{"id": "c552", "title": "C552 — Generate the cumulative root family", "filename": "C552.md", "role": "Research action", "step": 552, "sha256": "f571c54a3f372a08aa26086d3c1beb883a3a4fdec7cd8ccd83e95435e5ccd1ff", "bytes": 1736, "origins": ["C480–C1634/Research_Cycles/C0532_C0631/journal.json#C552"], "download": "/sources/f571c54a3f372a08aa26086d3c1beb883a3a4fdec7cd8ccd83e95435e5ccd1ff.md", "format": "md", "derived": true, "tags": ["Cumulative", "Covenant"], "excerpt": "Does one affine rule reconstruct all six source rails?", "content": "# C552 — Generate the cumulative root family\n\n## Question\n\nDoes one affine rule reconstruct all six source rails?\n\n## Inputs\n\n```json\n{\n  \"base\": [\n    2435,\n    2260,\n    2080,\n    1933,\n    1796,\n    1663,\n    1526\n  ],\n  \"phases\": [\n    0,\n    \"7/2\"\n  ],\n  \"clutch\": [\n    0,\n    7,\n    14\n  ]\n}\n```\n\n## Sources\n\n```json\n[\n  \"File62 §§1.2–1.4; File61 §§7.3A–7.6\"\n]\n```\n\n## Opened utc\n\n2026-09-28T00:12:31.275020+00:00\n\n## Results\n\n```json\n{\n  \"rails\": [\n    [\n      2435,\n      2260,\n      2080,\n      1933,\n      1796,\n      1663,\n      1526\n    ],\n    [\n      2428,\n      2253,\n      2073,\n      1926,\n      1789,\n      1656,\n      1519\n    ],\n    [\n      2421,\n      2246,\n      2066,\n      1919,\n      1782,\n      1649,\n      1512\n    ],\n    [\n      \"4877/2\",\n      \"4527/2\",\n      \"4167/2\",\n      \"3873/2\",\n      \"3599/2\",\n      \"3333/2\",\n      \"3059/2\"\n    ],\n    [\n      \"4863/2\",\n      \"4513/2\",\n      \"4153/2\",\n      \"3859/2\",\n      \"3585/2\",\n      \"3319/2\",\n      \"3045/2\"\n    ],\n    [\n      \"4849/2\",\n      \"4499/2\",\n      \"4139/2\",\n      \"3845/2\",\n      \"3571/2\",\n      \"3305/2\",\n      \"3031/2\"\n    ]\n  ],\n  \"coordinate_matches\": 42\n}\n```\n\n## Finding\n\nC(p,d)=C0+p−d reconstructs all42 source coordinates. This is one family generated from seven inputs and two local state parameters, not42 independent successes.\n\n## Reassessment\n\nEstablish why the source clutch is14 and whether its three envelopes are independent.\n\n## Checks\n\n```json\n{\n  \"six_rails\": true,\n  \"invariant_spans\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T00:12:31.275664+00:00\n\n## Record provenance\n\nExact record hash: `ed4d4ba1528f03351c874e6224383840e9da8b1b703b22a8c50818d742eda54a`\n\nSource journal: `Research_Cycles/C0532_C0631/journal.json`", "journalDownload": "/sources/7a2e1117efc741218b68e2db8bb20eadd33cab34e00384e9b903708031da1d2d.json", "evidenceLinks": [{"id": "d-be42daca1d82dac9", "title": "File 62"}, {"id": "d-d580afd48d6e12d6", "title": "File 61"}]}