{"id": "c1191", "title": "C1191 — Count the exact residual fibre", "filename": "C1191.md", "role": "Research action", "step": 1191, "sha256": "b383e1401798682b0b78b635e335ee80cb557c0d6e2570e7afd81ecb904c9a8d", "bytes": 1127, "origins": ["C480–C1634/Research_Cycles/C1132_C1431_Recovered/journal.json#C1191"], "download": "/sources/b383e1401798682b0b78b635e335ee80cb557c0d6e2570e7afd81ecb904c9a8d.md", "format": "md", "derived": true, "tags": ["Rounded"], "excerpt": "How many original decompositions share B,R,L away from zero?", "content": "# C1191 — Count the exact residual fibre\n\n## Question\n\nHow many original decompositions share B,R,L away from zero?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"C1190\"\n]\n```\n\n## Opened utc\n\n2026-09-28T05:22:33.812921+00:00\n\n## Results\n\n```json\n{\n  \"fibre_count\": {\n    \"path\": \"model/joint_rounding_fibre_count.json\",\n    \"sha256\": \"675aded4ec0b4aa373b5fb41a62a59b066ba872990fb481b07f80f5fd2ee610f\",\n    \"bytes\": 388\n  },\n  \"counts\": {\n    \"-5\": 0,\n    \"-4\": 1,\n    \"-3\": 2,\n    \"-2\": 3,\n    \"-1\": 4,\n    \"0\": 5,\n    \"1\": 4,\n    \"2\": 3,\n    \"3\": 2,\n    \"4\": 1,\n    \"5\": 0\n  }\n}\n```\n\n## Finding\n\nInterior joint fibres have5−|z| members for |z|<=4. A singleton occurs only at z=±4, where both residuals must be the same extreme ±2.\n\n## Reassessment\n\nApply this criterion to the complete55-row ordinary source domain.\n\n## Checks\n\n```json\n{\n  \"all_counts\": true,\n  \"singletons\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T05:22:33.813364+00:00\n\n## Record provenance\n\nExact record hash: `a7bac3e57a118615956bdade02d54316c9c306183c353f7e4b805504c61bb97f`\n\nSource journal: `Research_Cycles/C1132_C1431_Recovered/journal.json`", "journalDownload": "/sources/6adb632ce171623c2bce60d7ed58ae319ccb379cf76b751c0a477c1742fd348c.json", "evidenceLinks": [{"id": "d-675aded4ec0b4aa3", "title": "model/joint_rounding_fibre_count.json"}]}