{"id": "c1365", "title": "C1365 — Preserve the inverse register proof in the companion", "filename": "C1365.md", "role": "Research action", "step": 1365, "sha256": "2a08937d053faf3d67b3b0324eca3d7e3af4990caa78deb30b6941beeb7c2112", "bytes": 1011, "origins": ["C480–C1634/Research_Cycles/C1132_C1431_Recovered/journal.json#C1365"], "download": "/sources/2a08937d053faf3d67b3b0324eca3d7e3af4990caa78deb30b6941beeb7c2112.md", "format": "md", "derived": true, "tags": ["Cumulative", "Inverse"], "excerpt": "What exact hypotheses support the aggregate convergence?", "content": "# C1365 — Preserve the inverse register proof in the companion\n\n## Question\n\nWhat exact hypotheses support the aggregate convergence?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"prep/final_inverse_keys_draft.md\",\n  \"C1352\"\n]\n```\n\n## Opened utc\n\n2026-09-28T06:36:17.980344+00:00\n\n## Results\n\n```json\n{\n  \"supplement\": {\n    \"path\": \"draft/technical_04_inverse.md\",\n    \"sha256\": \"9c40e316533e3f5be3bce7ed2b629c54ca3a313adea1db781d6ba1af4f4dfa4c\",\n    \"bytes\": 1289\n  }\n}\n```\n\n## Finding\n\nThe companion retains the full register theorem with its two-component domain, carry alternatives and source-selected cumulative branch.\n\n## Reassessment\n\nWrite the anchored-Key domain supplement.\n\n## Checks\n\n```json\n{\n  \"domain\": true,\n  \"branches\": true,\n  \"source_cores\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T06:36:17.980859+00:00\n\n## Record provenance\n\nExact record hash: `ad7bb8b329e68c998f1fa70a1df73a3491fb0cb8ef0cfce7a4866cafcdb81789`\n\nSource journal: `Research_Cycles/C1132_C1431_Recovered/journal.json`", "journalDownload": "/sources/6adb632ce171623c2bce60d7ed58ae319ccb379cf76b751c0a477c1742fd348c.json", "evidenceLinks": [{"id": "d-9c40e316533e3f5b", "title": "draft/technical_04_inverse.md"}]}