{"id": "c755", "title": "C755 — Invert and classify the MT residual field", "filename": "C755.md", "role": "Research action", "step": 755, "sha256": "ac24b4786db89a438824f16e362b1b854c7df87490f9b1999ba70a9ac18c30a6", "bytes": 1721, "origins": ["C480–C1634/Research_Cycles/C0732_C0831/journal.json#C755"], "download": "/sources/ac24b4786db89a438824f16e362b1b854c7df87490f9b1999ba70a9ac18c30a6.md", "format": "md", "derived": true, "tags": ["Rounded", "Inverse", "Covenant"], "excerpt": "Which entire interval families survive rounding exactly?", "content": "# C755 — Invert and classify the MT residual field\n\n## Question\n\nWhich entire interval families survive rounding exactly?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"C754\"\n]\n```\n\n## Opened utc\n\n2026-09-28T01:54:10.979733+00:00\n\n## Results\n\n```json\n{\n  \"recovered_e\": [\n    0,\n    -2,\n    0,\n    0,\n    0,\n    -2,\n    0,\n    1,\n    -2,\n    0,\n    0,\n    2,\n    2,\n    1,\n    1,\n    1,\n    0,\n    2,\n    0,\n    0,\n    0,\n    -2,\n    -2,\n    2,\n    -2,\n    0\n  ],\n  \"equal_residual_classes\": {\n    \"-4\": [\n      \"Terah\",\n      \"Abraham\",\n      \"Isaac\",\n      \"Jacob\"\n    ],\n    \"-2\": [\n      \"Serug\",\n      \"Nahor\",\n      \"Levi\",\n      \"Amram\"\n    ],\n    \"-1\": [\n      \"Reu\"\n    ],\n    \"0\": [\n      \"Adam\",\n      \"Seth\",\n      \"Peleg\",\n      \"Kohath\",\n      \"Moses\",\n      \"terminal1406\"\n    ],\n    \"1\": [\n      \"Eber\"\n    ],\n    \"2\": [\n      \"Enosh\",\n      \"Kenan\",\n      \"Mahalalel\",\n      \"Jared\"\n    ],\n    \"3\": [\n      \"Lamech\",\n      \"Shelah\"\n    ],\n    \"4\": [\n      \"Enoch\",\n      \"Methuselah\"\n    ],\n    \"5\": [\n      \"Noah\",\n      \"Shem\",\n      \"Arphaxad\"\n    ]\n  },\n  \"interval_rule\": \"rounded(i,j)-actual(i,j)=D_i-D_j\"\n}\n```\n\n## Finding\n\nEvery pair within one residual class preserves its interval. These are consequences of one field, not independent numerical hits. Adjacent differences recover every row residual.\n\n## Reassessment\n\nTransfer the full residual operator to LXX and isolate changed row support.\n\n## Checks\n\n```json\n{\n  \"inverse\": true,\n  \"interval_identity\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T01:54:10.980078+00:00\n\n## Record provenance\n\nExact record hash: `b6b9a4bf00039ec2e00aea2aa885f410548a951dd6d84a46c3b6972ca86ae596`\n\nSource journal: `Research_Cycles/C0732_C0831/journal.json`", "journalDownload": "/sources/8ea2b882289fbcea5cf11177923617f0c1d1ad7e6eaa3bffb174c6f89699d97d.json"}