{"id": "c689", "title": "C689 — Explain the normalized13440 register", "filename": "C689.md", "role": "Research action", "step": 689, "sha256": "4b38135f6e0fa5308aa7f227c4532aeedb2003a6fa0e4334fdb8ff03080d83dd", "bytes": 1152, "origins": ["C480–C1634/Research_Cycles/C0632_C0731/journal.json#C689"], "download": "/sources/4b38135f6e0fa5308aa7f227c4532aeedb2003a6fa0e4334fdb8ff03080d83dd.md", "format": "md", "derived": true, "tags": ["Cumulative", "Calendar Keys"], "excerpt": "What added quantity separates PhaseNorm40 from the calibrated micro completion?", "content": "# C689 — Explain the normalized13440 register\n\n## Question\n\nWhat added quantity separates PhaseNorm40 from the calibrated micro completion?\n\n## Inputs\n\n```json\n{\n  \"E_count\": \"75/2\",\n  \"normalized_count\": 40,\n  \"Priestly_calendar\": 336\n}\n```\n\n## Sources\n\n```json\n[\n  \"Supplement A §§4.3,6\"\n]\n```\n\n## Opened utc\n\n2026-09-28T01:14:01.247385+00:00\n\n## Results\n\n```json\n{\n  \"calibrated_volume\": 12600,\n  \"normalized_volume\": 13440,\n  \"residual_volume\": 840,\n  \"identity\": \"40×336 = E(34.5)×336 + 2.5×336\"\n}\n```\n\n## Finding\n\nThe normalized13440 body adds exactly840 to12600, because the source’s2.5 residual is measured in336-day units. This explains the extra completion without assigning it to a new event or applying another Key.\n\n## Reassessment\n\nCompare these scalar registers with the source’s retained2940 cumulative partition.\n\n## Checks\n\n```json\n{\n  \"volumes\": true,\n  \"additivity\": true,\n  \"residual_count\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T01:14:01.247647+00:00\n\n## Record provenance\n\nExact record hash: `445aa97ebd598e316fcc5451eea28d34d0ea5b4ef6486afe7a2b983ac1915aa2`\n\nSource journal: `Research_Cycles/C0632_C0731/journal.json`", "journalDownload": "/sources/f0643e934c6a7443706351fa40040684d915ed0ae25c0f9188a4c4dba12814ff.json"}