{"id": "c776", "title": "C776 — Test the finite switch algebra", "filename": "C776.md", "role": "Research action", "step": 776, "sha256": "c4585998a94b48a79fdf5039549e1bf4808a9338a64eefe7c914132ed64c8867", "bytes": 1010, "origins": ["C480–C1634/Research_Cycles/C0732_C0831/journal.json#C776"], "download": "/sources/c4585998a94b48a79fdf5039549e1bf4808a9338a64eefe7c914132ed64c8867.md", "format": "md", "derived": true, "tags": [], "excerpt": "Do variant switches commute without becoming unlimited translations?", "content": "# C776 — Test the finite switch algebra\n\n## Question\n\nDo variant switches commute without becoming unlimited translations?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"C772–775\"\n]\n```\n\n## Opened utc\n\n2026-09-28T02:00:33.461502+00:00\n\n## Results\n\n```json\n{\n  \"state_count\": 8,\n  \"switch_amount_rule\": \"weight*(1−2*current_bit)*support_mask\",\n  \"domain\": \"finite source labels; not repeated positive additions\"\n}\n```\n\n## Finding\n\nThe three switches commute and undo themselves on binary state labels. Their numeric direction changes on return; this supplies a bounded configuration rather than an unrestricted translation rule.\n\n## Reassessment\n\nUse support differences to predict entire interval responses.\n\n## Checks\n\n```json\n{\n  \"involutions\": true,\n  \"commutation\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T02:00:33.461832+00:00\n\n## Record provenance\n\nExact record hash: `a3328635745bd28704c6b914c97cc5d930d6754f75bf209c21ab50d060c3260b`\n\nSource journal: `Research_Cycles/C0732_C0831/journal.json`", "journalDownload": "/sources/8ea2b882289fbcea5cf11177923617f0c1d1ad7e6eaa3bffb174c6f89699d97d.json"}