{"id": "c707", "title": "C707 — Derive the fixed-template placement condition", "filename": "C707.md", "role": "Research action", "step": 707, "sha256": "c7cc583ccccbcdacc883c68f4ec9d951e239a3af33b86d59983e50efc446d108", "bytes": 1265, "origins": ["C480–C1634/Research_Cycles/C0632_C0731/journal.json#C707"], "download": "/sources/c7cc583ccccbcdacc883c68f4ec9d951e239a3af33b86d59983e50efc446d108.md", "format": "md", "derived": true, "tags": ["Calendar Keys", "Mirror / 529"], "excerpt": "What does whole-field mirror closure determine once the shape is fixed?", "content": "# C707 — Derive the fixed-template placement condition\n\n## Question\n\nWhat does whole-field mirror closure determine once the shape is fixed?\n\n## Inputs\n\n```json\n{\n  \"translation\": 5842,\n  \"symmetric_template_center\": 0,\n  \"shape\": \"fixed literal twelve-node template\"\n}\n```\n\n## Sources\n\n```json\n[\n  \"Supplement A §13.4\"\n]\n```\n\n## Opened utc\n\n2026-09-28T01:19:05.456745+00:00\n\n## Results\n\n```json\n{\n  \"required_center\": -2921,\n  \"center_equation\": \"c+L=−c\",\n  \"template_symmetric\": true,\n  \"scope\": \"unique placement conditional on fixed shape, chart and L\"\n}\n```\n\n## Finding\n\nWhole-field closure forces c=−L/2=−2921, and the fixed symmetric template makes that condition sufficient. The period determines placement only after shape, phase chart and closure requirement have been supplied; it does not independently determine them.\n\n## Reassessment\n\nCompare the source’s anchored calendar-body placement packet with this fixed-template result.\n\n## Checks\n\n```json\n{\n  \"necessary\": true,\n  \"sufficient_shape\": true,\n  \"center\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T01:19:05.457229+00:00\n\n## Record provenance\n\nExact record hash: `062f407ed4f4fa4183b5ad1794b7a89688d417b795fa4d964b1782571a665f12`\n\nSource journal: `Research_Cycles/C0632_C0731/journal.json`", "journalDownload": "/sources/f0643e934c6a7443706351fa40040684d915ed0ae25c0f9188a4c4dba12814ff.json"}