{"id": "c758", "title": "C758 — Classify cross-tradition interval preservation", "filename": "C758.md", "role": "Research action", "step": 758, "sha256": "4035b194ddeaf9d375f87551e056703053ac76ac7246090a20270175e053a83b", "bytes": 2085, "origins": ["C480–C1634/Research_Cycles/C0732_C0831/journal.json#C758"], "download": "/sources/4035b194ddeaf9d375f87551e056703053ac76ac7246090a20270175e053a83b.md", "format": "md", "derived": true, "tags": ["Rounded", "Covenant"], "excerpt": "When does rounding preserve a difference between traditions?", "content": "# C758 — Classify cross-tradition interval preservation\n\n## Question\n\nWhen does rounding preserve a difference between traditions?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"C754–757\"\n]\n```\n\n## Opened utc\n\n2026-09-28T01:55:25.793261+00:00\n\n## Results\n\n```json\n{\n  \"comparison_classes\": {\n    \"LXX_native_ON\": {\n      \"-4\": [\n        \"Noah\",\n        \"Shem\",\n        \"Arphaxad\"\n      ],\n      \"-2\": [\n        \"Shelah\"\n      ],\n      \"0\": [\n        \"Adam\",\n        \"Seth\",\n        \"Enosh\",\n        \"Kenan\",\n        \"Mahalalel\",\n        \"Jared\",\n        \"Enoch\",\n        \"Methuselah\",\n        \"Lamech\",\n        \"Eber\",\n        \"Peleg\",\n        \"Reu\",\n        \"Serug\",\n        \"Nahor\",\n        \"Terah\",\n        \"Abraham\",\n        \"Isaac\",\n        \"Jacob\",\n        \"Levi\",\n        \"Kohath\",\n        \"Amram\",\n        \"Moses\"\n      ]\n    },\n    \"SP_native_OFF\": {\n      \"0\": [\n        \"Noah\",\n        \"Shem\",\n        \"Arphaxad\",\n        \"Shelah\",\n        \"Eber\",\n        \"Peleg\",\n        \"Reu\",\n        \"Serug\",\n        \"Nahor\",\n        \"Terah\",\n        \"Abraham\",\n        \"Isaac\",\n        \"Jacob\",\n        \"Levi\",\n        \"Kohath\",\n        \"Amram\",\n        \"Moses\"\n      ],\n      \"3\": [\n        \"Adam\",\n        \"Seth\",\n        \"Enosh\",\n        \"Kenan\",\n        \"Mahalalel\",\n        \"Jared\",\n        \"Enoch\",\n        \"Methuselah\"\n      ],\n      \"4\": [\n        \"Lamech\"\n      ]\n    }\n  },\n  \"criterion\": \"DeltaD_i=DeltaD_j iff the cross-tradition interval difference is unchanged by rounding\"\n}\n```\n\n## Finding\n\nEqual comparison-residual plateaus identify complete preserved interval families. Cross-tradition compatibility follows from two local field values, without a new list of isolated matches.\n\n## Reassessment\n\nTest whether admitted Cainan insertion preserves these residual fields.\n\n## Checks\n\n```json\n{\n  \"LXX_classes\": true,\n  \"SP_classes\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T01:55:25.793611+00:00\n\n## Record provenance\n\nExact record hash: `5180a2af056b70ea8608a815c5c40b7409cfcd39df4f1881d14a4d897f01219f`\n\nSource journal: `Research_Cycles/C0732_C0831/journal.json`", "journalDownload": "/sources/8ea2b882289fbcea5cf11177923617f0c1d1ad7e6eaa3bffb174c6f89699d97d.json"}