{"id": "c1466", "title": "C1466 — Measure stage–Key interaction", "filename": "C1466.md", "role": "Research action", "step": 1466, "sha256": "e7e2fbb72fe0fa84fe884f8645b6a124d075d0cb60646d2748cac34e6f193b94", "bytes": 1336, "origins": ["C480–C1634/Research_Cycles/C1433_C1482/journal.json#C1466"], "download": "/sources/e7e2fbb72fe0fa84fe884f8645b6a124d075d0cb60646d2748cac34e6f193b94.md", "format": "md", "derived": true, "tags": ["Regular", "Cumulative", "Inverse", "Covenant"], "excerpt": "Does translating a spine by2700 commute with the existing anchored Key relations?", "content": "# C1466 — Measure stage–Key interaction\n\n## Question\n\nDoes translating a spine by2700 commute with the existing anchored Key relations?\n\n## Sources\n\n```json\n[\n  \"Universal stage law\",\n  \"C1432 Covenant map\",\n  \"LXX paired join\"\n]\n```\n\n## Opened utc\n\n2026-09-29T01:19:39.213431+00:00\n\n## Results\n\n```json\n{\n  \"Covenant_two_stage_image\": \"257168/23\",\n  \"SP_two_stage_target\": 11416,\n  \"Covenant_two_stage_residual\": \"-5400/23\",\n  \"LXX_two_stage_regular_join\": \"14278/23\",\n  \"LXX_two_stage_cumulative_join\": \"14278/23\",\n  \"positive_stage_commutator\": \"5400/23\",\n  \"correction\": \"The first expectation used the positive-stage sign. Reducing both heads by2700 gives residual−5400/23, not+5400/23; no input changed.\"\n}\n```\n\n## Finding\n\nKeeping Covenant1866 fixed sends the two-stage LXX head5400/23 later than the SP target (signed residual−5400/23). The LXX paired join remains equal between modes at14278/23.\n\n## Reassessment\n\nGroup successful equalities and exact misses into a compact explanatory dependency structure.\n\n## Checks\n\n```json\n{\n  \"negative_residual_exact\": true,\n  \"LXX_pair_still_equal\": true\n}\n```\n\n## Closed utc\n\n2026-09-29T01:20:19.733340+00:00\n\n## Record provenance\n\nExact record hash: `df68b26433259fb63de992932047d66f9d1f759ea57a6f5802937d7aa7162783`\n\nSource journal: `Research_Cycles/C1433_C1482/journal.json`", "journalDownload": "/sources/ca542c4d870fa9b9292d3dd24718f08766a5353e1b27cbb1e7c0d69061b00ecf.json"}