{"id": "c1028", "title": "C1028 — General reflection descent criterion", "filename": "C1028.md", "role": "Research action", "step": 1028, "sha256": "11f367b98210cbdb91f915a2423a4502ba612b2c215b6dfb38aac803a36f9b3b", "bytes": 1191, "origins": ["C480–C1634/Research_Cycles/C0932_C1131/journal.json#C1028"], "download": "/sources/11f367b98210cbdb91f915a2423a4502ba612b2c215b6dfb38aac803a36f9b3b.md", "format": "md", "derived": true, "tags": [], "excerpt": "When does a source grouping carry an existing involution?", "content": "# C1028 — General reflection descent criterion\n\n## Question\n\nWhen does a source grouping carry an existing involution?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"C1025\",\n  \"C1027\"\n]\n```\n\n## Opened utc\n\n2026-09-28T04:00:42.389009+00:00\n\n## Results\n\n```json\n{\n  \"point_quotient\": \"q(x)=q(y) implies q(Rx)=q(Ry).\",\n  \"boundary_subset\": \"Selected boundaries must be invariant under R.\",\n  \"interval_coarsening\": \"R must permute complete coarse blocks.\",\n  \"proof\": \"The proposed map q(x)↦q(Rx) is well-defined exactly when representatives of one class have a common image class.\"\n}\n```\n\n## Finding\n\nReflection can pass to a grouped object only when the grouping respects its action. Point identification, interval coarsening and boundary selection require their own checks.\n\n## Reassessment\n\nTest the source NT490 coarsening as a contrasting complete field.\n\n## Checks\n\n```json\n{\n  \"Toledot_counterexample\": true,\n  \"representative_condition_explicit\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T04:00:42.389353+00:00\n\n## Record provenance\n\nExact record hash: `5653889cd9b0ba5b0bdabd7dffa729ca3c51cbf82040188864e6115170a16e11`\n\nSource journal: `Research_Cycles/C0932_C1131/journal.json`", "journalDownload": "/sources/f6bdc7aaaaa4fd40f1151b367204ddee7f0f9b77a9c43ae8764831b52d862670.json"}