{"id": "c741", "title": "C741 — Recover SP local changes from its boundary profile", "filename": "C741.md", "role": "Research action", "step": 741, "sha256": "3b04d071ce23d4ae0faf522fa1ba61737d54dac029a2da438746e6ae673ce0aa", "bytes": 1828, "origins": ["C480–C1634/Research_Cycles/C0732_C0831/journal.json#C741"], "download": "/sources/3b04d071ce23d4ae0faf522fa1ba61737d54dac029a2da438746e6ae673ce0aa.md", "format": "md", "derived": true, "tags": ["Regular", "Cumulative", "Counts & NT"], "excerpt": "Which source rows and counting terms generateSP’s entire displacement staircase?", "content": "# C741 — Recover SP local changes from its boundary profile\n\n## Question\n\nWhich source rows and counting terms generateSP’s entire displacement staircase?\n\n## Inputs\n\n```json\n{\n  \"profile\": \"SPminusMT\",\n  \"Lamech_regular\": \"53counted versus52completed\"\n}\n```\n\n## Sources\n\n```json\n[\n  \"C739; File18 §§3.1–3.2,6C\"\n]\n```\n\n## Opened utc\n\n2026-09-28T01:44:42.031795+00:00\n\n## Results\n\n```json\n{\n  \"nonzero_edge_changes\": {\n    \"R\": {\n      \"Jared\": -100,\n      \"Methuselah\": -120,\n      \"Lamech\": -130,\n      \"Arphaxad\": 100,\n      \"Shelah\": 100,\n      \"Eber\": 100,\n      \"Peleg\": 100,\n      \"Reu\": 100,\n      \"Serug\": 100,\n      \"Nahor\": 50\n    },\n    \"C_lower\": {\n      \"Jared\": -115,\n      \"Methuselah\": -249,\n      \"Lamech\": -124,\n      \"Eber\": -60,\n      \"Terah\": -60\n    },\n    \"G\": {\n      \"Jared\": -15,\n      \"Methuselah\": -129,\n      \"Lamech\": 6,\n      \"Arphaxad\": -100,\n      \"Shelah\": -100,\n      \"Eber\": -160,\n      \"Peleg\": -100,\n      \"Reu\": -100,\n      \"Serug\": -100,\n      \"Nahor\": -50,\n      \"Terah\": -60\n    }\n  },\n  \"Lamech_regular_decomposition\": [\n    -129,\n    -1\n  ]\n}\n```\n\n## Finding\n\nTheSP profile localizes its regular130-yearLamech difference as129 from the nominal age plus one completed-year correction. Cumulative support remains the five lifespan changes. The whole staircase therefore explains both the shared plateaus and the different mode response.\n\n## Reassessment\n\nTest the entire post-ShelahLXX/SP family where births agree but cumulative coordinates differ.\n\n## Checks\n\n```json\n{\n  \"Lamech_regular\": true,\n  \"cumulative_support\": true,\n  \"support_locality\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T01:44:42.032103+00:00\n\n## Record provenance\n\nExact record hash: `11bd6ee787eb179e42d7df33609e7119948470bbaa6808679f8696da8e44c2f2`\n\nSource journal: `Research_Cycles/C0732_C0831/journal.json`", "journalDownload": "/sources/8ea2b882289fbcea5cf11177923617f0c1d1ad7e6eaa3bffb174c6f89699d97d.json", "evidenceLinks": [{"id": "d-68301ab760bfbe2e", "title": "File 18"}]}