{"id": "c495", "title": "C495 — Rounded chronology as path evaluation", "filename": "C495.md", "role": "Research action", "step": 495, "sha256": "6f9f2b10cbe5e99e7c034ec9b2bcc81635783f645629b879b93a53a6502387ab", "bytes": 1617, "origins": ["C480–C1634/Research_Cycles/C0482_C0531/journal.json#C495"], "download": "/sources/6f9f2b10cbe5e99e7c034ec9b2bcc81635783f645629b879b93a53a6502387ab.md", "format": "md", "derived": true, "tags": ["Regular", "Cumulative", "Rounded", "Inverse"], "excerpt": "Can one rule explain both convergence and the LXX miss?", "content": "# C495 — Rounded chronology as path evaluation\n\n## Question\n\nCan one rule explain both convergence and the LXX miss?\n\n## Inputs\n\n```json\n{\n  \"anchor\": 1406,\n  \"paths\": {\n    \"MT_regular\": [\n      1650,\n      1050\n    ],\n    \"MT_cumulative\": [\n      9170,\n      3430\n    ],\n    \"LXX_regular\": [\n      2250,\n      1830\n    ]\n  }\n}\n```\n\n## Sources\n\n```json\n[\n  \"File52c §3.3\",\n  \"C489\"\n]\n```\n\n## Opened utc\n\n2026-09-27T22:42:21.243193+00:00\n\n## Results\n\n```json\n{\n  \"rule\": \"V_a(path)=a+sum I(segment); chi(path)=sum(I(segment)-segment)\",\n  \"paths\": {\n    \"MT_regular\": {\n      \"raw_total\": 2700,\n      \"reversal_gain\": 7920,\n      \"evaluated_endpoint\": 12026\n    },\n    \"MT_cumulative\": {\n      \"raw_total\": 12600,\n      \"reversal_gain\": -1980,\n      \"evaluated_endpoint\": 12026\n    },\n    \"LXX_regular\": {\n      \"raw_total\": 4080,\n      \"reversal_gain\": 4950,\n      \"evaluated_endpoint\": 10436\n    }\n  },\n  \"composition\": \"chi(P followed by Q)=chi(P)+chi(Q), for an admitted concatenation\"\n}\n```\n\n## Finding\n\nPath gains are additive over retained segment lists. The MT regular gain7920 and cumulative gain−1980 offset their original9900 difference; LXX has different gains. Forgetting the partition discards necessary input.\n\n## Reassessment\n\nMeasure the exact effect of only the source-admitted Noah and Shem refinements.\n\n## Checks\n\n```json\n{\n  \"MT_convergence\": true,\n  \"LXX_miss\": true\n}\n```\n\n## Closed utc\n\n2026-09-27T22:42:21.243412+00:00\n\n## Record provenance\n\nExact record hash: `8a4cd775dc33fc52edf7cde89eb38e1dff9f3e623e580d94d57784d9a342abdf`\n\nSource journal: `Research_Cycles/C0482_C0531/journal.json`", "journalDownload": "/sources/6eaeccad4734eff2f6ac20ba847967877b944f9758c53c712ac8b5be2ddf61eb.json", "evidenceLinks": [{"id": "file52c", "title": "File 52c"}]}