{"id": "c1050", "title": "C1050 — Exact-phase and lifespan constraints", "filename": "C1050.md", "role": "Research action", "step": 1050, "sha256": "d885a9a7e008bfe57358d2c2b7af3db08da0717a196e26dd2f316e1d3b369ffe", "bytes": 1061, "origins": ["C480–C1634/Research_Cycles/C0932_C1131/journal.json#C1050"], "download": "/sources/d885a9a7e008bfe57358d2c2b7af3db08da0717a196e26dd2f316e1d3b369ffe.md", "format": "md", "derived": true, "tags": ["Cumulative"], "excerpt": "How do source equalities reduce the array without merging distinct phase policies?", "content": "# C1050 — Exact-phase and lifespan constraints\n\n## Question\n\nHow do source equalities reduce the array without merging distinct phase policies?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"C1048\",\n  \"C1049\",\n  \"File62 §1.3\"\n]\n```\n\n## Opened utc\n\n2026-09-28T04:06:39.794808+00:00\n\n## Results\n\n```json\n{\n  \"dimension_phase_only\": 8,\n  \"dimension_equal_lives_only\": 8,\n  \"dimension_both\": 7,\n  \"exact_phase_residual\": 0,\n  \"whole_year_phase_residual\": 1\n}\n```\n\n## Finding\n\nThe exact7=2×3.5 link and repeated137 life each remove one degree of freedom; together they leave seven. The whole-year phase3 does not satisfy the same equality and stays a separate model.\n\n## Reassessment\n\nGenerate the seven base boundaries from the source lifespan path.\n\n## Checks\n\n```json\n{\n  \"independent_constraints\": true,\n  \"exact_vs_whole\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T04:06:39.795440+00:00\n\n## Record provenance\n\nExact record hash: `6a0b3a36270f54441c0f2c9b1b21816a76866ac87a766052863c10dd837d3e4d`\n\nSource journal: `Research_Cycles/C0932_C1131/journal.json`", "journalDownload": "/sources/f6bdc7aaaaa4fd40f1151b367204ddee7f0f9b77a9c43ae8764831b52d862670.json", "evidenceLinks": [{"id": "d-be42daca1d82dac9", "title": "File 62"}]}