{"id": "c1565", "title": "C1565 — Verify consistency of merge order", "filename": "C1565.md", "role": "Research action", "step": 1565, "sha256": "c16ab889acd45b7ded1a17470996e1c50edd69f39d5167efb6695b99ea272323", "bytes": 925, "origins": ["C480–C1634/Research_Cycles/C1483_C1582/c1483_c1582/journal.json#C1565"], "download": "/sources/c16ab889acd45b7ded1a17470996e1c50edd69f39d5167efb6695b99ea272323.md", "format": "md", "derived": true, "tags": [], "excerpt": "Do the two routes through the lower three original legs have the same total local effect?", "content": "# C1565 — Verify consistency of merge order\n\n## Question\n\nDo the two routes through the lower three original legs have the same total local effect?\n\n## Sources\n\n```json\n[]\n```\n\n## Opened utc\n\n2026-09-29T02:42:15.243222+00:00\n\n## Results\n\n```json\n{\n  \"MT\": {\n    \"left\": 4320,\n    \"right\": 4320\n  },\n  \"LXX\": {\n    \"left\": 4320,\n    \"right\": 4320\n  },\n  \"SP\": {\n    \"left\": 4320,\n    \"right\": 4320\n  }\n}\n```\n\n## Finding\n\nBoth routes give4320 in all three cases. The identity D(x,y)+D(x+y,z)=D(y,z)+D(x,y+z) follows by cancellation for any fixedI.\n\n## Reassessment\n\nUse that general relation as explanation of path consistency, not another independentnumerical result.\n\n## Checks\n\n```json\n{}\n```\n\n## Closed utc\n\n2026-09-29T02:42:15.243785+00:00\n\n## Record provenance\n\nExact record hash: `fb6d3c4d630456d92076ff8c20d0d2dc87f6d45a319ca89b90c9105dd09b1740`\n\nSource journal: `Research_Cycles/C1483_C1582/c1483_c1582/journal.json`", "journalDownload": "/sources/7241bc8dee3ba293341214bcb88dc4f80832f7d0207eb9e07f9364c06d3847c8.json"}