{"id": "c1065", "title": "C1065 — Symbolic branch support conditions", "filename": "C1065.md", "role": "Research action", "step": 1065, "sha256": "72613211b64ae1d7a9bd7df12e99c2f65344a0130b70c0bea1a93a4ba002abf2", "bytes": 1554, "origins": ["C480–C1634/Research_Cycles/C0932_C1131/journal.json#C1065"], "download": "/sources/72613211b64ae1d7a9bd7df12e99c2f65344a0130b70c0bea1a93a4ba002abf2.md", "format": "md", "derived": true, "tags": ["Mirror / 529"], "excerpt": "How do the source branch formulas constrain a common integer pivot?", "content": "# C1065 — Symbolic branch support conditions\n\n## Question\n\nHow do the source branch formulas constrain a common integer pivot?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"C1064\",\n  \"C850–C858\"\n]\n```\n\n## Opened utc\n\n2026-09-28T04:10:50.964993+00:00\n\n## Results\n\n```json\n{\n  \"branch_conditions\": [\n    {\n      \"branch\": \"three-to-two core\",\n      \"gap\": \"90(14+a−b−10c)\",\n      \"remaining_divisors\": [\n        23,\n        23,\n        299\n      ]\n    },\n    {\n      \"branch\": \"three-to-one core\",\n      \"gap\": \"990(1−c)\",\n      \"remaining_divisors\": [\n        23,\n        23,\n        299\n      ]\n    },\n    {\n      \"branch\": \"retained-zero Jacob\",\n      \"gap\": 0,\n      \"difference_obstruction\": false\n    },\n    {\n      \"branch\": \"retained-zero Adam\",\n      \"gap\": 7200,\n      \"difference_obstruction\": true\n    }\n  ],\n  \"qualification\": \"difference compatibility never supplies the missing pivot residue or source authorization\"\n}\n```\n\n## Finding\n\nThe paired-branch law gives divisibility conditions before any pivot placement is considered. A zero gap removes only the difference obstruction; it does not appoint a pivot.\n\n## Reassessment\n\nRepresent the complete paired field and inherited nine-member field by their difference meshes.\n\n## Checks\n\n```json\n{\n  \"reduced_divisors\": true,\n  \"Adam_obstructed\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T04:10:50.965550+00:00\n\n## Record provenance\n\nExact record hash: `309e21350a593f4dddd6f9a5bb209e9cabc5f795296d812a3fed0bf52aba35ca`\n\nSource journal: `Research_Cycles/C0932_C1131/journal.json`", "journalDownload": "/sources/f6bdc7aaaaa4fd40f1151b367204ddee7f0f9b77a9c43ae8764831b52d862670.json"}