{"id": "c901", "title": "C901 — Unify endpoint interpolation and extrapolation", "filename": "C901.md", "role": "Research action", "step": 901, "sha256": "bcedbe153c4aae9ee24e6e0c120a187ed35b23dcf1e1f43d6db6e7427eb1ca7c", "bytes": 1277, "origins": ["C480–C1634/Research_Cycles/C0832_C0931/journal.json#C901"], "download": "/sources/bcedbe153c4aae9ee24e6e0c120a187ed35b23dcf1e1f43d6db6e7427eb1ca7c.md", "format": "md", "derived": true, "tags": [], "excerpt": "Can one span and one generated coordinate retain the entire source pair?", "content": "# C901 — Unify endpoint interpolation and extrapolation\n\n## Question\n\nCan one span and one generated coordinate retain the entire source pair?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"C892\",\n  \"C831 weighted Creation bridge\"\n]\n```\n\n## Opened utc\n\n2026-09-28T02:54:05.215910+00:00\n\n## Results\n\n```json\n{\n  \"basis\": {\n    \"path\": \"model/endpoint_coordinate_basis.json\",\n    \"sha256\": \"47b0713d83431b05bb871bd6fd461cc179ef1d3d5de57403a84c8f817a06e7d7\",\n    \"bytes\": 391\n  },\n  \"symbolic_coefficients\": {\n    \"R_recovered\": [\n      0,\n      1\n    ],\n    \"C_recovered\": [\n      1,\n      0\n    ]\n  }\n}\n```\n\n## Finding\n\nThe pair (D,W_lambda) is an exact coordinate system for (C,R), for every fixed lambda. The old weighted bridge and new twelvefold head use the same endpoint algebra with different source-appointed coefficients and roles.\n\n## Reassessment\n\nRecover every macro source pair and both inherited weighted Creation pairs from this basis.\n\n## Checks\n\n```json\n{\n  \"determinant\": true,\n  \"R_coefficients\": true,\n  \"C_coefficients\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T02:54:05.216450+00:00\n\n## Record provenance\n\nExact record hash: `7fd7b24f3969631c5c1071c6eef86b55f1226912df43c3452060b7e55239fefc`\n\nSource journal: `Research_Cycles/C0832_C0931/journal.json`", "journalDownload": "/sources/6a37be4e218f9f467cbde5e9db3723ce9c79dc78cc97d1a289422b96cb9971e0.json", "evidenceLinks": [{"id": "d-47b0713d83431b05", "title": "model/endpoint_coordinate_basis.json"}]}