{"id": "c500", "title": "C500 — The calendar family’s common measure", "filename": "C500.md", "role": "Research action", "step": 500, "sha256": "8b06402c567646b9fac681b48c94c94f93d5ae0d2cace34815e3f9b1bc08627b", "bytes": 1407, "origins": ["C480–C1634/Research_Cycles/C0482_C0531/journal.json#C500"], "download": "/sources/8b06402c567646b9fac681b48c94c94f93d5ae0d2cace34815e3f9b1bc08627b.md", "format": "md", "derived": true, "tags": ["Calendar Keys"], "excerpt": "Do the three Keys share a conserved quantity despite producing different year counts?", "content": "# C500 — The calendar family’s common measure\n\n## Question\n\nDo the three Keys share a conserved quantity despite producing different year counts?\n\n## Inputs\n\n```json\n{\n  \"ratios\": {\n    \"E\": \"25/23\",\n    \"P\": \"70/69\",\n    \"J\": \"300/299\"\n  },\n  \"year_lengths\": {\n    \"E\": 336,\n    \"P\": 360,\n    \"J\": 364\n  },\n  \"source_seed\": 12558\n}\n```\n\n## Sources\n\n```json\n[\n  \"Strategy §3.3\",\n  \"File52c §3.15\",\n  \"C481\"\n]\n```\n\n## Opened utc\n\n2026-09-27T22:43:36.399128+00:00\n\n## Results\n\n```json\n{\n  \"E\": {\n    \"calibration\": \"8400/23\",\n    \"seed_output\": 13650,\n    \"modeled_day_volume\": 4586400\n  },\n  \"P\": {\n    \"calibration\": \"8400/23\",\n    \"seed_output\": 12740,\n    \"modeled_day_volume\": 4586400\n  },\n  \"J\": {\n    \"calibration\": \"8400/23\",\n    \"seed_output\": 12600,\n    \"modeled_day_volume\": 4586400\n  }\n}\n```\n\n## Finding\n\nAll three use K=8400/23 and give the same modeled day-volume4586400 for seed12558. The reusable rule is K_d(s)=(K/d)s. This explains common measurement, not every selected chronological placement.\n\n## Reassessment\n\nFind the common integral input domain and apply it to the Jared–Noah–Flood field.\n\n## Checks\n\n```json\n{\n  \"calibration\": true,\n  \"volume\": true\n}\n```\n\n## Closed utc\n\n2026-09-27T22:43:36.399427+00:00\n\n## Record provenance\n\nExact record hash: `d42d5541b7b56a6b572d1f47c84cc3c164902a1d8468fc4199f99ad243a12eab`\n\nSource journal: `Research_Cycles/C0482_C0531/journal.json`", "journalDownload": "/sources/6eaeccad4734eff2f6ac20ba847967877b944f9758c53c712ac8b5be2ddf61eb.json", "evidenceLinks": [{"id": "file52c", "title": "File 52c"}]}