": [\n    4114,\n    3056\n  ],\n  \"LXX\": [\n    5494,\n    3836\n  ],\n  \"SP_equalized\": [\n    4414,\n    3706\n  ]\n}\n```\n\n## Sources\n\n```json\n[\n  \"File18 comparison rows\",\n  \"File52c §§3.14–3.15\",\n  \"C481\"\n]\n```\n\n## Opened utc\n\n2026-09-27T22:44:56.887379+00:00\n\n## Results\n\n```json\n{\n  \"MT\": {\n    \"Creation_Noah_width\": 1058,\n    \"tenfold_width\": 10580,\n    \"residual_against_10580\": 0,\n    \"width_mod529\": 0\n  },\n  \"LXX\": {\n    \"Creation_Noah_width\": 1658,\n    \"tenfold_width\": 16580,\n    \"residual_against_10580\": 6000,\n    \"width_mod529\": 71\n  },\n  \"SP_equalized\": {\n    \"Creation_Noah_width\": 708,\n    \"tenfold_width\": 7080,\n    \"residual_against_10580\": -3500,\n    \"width_mod529\": 179\n  }\n}\n```\n\n## Finding\n\nOnly the selected MT width1058=2×529 satisfies the fixed tenfold placement. LXX1658 and SP708 miss by6000 and−3500 after scaling. The shared529 duration rule can still organize other sourced families without making this MT input universal.\n\n## Reassessment\n\nDerive that duration rule independently of endpoints and compare C480’s smaller ladder with the rounded macro ladder.\n\n## Checks\n\n```json\n{\n  \"MT\": true,\n  \"misses\": true\n}\n```\n\n## Closed utc\n\n2026-09-27T22:44:56.887586+00:00\n\n## Record provenance\n\nExact record hash: `8a31561685806c113eb10063bb57d1ccf8ab04ff224fce3138624d45271afe9c`\n\nSource journal: `Research_Cycles/C0482_C0531/journal.json`", "journalDownload": "/sources/6eaeccad4734eff2f6ac20ba847967877b944f9758c53c712ac8b5be2ddf61eb.json", "evidenceLinks": [{"id": "file52c", "title": "File 52c"}, {"id": "d-68301ab760bfbe2e", "title": "File 18"}]}