{"id": "c1464", "title": "C1464 — Explain the LXX paired-Key join by its mode gap", "filename": "C1464.md", "role": "Research action", "step": 1464, "sha256": "788608dcd6f8691990191714f6227d8ed38c113e1bcdc73378022c677f770c9a", "bytes": 1083, "origins": ["C480–C1634/Research_Cycles/C1433_C1482/journal.json#C1464"], "download": "/sources/788608dcd6f8691990191714f6227d8ed38c113e1bcdc73378022c677f770c9a.md", "format": "md", "derived": true, "tags": ["Regular", "Cumulative", "Calendar Keys"], "excerpt": "Why do LXX cumulative-to-Exodus and regular-to-Conquest Priestly routes meet at386?", "content": "# C1464 — Explain the LXX paired-Key join by its mode gap\n\n## Question\n\nWhy do LXX cumulative-to-Exodus and regular-to-Conquest Priestly routes meet at386?\n\n## Sources\n\n```json\n[\n  \"Comparative Study §4.3\",\n  \"LXX mode difference500\"\n]\n```\n\n## Opened utc\n\n2026-09-29T01:19:39.207475+00:00\n\n## Results\n\n```json\n{\n  \"head_gap\": 500,\n  \"target_gap\": 40,\n  \"head_gap_required\": 500,\n  \"regular_output\": 386,\n  \"cumulative_output\": 386,\n  \"output_difference_formula\": 0\n}\n```\n\n## Finding\n\nThe500-year LXX head gap is exactly(25/2)×40, the condition for the two head-held Priestly routes to share a target. The known386 join is an algebraic expression of that compatibility.\n\n## Reassessment\n\nApply the same fixed Exodus/Conquest comparison to the other two manuscripts, retaining every result.\n\n## Checks\n\n```json\n{\n  \"join386\": true,\n  \"criterion_exact\": true\n}\n```\n\n## Closed utc\n\n2026-09-29T01:19:39.208000+00:00\n\n## Record provenance\n\nExact record hash: `1c8a743eadabf9a6b202e7e68b557c234c8bdefba8afa10963f98bd9df4dbbd8`\n\nSource journal: `Research_Cycles/C1433_C1482/journal.json`", "journalDownload": "/sources/ca542c4d870fa9b9292d3dd24718f08766a5353e1b27cbb1e7c0d69061b00ecf.json"}