{"id": "c1309", "title": "C1309 — Register measure-preserving grouping and symmetry descent", "filename": "C1309.md", "role": "Research action", "step": 1309, "sha256": "e3c14f05d5f74577ff401cba9fd8b5855a11f0ec9108ae799b156f6491b22bab", "bytes": 1169, "origins": ["C480–C1634/Research_Cycles/C1132_C1431_Recovered/journal.json#C1309"], "download": "/sources/e3c14f05d5f74577ff401cba9fd8b5855a11f0ec9108ae799b156f6491b22bab.md", "format": "md", "derived": true, "tags": ["Inverse"], "excerpt": "What additionalcondition letsreflection act onagroupedobject?", "content": "# C1309 — Register measure-preserving grouping and symmetry descent\n\n## Question\n\nWhat additionalcondition letsreflection act onagroupedobject?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"C1308\",\n  \"inherited/model/toledot_quotient.json\",\n  \"C1024–C1029 inherited\"\n]\n```\n\n## Opened utc\n\n2026-09-28T06:12:25.483264+00:00\n\n## Results\n\n```json\n{\n  \"grouping_relation\": {\n    \"path\": \"model/relation_grouping_reflection.json\",\n    \"sha256\": \"4c6ff0cb4fb2a646e79edc4982ea4aaa54b2a197bb01ec1f55131bbfa7b2425b\",\n    \"bytes\": 745\n  }\n}\n```\n\n## Finding\n\nToledot’scollapsedEsauoccurrences reflectintodifferentsections, soitsreflectiondoesnotdescend even thoughmultiplicitypreserves themeasure. TheNT groupingworks becauseitsfibres respectitsreflection.\n\n## Reassessment\n\nRegister theinversefamily’s dependenceontheoriginalpartition.\n\n## Checks\n\n```json\n{\n  \"different_classes\": true,\n  \"images\": true,\n  \"occurrence_count\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T06:12:25.483729+00:00\n\n## Record provenance\n\nExact record hash: `aec788c1a21015282640fcdc1446ed46d6e1926cd6c6cef01c2792438d82b6ee`\n\nSource journal: `Research_Cycles/C1132_C1431_Recovered/journal.json`", "journalDownload": "/sources/6adb632ce171623c2bce60d7ed58ae319ccb379cf76b751c0a477c1742fd348c.json", "evidenceLinks": [{"id": "d-4c6ff0cb4fb2a646", "title": "model/relation_grouping_reflection.json"}, {"id": "d-a6887ca0cf82c69f", "title": "inherited/model/toledot_quotient.json"}]}