{"id": "c813", "title": "C813 — Integrate the primary File52c component paths", "filename": "C813.md", "role": "Research action", "step": 813, "sha256": "d799e9dbac27c559a81bc9f66034a3992489054c0ab3faa5eb0710b02d7f31f4", "bytes": 1667, "origins": ["C480–C1634/Research_Cycles/C0732_C0831/journal.json#C813"], "download": "/sources/d799e9dbac27c559a81bc9f66034a3992489054c0ab3faa5eb0710b02d7f31f4.md", "format": "md", "derived": true, "tags": ["Regular", "Cumulative", "Inverse"], "excerpt": "How do the primary regular and cumulative inverse paths meet in the shared path model?", "content": "# C813 — Integrate the primary File52c component paths\n\n## Question\n\nHow do the primary regular and cumulative inverse paths meet in the shared path model?\n\n## Inputs\n\n```json\n{\n  \"regular\": [\n    1650,\n    1050\n  ],\n  \"cumulative\": [\n    9170,\n    3430\n  ],\n  \"anchor\": 1406\n}\n```\n\n## Sources\n\n```json\n[\n  \"latest File52c §§3.3–3.4; inherited C731\"\n]\n```\n\n## Opened utc\n\n2026-09-28T02:10:44.686801+00:00\n\n## Results\n\n```json\n{\n  \"paths\": {\n    \"regular\": {\n      \"source_components\": [\n        1650,\n        1050\n      ],\n      \"single_pass_components\": [\n        5610,\n        5010\n      ],\n      \"endpoint\": 12026,\n      \"unsplit_single_pass_endpoint\": 8606\n    },\n    \"cumulative\": {\n      \"source_components\": [\n        9170,\n        3430\n      ],\n      \"single_pass_components\": [\n        7190,\n        3430\n      ],\n      \"endpoint\": 12026,\n      \"unsplit_single_pass_endpoint\": 63506\n    }\n  },\n  \"status\": \"integration check of established File52c constructions; no second inversion\"\n}\n```\n\n## Finding\n\nBoth admitted subdivided paths evaluate to12026. Their unsplit totals yield different endpoints, confirming why the component list belongs to the source object. This integrates an established result rather than adding another independent hit.\n\n## Reassessment\n\nCompare the retained-component and whole-span Key paths at their shared completion.\n\n## Checks\n\n```json\n{\n  \"primary_endpoint\": true,\n  \"subdivision_required\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T02:10:44.687068+00:00\n\n## Record provenance\n\nExact record hash: `6030f78645e32795e8736429f2c55facd2d5ca73af2e288dfebc663e3032a34c`\n\nSource journal: `Research_Cycles/C0732_C0831/journal.json`", "journalDownload": "/sources/8ea2b882289fbcea5cf11177923617f0c1d1ad7e6eaa3bffb174c6f89699d97d.json", "evidenceLinks": [{"id": "file52c", "title": "File 52c"}]}