{"id": "c1451", "title": "C1451 — Derive the two local partition laws", "filename": "C1451.md", "role": "Research action", "step": 1451, "sha256": "b5f42256c3c365dc21693c173512c4818ce8f004e0b6da92365d9962600651ac", "bytes": 1432, "origins": ["C480–C1634/Research_Cycles/C1433_C1482/journal.json#C1451"], "download": "/sources/b5f42256c3c365dc21693c173512c4818ce8f004e0b6da92365d9962600651ac.md", "format": "md", "derived": true, "tags": ["Regular", "Cumulative"], "excerpt": "Can two local additivity differences reconstruct every observed change of partition?", "content": "# C1451 — Derive the two local partition laws\n\n## Question\n\nCan two local additivity differences reconstruct every observed change of partition?\n\n## Sources\n\n```json\n[\n  \"Eighteen named-node paths\"\n]\n```\n\n## Opened utc\n\n2026-09-29T01:16:15.050661+00:00\n\n## Results\n\n```json\n{\n  \"MT_regular\": {\n    \"dL\": 0,\n    \"dU\": 0,\n    \"alternate_change\": 0,\n    \"refined_change\": 0\n  },\n  \"MT_cumulative\": {\n    \"dL\": -990,\n    \"dU\": -990,\n    \"alternate_change\": 0,\n    \"refined_change\": 990\n  },\n  \"LXX_regular\": {\n    \"dL\": -990,\n    \"dU\": -990,\n    \"alternate_change\": 0,\n    \"refined_change\": 990\n  },\n  \"LXX_cumulative\": {\n    \"dL\": 0,\n    \"dU\": -990,\n    \"alternate_change\": 990,\n    \"refined_change\": 990\n  },\n  \"SP_regular\": {\n    \"dL\": -4500,\n    \"dU\": 1800,\n    \"alternate_change\": -6300,\n    \"refined_change\": -1800\n  },\n  \"SP_cumulative\": {\n    \"dL\": 0,\n    \"dU\": 0,\n    \"alternate_change\": 0,\n    \"refined_change\": 0\n  }\n}\n```\n\n## Finding\n\nTwo local defects explain all eighteen results: alternate−primary=dL−dU; refined−primary=−dU.\n\n## Reassessment\n\nClassify the exact shared responses without confusing cancellation with local additivity.\n\n## Checks\n\n```json\n{\n  \"all_six_reconstructed\": true\n}\n```\n\n## Closed utc\n\n2026-09-29T01:16:15.051662+00:00\n\n## Record provenance\n\nExact record hash: `4118f860f6c975f2660634312f7795f49b73145a8fb6bc12e01ef0eaa6360662`\n\nSource journal: `Research_Cycles/C1433_C1482/journal.json`", "journalDownload": "/sources/ca542c4d870fa9b9292d3dd24718f08766a5353e1b27cbb1e7c0d69061b00ecf.json"}