{"id": "c1012", "title": "C1012 — Alternative complete walk basis", "filename": "C1012.md", "role": "Research action", "step": 1012, "sha256": "b6beda35af48ec5f6b08a58f6f54be1e2da8258790284d36572ca5b6d206875b", "bytes": 1064, "origins": ["C480–C1634/Research_Cycles/C0932_C1131/journal.json#C1012"], "download": "/sources/b6beda35af48ec5f6b08a58f6f54be1e2da8258790284d36572ca5b6d206875b.md", "format": "md", "derived": true, "tags": ["Counts & NT"], "excerpt": "Do the clean and unclean ordered walks together recover the same list?", "content": "# C1012 — Alternative complete walk basis\n\n## Question\n\nDo the clean and unclean ordered walks together recover the same list?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"C1008\",\n  \"File58 §§13.3–13.4\"\n]\n```\n\n## Opened utc\n\n2026-09-28T03:57:57.876332+00:00\n\n## Results\n\n```json\n{\n  \"measurements\": [\n    20,\n    40,\n    50,\n    250,\n    450,\n    490,\n    20,\n    50,\n    60\n  ],\n  \"determinant\": -1,\n  \"recovered\": [\n    200,\n    20,\n    200,\n    20,\n    40,\n    10,\n    30,\n    20,\n    10\n  ]\n}\n```\n\n## Finding\n\nThe two complete walks form another integer basis. The same accumulation-and-difference operation used for genealogical paths reconstructs this counted list.\n\n## Reassessment\n\nSeparate universal register dependencies from source-specific equalities.\n\n## Checks\n\n```json\n{\n  \"unimodular\": true,\n  \"prefixes\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T03:57:57.881574+00:00\n\n## Record provenance\n\nExact record hash: `7465c438c9beef8f72a018ea0ef5741b7ea5d31d8053999b2787768448e96202`\n\nSource journal: `Research_Cycles/C0932_C1131/journal.json`", "journalDownload": "/sources/f6bdc7aaaaa4fd40f1151b367204ddee7f0f9b77a9c43ae8764831b52d862670.json", "evidenceLinks": [{"id": "d-924db415dff003d2", "title": "File 58"}]}