{"id": "c666", "title": "C666 — Generate the complete retained-flank table", "filename": "C666.md", "role": "Research action", "step": 666, "sha256": "32942efa04745ed974f1273c33901fc2c7640b56344dbf5aa19b565583ffc6b8", "bytes": 1255, "origins": ["C480–C1634/Research_Cycles/C0632_C0731/journal.json#C666"], "download": "/sources/32942efa04745ed974f1273c33901fc2c7640b56344dbf5aa19b565583ffc6b8.md", "format": "md", "derived": true, "tags": [], "excerpt": "Can one formula produce every native and converted bracket column?", "content": "# C666 — Generate the complete retained-flank table\n\n## Question\n\nCan one formula produce every native and converted bracket column?\n\n## Inputs\n\n```json\n{\n  \"core\": 690,\n  \"flank\": 30,\n  \"operators\": [\n    \"identity\",\n    \"P\",\n    \"E\"\n  ]\n}\n```\n\n## Sources\n\n```json\n[\n  \"Supplement A §§1.1–1.2\"\n]\n```\n\n## Opened utc\n\n2026-09-28T01:08:43.934003+00:00\n\n## Results\n\n```json\n{\n  \"columns\": [\n    \"core\",\n    \"gain\",\n    \"one_flank\",\n    \"two_flanks\"\n  ],\n  \"rows\": [\n    [\n      690,\n      0,\n      720,\n      750\n    ],\n    [\n      700,\n      10,\n      730,\n      760\n    ],\n    [\n      750,\n      60,\n      780,\n      810\n    ]\n  ]\n}\n```\n\n## Finding\n\nApplying each Key to the core while retaining30-unit flanks generates the full source table:690/720/750,700/730/760 and750/780/810. The gain belongs to the core; a whole-bracket conversion is a different operation.\n\n## Reassessment\n\nMeasure the exact difference between retained-flank and whole-bracket conversion.\n\n## Checks\n\n```json\n{\n  \"source_table\": true,\n  \"gains\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T01:08:43.934579+00:00\n\n## Record provenance\n\nExact record hash: `13f081be334a5e06920e021097c80171ecc6103e09c820fb6f6241482071ebd6`\n\nSource journal: `Research_Cycles/C0632_C0731/journal.json`", "journalDownload": "/sources/f0643e934c6a7443706351fa40040684d915ed0ae25c0f9188a4c4dba12814ff.json"}