{"id": "c1452", "title": "C1452 — Identify the complementary manuscript-mode pairings", "filename": "C1452.md", "role": "Research action", "step": 1452, "sha256": "d7f1df1633d47343dd92c124aca03c6a5e3196eee96a235edc313a6588f1ab70", "bytes": 1103, "origins": ["C480–C1634/Research_Cycles/C1433_C1482/journal.json#C1452"], "download": "/sources/d7f1df1633d47343dd92c124aca03c6a5e3196eee96a235edc313a6588f1ab70.md", "format": "md", "derived": true, "tags": ["Regular", "Cumulative"], "excerpt": "When is invariance genuine at both merges, and when does it arise from cancellation?", "content": "# C1452 — Identify the complementary manuscript-mode pairings\n\n## Question\n\nWhen is invariance genuine at both merges, and when does it arise from cancellation?\n\n## Sources\n\n```json\n[\n  \"Partition law\"\n]\n```\n\n## Opened utc\n\n2026-09-29T01:16:15.053664+00:00\n\n## Results\n\n```json\n{\n  \"(0, 0)\": [\n    \"MT_regular\",\n    \"SP_cumulative\"\n  ],\n  \"(-990, -990)\": [\n    \"MT_cumulative\",\n    \"LXX_regular\"\n  ],\n  \"(0, -990)\": [\n    \"LXX_cumulative\"\n  ],\n  \"(-4500, 1800)\": [\n    \"SP_regular\"\n  ]\n}\n```\n\n## Finding\n\nMT Regular and SP Cumulative have two zero defects; LXX Regular and MT Cumulative have two equal−990 defects. The second pair preserves coarse totals by cancellation while refinement adds990.\n\n## Reassessment\n\nInspect the complete source-node displacement vectors for an actual multi-node translation.\n\n## Checks\n\n```json\n{\n  \"stable_pair\": true,\n  \"balanced_pair\": true\n}\n```\n\n## Closed utc\n\n2026-09-29T01:16:15.054244+00:00\n\n## Record provenance\n\nExact record hash: `2f4f935ce19aeaa54efac9d623fa13026d4a35fa482210a628dae010f28aef5f`\n\nSource journal: `Research_Cycles/C1433_C1482/journal.json`", "journalDownload": "/sources/ca542c4d870fa9b9292d3dd24718f08766a5353e1b27cbb1e7c0d69061b00ecf.json"}