{"id": "c961", "title": "C961 — Nonredundant synchronization", "filename": "C961.md", "role": "Research action", "step": 961, "sha256": "9e0091394831398128d99c76068ec5bb8b132491bdba06b8c47e2554fcb10b64", "bytes": 927, "origins": ["C480–C1634/Research_Cycles/C0932_C1131/journal.json#C961"], "download": "/sources/9e0091394831398128d99c76068ec5bb8b132491bdba06b8c47e2554fcb10b64.md", "format": "md", "derived": true, "tags": ["Mirror / 529"], "excerpt": "How many extra constraints join the three caps to one parameter?", "content": "# C961 — Nonredundant synchronization\n\n## Question\n\nHow many extra constraints join the three caps to one parameter?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"C954\",\n  \"C956\",\n  \"C960\"\n]\n```\n\n## Opened utc\n\n2026-09-28T03:47:16.038529+00:00\n\n## Results\n\n```json\n{\n  \"k_from_each\": [\n    601,\n    601,\n    601\n  ],\n  \"pairwise_residuals\": [\n    0,\n    0,\n    0\n  ],\n  \"independent_synchronization_equations\": 2\n}\n```\n\n## Finding\n\nOne cap fixes k; two further equations synchronize the remaining caps. The third pairwise comparison is their sum.\n\n## Reassessment\n\nDetermine how much weaker clipped-row support alone would be.\n\n## Checks\n\n```json\n{\n  \"common_k\": true,\n  \"dependent_third\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T03:47:16.038776+00:00\n\n## Record provenance\n\nExact record hash: `659013cef1eeb9344f8f0afff07327a70bc198cd84a5dfb2fbbbd80bcde93671`\n\nSource journal: `Research_Cycles/C0932_C1131/journal.json`", "journalDownload": "/sources/f6bdc7aaaaa4fd40f1151b367204ddee7f0f9b77a9c43ae8764831b52d862670.json"}