{"id": "c764", "title": "C764 — Attach the residual decomposition to the Strategy rectangle", "filename": "C764.md", "role": "Research action", "step": 764, "sha256": "8d5d0abf157a9b9c3fed4b3b9f4faf422851493eba25a83879a91878ac5b5e23", "bytes": 1287, "origins": ["C480–C1634/Research_Cycles/C0732_C0831/journal.json#C764"], "download": "/sources/8d5d0abf157a9b9c3fed4b3b9f4faf422851493eba25a83879a91878ac5b5e23.md", "format": "md", "derived": true, "tags": ["Regular", "Cumulative"], "excerpt": "What part of the SP equal-gain rectangle is now explained?", "content": "# C764 — Attach the residual decomposition to the Strategy rectangle\n\n## Question\n\nWhat part of the SP equal-gain rectangle is now explained?\n\n## Inputs\n\n```json\n{\n  \"regular_head\": 4206,\n  \"cumulative_head\": 13406,\n  \"origin\": 1446,\n  \"target\": 1406\n}\n```\n\n## Sources\n\n```json\n[\n  \"Strategy §4.3; C763\"\n]\n```\n\n## Opened utc\n\n2026-09-28T01:56:59.196107+00:00\n\n## Results\n\n```json\n{\n  \"native_spans\": [\n    2760,\n    11960\n  ],\n  \"expanded_spans\": [\n    2800,\n    12000\n  ],\n  \"gains\": [\n    40,\n    40\n  ],\n  \"preserved_gap\": [\n    9200,\n    9200\n  ],\n  \"new_explanation\": \"conditional cumulative-head provenance+2/+3/+5\",\n  \"remaining_input\": \"the regular4206 branch and application status remain source-controlled\"\n}\n```\n\n## Finding\n\nThe existing rectangle survives exactly. This cycle adds a row-based explanation for its cumulative-head offset, not a new independent rectangle or permission to tune other heads.\n\n## Reassessment\n\nTest how lifespan splitting changes the whole accumulated comparison.\n\n## Checks\n\n```json\n{\n  \"same_gain\": true,\n  \"gap\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T01:56:59.197379+00:00\n\n## Record provenance\n\nExact record hash: `3c9f212f167946a02885e388e7a5d4aff3a7c77dea3a32dfaf5760bb156bb85e`\n\nSource journal: `Research_Cycles/C0732_C0831/journal.json`", "journalDownload": "/sources/8ea2b882289fbcea5cf11177923617f0c1d1ad7e6eaa3bffb174c6f89699d97d.json"}