{"id": "c639", "title": "C639 — Solve the two-calendar compatibility equation", "filename": "C639.md", "role": "Research action", "step": 639, "sha256": "5674fcaf82ffcf41e37c30517b845718db5cf90f9591f7c901dd487c97710e5f", "bytes": 1321, "origins": ["C480–C1634/Research_Cycles/C0632_C0731/journal.json#C639"], "download": "/sources/5674fcaf82ffcf41e37c30517b845718db5cf90f9591f7c901dd487c97710e5f.md", "format": "md", "derived": true, "tags": ["Calendar Keys"], "excerpt": "What count family permits an Enochian corresponding span and a Priestly minimum fourteen years shorter?", "content": "# C639 — Solve the two-calendar compatibility equation\n\n## Question\n\nWhat count family permits an Enochian corresponding span and a Priestly minimum fourteen years shorter?\n\n## Inputs\n\n```json\n{\n  \"equation\": \"182m−14=168n\",\n  \"positive_integer_counts\": true\n}\n```\n\n## Sources\n\n```json\n[\n  \"Derived from File70 §6 source geometry\"\n]\n```\n\n## Opened utc\n\n2026-09-28T00:58:22.881303+00:00\n\n## Results\n\n```json\n{\n  \"reduced_equation\": \"13m−12n=1\",\n  \"general_solution\": \"m=1+12q; n=1+13q\",\n  \"examples_m_n\": [\n    [\n      1,\n      1\n    ],\n    [\n      13,\n      14\n    ],\n    [\n      25,\n      27\n    ],\n    [\n      37,\n      40\n    ]\n  ],\n  \"source_choice_q\": 1\n}\n```\n\n## Finding\n\nThe pair of calendar requirements has an infinite integer family. Its source member is m=13,n=14; the smaller m=n=1 also fits the two-calendar equation. The exposure condition must supply any stronger selection.\n\n## Reassessment\n\nAdd the fixed thirteen-year exposure flanks and solve the complete three-calendar system.\n\n## Checks\n\n```json\n{\n  \"examples\": true,\n  \"source_member\": true,\n  \"not_unique_pair\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T00:58:22.881481+00:00\n\n## Record provenance\n\nExact record hash: `2d75bc9bfb77ad832fbb24b55007d44225e7432b192eeef77c2166cdfd940f33`\n\nSource journal: `Research_Cycles/C0632_C0731/journal.json`", "journalDownload": "/sources/f0643e934c6a7443706351fa40040684d915ed0ae25c0f9188a4c4dba12814ff.json", "evidenceLinks": [{"id": "d-0fa80217c94b3951", "title": "File 70"}]}