{"id": "c508", "title": "C508 — SP equal-gain rectangle", "filename": "C508.md", "role": "Research action", "step": 508, "sha256": "8ed96e430eccdeed277982d6c3a6a2ed81bbad86e3c4e20a89de75d208ba2826", "bytes": 1477, "origins": ["C480–C1634/Research_Cycles/C0482_C0531/journal.json#C508"], "download": "/sources/8ed96e430eccdeed277982d6c3a6a2ed81bbad86e3c4e20a89de75d208ba2826.md", "format": "md", "derived": true, "tags": ["Calendar Keys"], "excerpt": "Can the calendar grammar reconstruct the Strategy’s separately declared SP rectangle?", "content": "# C508 — SP equal-gain rectangle\n\n## Question\n\nCan the calendar grammar reconstruct the Strategy’s separately declared SP rectangle?\n\n## Inputs\n\n```json\n{\n  \"Strategy_ReportIV_comparison_heads\": [\n    4206,\n    13406\n  ],\n  \"Exodus\": 1446,\n  \"Conquest\": 1406,\n  \"state_note\": \"historical Strategy SP−215 rectangle; not the File18 completion pair used in C483\"\n}\n```\n\n## Sources\n\n```json\n[\n  \"Strategy §4.3\"\n]\n```\n\n## Opened utc\n\n2026-09-27T22:46:21.831060+00:00\n\n## Results\n\n```json\n{\n  \"input_radii\": [\n    2760,\n    11960\n  ],\n  \"P_and_J_outputs\": [\n    2800,\n    12000\n  ],\n  \"gains\": [\n    40,\n    40\n  ],\n  \"preserved_difference\": [\n    9200,\n    9200\n  ],\n  \"E_difference\": 10000,\n  \"general_rule\": \"69m ->70m and299m ->300m; common gain m and preserved separation230m\"\n}\n```\n\n## Finding\n\nAt m=40, two distinct Keys add the same40, preserving9200 while terminating at the shared1406 target with the two heads held. This is a reusable equal-gain construction, separate from the newer File18 completion comparison.\n\n## Reassessment\n\nDerive how anchor changes affect otherwise identical expansions, needed to relate the14726 family’s two presentations.\n\n## Checks\n\n```json\n{\n  \"radii\": true,\n  \"gain\": true,\n  \"difference\": true,\n  \"E\": true\n}\n```\n\n## Closed utc\n\n2026-09-27T22:46:21.831361+00:00\n\n## Record provenance\n\nExact record hash: `2ef24055f1beab32a97f09e24cd39b9112cab3fa4561d565eb93cf445d5ffb2b`\n\nSource journal: `Research_Cycles/C0482_C0531/journal.json`", "journalDownload": "/sources/6eaeccad4734eff2f6ac20ba847967877b944f9758c53c712ac8b5be2ddf61eb.json", "evidenceLinks": [{"id": "d-68301ab760bfbe2e", "title": "File 18"}]}