{"id": "c777", "title": "C777 — Derive the whole interval-response law", "filename": "C777.md", "role": "Research action", "step": 777, "sha256": "3f082f3bd729dbedc85545b65935ab68a5f7828f45d4f22ddc02d5007ef0413d", "bytes": 1443, "origins": ["C480–C1634/Research_Cycles/C0732_C0831/journal.json#C777"], "download": "/sources/3f082f3bd729dbedc85545b65935ab68a5f7828f45d4f22ddc02d5007ef0413d.md", "format": "md", "derived": true, "tags": [], "excerpt": "Which switches can affect a given interval?", "content": "# C777 — Derive the whole interval-response law\n\n## Question\n\nWhich switches can affect a given interval?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"C772–776\"\n]\n```\n\n## Opened utc\n\n2026-09-28T02:00:47.995272+00:00\n\n## Results\n\n```json\n{\n  \"formula\": \"delta span =215 ds(S_i−S_j)+60 dt(T_i−T_j)+130 dc(H_i−H_j)\",\n  \"examples\": {\n    \"Adam→Arphaxad\": {\n      \"000\": 1658,\n      \"001\": 1658,\n      \"010\": 1658,\n      \"011\": 1658,\n      \"100\": 1658,\n      \"101\": 1658,\n      \"110\": 1658,\n      \"111\": 1658\n    },\n    \"Arphaxad→Shelah\": {\n      \"000\": 35,\n      \"001\": 165,\n      \"010\": 35,\n      \"011\": 165,\n      \"100\": 35,\n      \"101\": 165,\n      \"110\": 35,\n      \"111\": 165\n    },\n    \"Terah→Abraham\": {\n      \"000\": 70,\n      \"001\": 70,\n      \"010\": 130,\n      \"011\": 130,\n      \"100\": 70,\n      \"101\": 70,\n      \"110\": 130,\n      \"111\": 130\n    }\n  },\n  \"dependent_comparisons\": 4560\n}\n```\n\n## Finding\n\nIntervals inside one support block are invariant; intervals crossing a hinge detect exactly that hinge. The entire finite family follows one incidence rule.\n\n## Reassessment\n\nTest matched configurations on the newly aligned SP/LXX birth suffix.\n\n## Checks\n\n```json\n{\n  \"whole_family\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T02:00:48.000725+00:00\n\n## Record provenance\n\nExact record hash: `ea806725fe23d742f5b493cf686ee6d48e2df963e9758ca425675b1623099ef0`\n\nSource journal: `Research_Cycles/C0732_C0831/journal.json`", "journalDownload": "/sources/8ea2b882289fbcea5cf11177923617f0c1d1ad7e6eaa3bffb174c6f89699d97d.json"}