{"id": "c523", "title": "C523 — Connect SP’s two comparison families", "filename": "C523.md", "role": "Research action", "step": 523, "sha256": "a36c7b574a6247e06c93b61a71554c3cf888edf48fd2871607d379d11402a559", "bytes": 1526, "origins": ["C480–C1634/Research_Cycles/C0482_C0531/journal.json#C523"], "download": "/sources/a36c7b574a6247e06c93b61a71554c3cf888edf48fd2871607d379d11402a559.md", "format": "md", "derived": true, "tags": ["Regular", "Cumulative"], "excerpt": "Can declared frame and node-class changes explain the9200 versus8982 SP gaps?", "content": "# C523 — Connect SP’s two comparison families\n\n## Question\n\nCan declared frame and node-class changes explain the9200 versus8982 SP gaps?\n\n## Inputs\n\n```json\n{\n  \"equalized_regular_completion\": 4414,\n  \"cumulative_lower_completion\": 13396,\n  \"native_week_opening\": 4206,\n  \"cumulative_implied_Day1\": 13406\n}\n```\n\n## Sources\n\n```json\n[\n  \"File18 §3.1 Creation-week row; §6C decade display\",\n  \"Strategy §4.3\",\n  \"C483,C508\"\n]\n```\n\n## Opened utc\n\n2026-09-27T22:52:23.265218+00:00\n\n## Results\n\n```json\n{\n  \"regular_frame_and_head_change\": [\n    -215,\n    7\n  ],\n  \"cumulative_head_change\": 10,\n  \"reconstructed_rectangle_heads\": [\n    4206,\n    13406\n  ],\n  \"completion_gap\": 8982,\n  \"rectangle_gap\": 9200,\n  \"gap_change\": 218,\n  \"decomposition\": \"218=215+(10−7)\"\n}\n```\n\n## Finding\n\nThe two SP families connect through source-declared changes: return the regular head to its native frame and week opening, and select the cumulative decade opening. Their gap changes by218 exactly. The9200 rectangle can therefore join the grammar without pretending its heads are the completion pair.\n\n## Reassessment\n\nCheck explicitly why these richer state changes cannot be replaced by one scalar map from regular to cumulative chronology.\n\n## Checks\n\n```json\n{\n  \"heads\": true,\n  \"gaps\": true,\n  \"delta\": true\n}\n```\n\n## Closed utc\n\n2026-09-27T22:52:23.265442+00:00\n\n## Record provenance\n\nExact record hash: `1e919881168b12163f7200267e4146b359ad97d41f6421b87ea27da640c1cb5e`\n\nSource journal: `Research_Cycles/C0482_C0531/journal.json`", "journalDownload": "/sources/6eaeccad4734eff2f6ac20ba847967877b944f9758c53c712ac8b5be2ddf61eb.json", "evidenceLinks": [{"id": "d-68301ab760bfbe2e", "title": "File 18"}]}