{"id": "c982", "title": "C982 — Cap as an irreversible operation", "filename": "C982.md", "role": "Research action", "step": 982, "sha256": "61aad1142bda8b83de08ff32045f3aa789deb3afaa0440ee17d2ac9b9895e13c", "bytes": 1085, "origins": ["C480–C1634/Research_Cycles/C0932_C1131/journal.json#C982"], "download": "/sources/61aad1142bda8b83de08ff32045f3aa789deb3afaa0440ee17d2ac9b9895e13c.md", "format": "md", "derived": true, "tags": ["Inverse"], "excerpt": "Which structural properties distinguish the cap from a frame translation?", "content": "# C982 — Cap as an irreversible operation\n\n## Question\n\nWhich structural properties distinguish the cap from a frame translation?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"C968\",\n  \"C970\",\n  \"C978\"\n]\n```\n\n## Opened utc\n\n2026-09-28T03:51:31.680453+00:00\n\n## Results\n\n```json\n{\n  \"properties\": [\n    \"monotone\",\n    \"idempotent\",\n    \"many-to-one\"\n  ],\n  \"inverse_available\": false,\n  \"domain\": \"resolved count vector with fixed capacity vector\"\n}\n```\n\n## Finding\n\nThe cap is a monotone idempotent projection with demonstrated information loss. The family’s operation grammar therefore includes irreversible maps as well as reversible translations.\n\n## Reassessment\n\nRegenerate the complete source family from the output-free packet and close the block.\n\n## Checks\n\n```json\n{\n  \"idempotent\": true,\n  \"many_to_one\": true,\n  \"monotone_increase\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T03:51:31.680750+00:00\n\n## Record provenance\n\nExact record hash: `c92a1b9d04dd5c54b733e15c157528bc3412a102733741e9dedb918291cbffdf`\n\nSource journal: `Research_Cycles/C0932_C1131/journal.json`", "journalDownload": "/sources/f6bdc7aaaaa4fd40f1151b367204ddee7f0f9b77a9c43ae8764831b52d862670.json"}