{"id": "c1027", "title": "C1027 — Formal closure reveals the missing source permission", "filename": "C1027.md", "role": "Research action", "step": 1027, "sha256": "cf5204ba7abd9090208cd3f877762433857175c1283063bfde68645ad73e55a0", "bytes": 1294, "origins": ["C480–C1634/Research_Cycles/C0932_C1131/journal.json#C1027"], "download": "/sources/cf5204ba7abd9090208cd3f877762433857175c1283063bfde68645ad73e55a0.md", "format": "md", "derived": true, "tags": [], "excerpt": "What extra merge would make the section grouping stable under reflection?", "content": "# C1027 — Formal closure reveals the missing source permission\n\n## Question\n\nWhat extra merge would make the section grouping stable under reflection?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"C1025\",\n  \"C1026\"\n]\n```\n\n## Opened utc\n\n2026-09-28T04:00:40.445959+00:00\n\n## Results\n\n```json\n{\n  \"formal_blocks\": [\n    [\n      1\n    ],\n    [\n      2,\n      3\n    ],\n    [\n      4\n    ],\n    [\n      5\n    ],\n    [\n      6\n    ],\n    [\n      7\n    ],\n    [\n      8\n    ],\n    [\n      9,\n      10\n    ],\n    [\n      11\n    ]\n  ],\n  \"extra_merge\": [\n    \"Adam\",\n    \"Noah\"\n  ],\n  \"status\": \"obstruction witness only; source does not authorize the extra merge\"\n}\n```\n\n## Finding\n\nA formal stable closure would merge Adam and Noah as well as the two Esau occurrences. That shows the cost of forcing quotient symmetry; the source sections are retained unchanged.\n\n## Reassessment\n\nState a general descent criterion and test it against a legitimate chronological coarsening.\n\n## Checks\n\n```json\n{\n  \"stable\": true,\n  \"nine_classes\": true,\n  \"extra_merge_required\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T04:00:40.446289+00:00\n\n## Record provenance\n\nExact record hash: `e2a2ad9cad5a693712877b7bb7f3534e84b45c559514b1b85a233d86b111fad9`\n\nSource journal: `Research_Cycles/C0932_C1131/journal.json`", "journalDownload": "/sources/f6bdc7aaaaa4fd40f1151b367204ddee7f0f9b77a9c43ae8764831b52d862670.json"}