{"id": "c1442", "title": "C1442 — Locate the obstruction to cross-mode coincidence", "filename": "C1442.md", "role": "Research action", "step": 1442, "sha256": "02e43bf7b8ed90869dce9d565a36fb77004ee900b590ef9e380c941eaecb544c", "bytes": 1324, "origins": ["C480–C1634/Research_Cycles/C1433_C1482/journal.json#C1442"], "download": "/sources/02e43bf7b8ed90869dce9d565a36fb77004ee900b590ef9e380c941eaecb544c.md", "format": "md", "derived": true, "tags": [], "excerpt": "Are LXX/SP nonzero head differences avoidable without altering their declared source states?", "content": "# C1442 — Locate the obstruction to cross-mode coincidence\n\n## Question\n\nAre LXX/SP nonzero head differences avoidable without altering their declared source states?\n\n## Sources\n\n```json\n[\n  \"Registered source mode gaps\",\n  \"Decimal gain laws\"\n]\n```\n\n## Opened utc\n\n2026-09-29T01:13:46.072488+00:00\n\n## Results\n\n```json\n{\n  \"MT\": {\n    \"source_gap\": 9900,\n    \"head_gap\": 0,\n    \"modulus\": 990,\n    \"residue\": 0,\n    \"same_residue\": true\n  },\n  \"LXX\": {\n    \"source_gap\": 9410,\n    \"head_gap\": 500,\n    \"modulus\": 990,\n    \"residue\": 500,\n    \"same_residue\": true\n  },\n  \"SP\": {\n    \"source_gap\": 8990,\n    \"head_gap\": -190,\n    \"modulus\": 90,\n    \"residue\": 80,\n    \"same_residue\": true\n  }\n}\n```\n\n## Finding\n\nMT and LXX primary spans preserve gaps modulo990; LXX residue500 prevents convergence. Across SP digit widths the safe common modulus90 leaves residue80, also preventing convergence.\n\n## Reassessment\n\nThe next test should change only source-named partitions, not tune inputs toward convergence.\n\n## Checks\n\n```json\n{\n  \"all_congruences\": true,\n  \"LXX_residue\": true,\n  \"SP_residue\": true\n}\n```\n\n## Closed utc\n\n2026-09-29T01:13:46.072973+00:00\n\n## Record provenance\n\nExact record hash: `27cc30a3a28136cc09e0f2bd013e3b270d528c6144fa0b0b1da65f669f63ec56`\n\nSource journal: `Research_Cycles/C1433_C1482/journal.json`", "journalDownload": "/sources/ca542c4d870fa9b9292d3dd24718f08766a5353e1b27cbb1e7c0d69061b00ecf.json"}