{"id": "c634", "title": "C634 — Generate the full cross-rail matrix", "filename": "C634.md", "role": "Research action", "step": 634, "sha256": "a5685c2c3ba19d90a55991ba23314da7dea5b4c4ff22305b1b721bbbbea14f9f", "bytes": 1412, "origins": ["C480–C1634/Research_Cycles/C0632_C0731/journal.json#C634"], "download": "/sources/a5685c2c3ba19d90a55991ba23314da7dea5b4c4ff22305b1b721bbbbea14f9f.md", "format": "md", "derived": true, "tags": [], "excerpt": "Does one indexed formula account for all nine span comparisons?", "content": "# C634 — Generate the full cross-rail matrix\n\n## Question\n\nDoes one indexed formula account for all nine span comparisons?\n\n## Inputs\n\n```json\n{\n  \"head_difference\": 2366,\n  \"rail_step\": 7,\n  \"indices\": [\n    0,\n    1,\n    2\n  ]\n}\n```\n\n## Sources\n\n```json\n[\n  \"File70 §§6.3,6.5; derived completion of source geometry\"\n]\n```\n\n## Opened utc\n\n2026-09-28T00:57:07.226648+00:00\n\n## Results\n\n```json\n{\n  \"span_matrix\": [\n    [\n      2366,\n      2373,\n      2380\n    ],\n    [\n      2359,\n      2366,\n      2373\n    ],\n    [\n      2352,\n      2359,\n      2366\n    ]\n  ],\n  \"multiplicities\": {\n    \"2352\": 1,\n    \"2359\": 2,\n    \"2366\": 3,\n    \"2373\": 2,\n    \"2380\": 1\n  },\n  \"formula\": \"D(i,j)=2366+7(j−i)\",\n  \"source_selected_extremes\": [\n    2352,\n    2366,\n    2380\n  ]\n}\n```\n\n## Finding\n\nThe complete matrix has five span values with multiplicities1,2,3,2,1. Minimum, corresponding and maximum spans are2366−14,2366,2366+14; the other entries are generated comparisons, not additional source appointments.\n\n## Reassessment\n\nExplain the separate exposure span using its two thirteen-year flanks.\n\n## Checks\n\n```json\n{\n  \"extremes\": true,\n  \"frequency\": true,\n  \"matrix_from_dates\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T00:57:07.226929+00:00\n\n## Record provenance\n\nExact record hash: `3bef9066b0c13130bfd753799a43e2aaee36086aa9fcaf0f767da80df7c64879`\n\nSource journal: `Research_Cycles/C0632_C0731/journal.json`", "journalDownload": "/sources/f0643e934c6a7443706351fa40040684d915ed0ae25c0f9188a4c4dba12814ff.json", "evidenceLinks": [{"id": "d-0fa80217c94b3951", "title": "File 70"}]}