{"id": "c688", "title": "C688 — Explain the two completed volume registers", "filename": "C688.md", "role": "Research action", "step": 688, "sha256": "5a8c64504bae19b4a50433012960c811f16a7b39465607dd4579670a120dee18", "bytes": 1217, "origins": ["C480–C1634/Research_Cycles/C0632_C0731/journal.json#C688"], "download": "/sources/5a8c64504bae19b4a50433012960c811f16a7b39465607dd4579670a120dee18.md", "format": "md", "derived": true, "tags": ["Calendar Keys"], "excerpt": "What operation distinguishes12600 from12740 at the same35 count?", "content": "# C688 — Explain the two completed volume registers\n\n## Question\n\nWhat operation distinguishes12600 from12740 at the same35 count?\n\n## Inputs\n\n```json\n{\n  \"count\": 35,\n  \"calendar_lengths\": [\n    360,\n    364\n  ],\n  \"root_volume\": 12558\n}\n```\n\n## Sources\n\n```json\n[\n  \"Supplement A §6\"\n]\n```\n\n## Opened utc\n\n2026-09-28T01:13:50.854956+00:00\n\n## Results\n\n```json\n{\n  \"volumes\": [\n    12600,\n    12740\n  ],\n  \"difference\": 140,\n  \"calendar_ratio\": \"91/90\",\n  \"cross_products\": [\n    4586400,\n    4586400\n  ],\n  \"root_outputs\": [\n    12600,\n    12740\n  ]\n}\n```\n\n## Finding\n\nThe12600/12740 pair uses the same completed count35 with360/364 calendar lengths. Their ratio91/90 and shared cross-product follow from this construction; the product is a register equality, not an additional chronology or independent witness.\n\n## Reassessment\n\nAccount for the PhaseNorm40 volume and its residual relative to12600.\n\n## Checks\n\n```json\n{\n  \"outputs\": true,\n  \"difference\": true,\n  \"cross_products\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T01:13:50.855260+00:00\n\n## Record provenance\n\nExact record hash: `6a57b724fbf99b68c4140eb5feef5e5089bec76a4cf0b92c0e3e3e75c48f3ba4`\n\nSource journal: `Research_Cycles/C0632_C0731/journal.json`", "journalDownload": "/sources/f0643e934c6a7443706351fa40040684d915ed0ae25c0f9188a4c4dba12814ff.json"}