{"id": "c687", "title": "C687 — Connect micro volume to the Actual/Rounded span", "filename": "C687.md", "role": "Research action", "step": 687, "sha256": "9ecbd3cd70dfeac796ea410d81b4e8e7bea43c65f2de14fcb8cc160e0468e907", "bytes": 1322, "origins": ["C480–C1634/Research_Cycles/C0632_C0731/journal.json#C687"], "download": "/sources/9ecbd3cd70dfeac796ea410d81b4e8e7bea43c65f2de14fcb8cc160e0468e907.md", "format": "md", "derived": true, "tags": ["Cumulative", "Rounded", "Calendar Keys"], "excerpt": "Which equation explains the matching12558→12600 structure across scales?", "content": "# C687 — Connect micro volume to the Actual/Rounded span\n\n## Question\n\nWhich equation explains the matching12558→12600 structure across scales?\n\n## Inputs\n\n```json\n{\n  \"micro_count\": \"69/2\",\n  \"calendar\": 364,\n  \"Actual_pair\": [\n    14004,\n    1446\n  ],\n  \"Rounded_pair\": [\n    14006,\n    1406\n  ]\n}\n```\n\n## Sources\n\n```json\n[\n  \"Supplement A §6; File52c latest; C631 Actual/Rounded interface\"\n]\n```\n\n## Opened utc\n\n2026-09-28T01:13:40.622784+00:00\n\n## Results\n\n```json\n{\n  \"micro_volume_days\": 12558,\n  \"Actual_elapsed_years\": 12558,\n  \"J_completed_numeric\": 12600,\n  \"Rounded_elapsed_years\": 12600,\n  \"identity\": \"J(364s)=360P(s)\"\n}\n```\n\n## Finding\n\nThe micro volume34.5×364 and Actual cumulative interval share the numerical input12558. Their12600 completion follows from364J=360P. This is a common conversion structure across distinct units; the Rounded14006/1406 pair supplies its own endpoint realization.\n\n## Reassessment\n\nDetermine why the alternative12740 register is a different calendar choice.\n\n## Checks\n\n```json\n{\n  \"shared_input\": true,\n  \"completion\": true,\n  \"identity\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T01:13:40.623049+00:00\n\n## Record provenance\n\nExact record hash: `332b3727acd8634833ea09bc05e689c5955eb17f94f698ba4696e00946bdaf58`\n\nSource journal: `Research_Cycles/C0632_C0731/journal.json`", "journalDownload": "/sources/f0643e934c6a7443706351fa40040684d915ed0ae25c0f9188a4c4dba12814ff.json", "evidenceLinks": [{"id": "file52c", "title": "File 52c"}]}