{"id": "c668", "title": "C668 — Generate the whole alternating720/30 ladder", "filename": "C668.md", "role": "Research action", "step": 668, "sha256": "95ea2d3c27ee24997095286d72e760088193f265c81a939a6b568e9facb498bf", "bytes": 1542, "origins": ["C480–C1634/Research_Cycles/C0632_C0731/journal.json#C668"], "download": "/sources/95ea2d3c27ee24997095286d72e760088193f265c81a939a6b568e9facb498bf.md", "format": "md", "derived": true, "tags": [], "excerpt": "Can the source’s ten coordinates be recovered without separate date fitting?", "content": "# C668 — Generate the whole alternating720/30 ladder\n\n## Question\n\nCan the source’s ten coordinates be recovered without separate date fitting?\n\n## Inputs\n\n```json\n{\n  \"head\": 4326,\n  \"core\": 690,\n  \"flank\": 30,\n  \"source\": [\n    4326,\n    4296,\n    3606,\n    3576,\n    2886,\n    2856,\n    2166,\n    2136,\n    1446,\n    1416\n  ]\n}\n```\n\n## Sources\n\n```json\n[\n  \"Supplement A §1.3; admitted source ladder only\"\n]\n```\n\n## Opened utc\n\n2026-09-28T01:09:07.681958+00:00\n\n## Results\n\n```json\n{\n  \"generated_nodes\": [\n    4326,\n    4296,\n    3606,\n    3576,\n    2886,\n    2856,\n    2166,\n    2136,\n    1446,\n    1416\n  ],\n  \"gaps\": [\n    30,\n    690,\n    30,\n    690,\n    30,\n    690,\n    30,\n    690,\n    30\n  ],\n  \"same_rail_steps\": [\n    [\n      720,\n      720,\n      720,\n      720\n    ],\n    [\n      720,\n      720,\n      720,\n      720\n    ]\n  ],\n  \"width\": 2910\n}\n```\n\n## Finding\n\nThe ten supplied positions are two720-step rails separated by30. Their interleaving generates the alternating30|690 path and2910 outer width. Source, dependency and generated-companion roles remain attached to the original positions; no new SKL transport is inferred.\n\n## Reassessment\n\nExtract the six-node1470 cell and explain its alternative partitions.\n\n## Checks\n\n```json\n{\n  \"whole_ladder\": true,\n  \"gaps\": true,\n  \"width\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T01:09:07.682365+00:00\n\n## Record provenance\n\nExact record hash: `ebb63304f38feeb2026c85d30e53b38622a7cd2260ae47abc076d873610e9378`\n\nSource journal: `Research_Cycles/C0632_C0731/journal.json`", "journalDownload": "/sources/f0643e934c6a7443706351fa40040684d915ed0ae25c0f9188a4c4dba12814ff.json"}