{"id": "c968", "title": "C968 — The inverse image of a capped life", "filename": "C968.md", "role": "Research action", "step": 968, "sha256": "1775a114b238b29df2d7dfb7c699640583b5066f375ee799854bbc91e3a64ec9", "bytes": 1706, "origins": ["C480–C1634/Research_Cycles/C0932_C1131/journal.json#C968"], "download": "/sources/1775a114b238b29df2d7dfb7c699640583b5066f375ee799854bbc91e3a64ec9.md", "format": "md", "derived": true, "tags": ["Cumulative", "Inverse"], "excerpt": "What does a capped output reveal about its input lifespan?", "content": "# C968 — The inverse image of a capped life\n\n## Question\n\nWhat does a capped output reveal about its input lifespan?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"C955\",\n  \"C956\"\n]\n```\n\n## Opened utc\n\n2026-09-28T03:49:07.314488+00:00\n\n## Results\n\n```json\n{\n  \"inverse_conditions\": [\n    {\n      \"row\": 0,\n      \"output\": 930,\n      \"input_condition\": \"equals 930\"\n    },\n    {\n      \"row\": 1,\n      \"output\": 912,\n      \"input_condition\": \"equals 912\"\n    },\n    {\n      \"row\": 2,\n      \"output\": 905,\n      \"input_condition\": \"equals 905\"\n    },\n    {\n      \"row\": 3,\n      \"output\": 910,\n      \"input_condition\": \"equals 910\"\n    },\n    {\n      \"row\": 4,\n      \"output\": 895,\n      \"input_condition\": \"equals 895\"\n    },\n    {\n      \"row\": 5,\n      \"output\": 847,\n      \"input_condition\": \"at least 847\"\n    },\n    {\n      \"row\": 6,\n      \"output\": 365,\n      \"input_condition\": \"equals 365\"\n    },\n    {\n      \"row\": 7,\n      \"output\": 720,\n      \"input_condition\": \"at least 720\"\n    },\n    {\n      \"row\": 8,\n      \"output\": 653,\n      \"input_condition\": \"at least 653\"\n    }\n  ],\n  \"exactly_recovered_rows\": [\n    0,\n    1,\n    2,\n    3,\n    4,\n    6\n  ]\n}\n```\n\n## Finding\n\nSix uncapped inputs are recoverable exactly; each clipped input is only bounded below. Clipping loses the original excess.\n\n## Reassessment\n\nTest whether even a supplied ancestral multiset restores the three lost row placements.\n\n## Checks\n\n```json\n{\n  \"six_exact\": true,\n  \"three_bounds\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T03:49:07.314754+00:00\n\n## Record provenance\n\nExact record hash: `bdd39456ef8857a2fc4fdb24e478bf4bbfa088762bcd8e93f8346ae41d785ca6`\n\nSource journal: `Research_Cycles/C0932_C1131/journal.json`", "journalDownload": "/sources/f6bdc7aaaaa4fd40f1151b367204ddee7f0f9b77a9c43ae8764831b52d862670.json"}