{"id": "c576", "title": "C576 — Generate the quarter-carrier ladder", "filename": "C576.md", "role": "Research action", "step": 576, "sha256": "3df3eee185524cf0411edd6a003b340d7d60c8f9e813b7d54df5659fb863e80a", "bytes": 1307, "origins": ["C480–C1634/Research_Cycles/C0532_C0631/journal.json#C576"], "download": "/sources/3df3eee185524cf0411edd6a003b340d7d60c8f9e813b7d54df5659fb863e80a.md", "format": "md", "derived": true, "tags": [], "excerpt": "Can all five source scales follow from40→40.25?", "content": "# C576 — Generate the quarter-carrier ladder\n\n## Question\n\nCan all five source scales follow from40→40.25?\n\n## Inputs\n\n```json\n{\n  \"multipliers\": [\n    3,\n    10,\n    12,\n    30,\n    300\n  ],\n  \"base_pair\": [\n    40,\n    \"161/4\"\n  ]\n}\n```\n\n## Sources\n\n```json\n[\n  \"File63 §§1.1–1.4,4.6\"\n]\n```\n\n## Opened utc\n\n2026-09-28T00:18:24.889741+00:00\n\n## Results\n\n```json\n{\n  \"multiplier_base_carrier_excess\": [\n    [\n      3,\n      120,\n      \"483/4\",\n      \"3/4\"\n    ],\n    [\n      10,\n      400,\n      \"805/2\",\n      \"5/2\"\n    ],\n    [\n      12,\n      480,\n      483,\n      3\n    ],\n    [\n      30,\n      1200,\n      \"2415/2\",\n      \"15/2\"\n    ],\n    [\n      300,\n      12000,\n      12075,\n      75\n    ]\n  ],\n  \"ratio\": \"161/160\"\n}\n```\n\n## Finding\n\nOne source replacement40→40.25 generates the entire ladder, including480→483 and12000→12075. The quarter-phase carrier is a scalar construction, not an additional biological generation unit.\n\n## Reassessment\n\nCompose the carrier replacement with existing Keys.\n\n## Checks\n\n```json\n{\n  \"constant_ratio\": true,\n  \"excess\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T00:18:24.889995+00:00\n\n## Record provenance\n\nExact record hash: `e99629441764b84e4eac3ad5e1bfeabbd26db83aa4fefeb6fb127742e1df0e15`\n\nSource journal: `Research_Cycles/C0532_C0631/journal.json`", "journalDownload": "/sources/7a2e1117efc741218b68e2db8bb20eadd33cab34e00384e9b903708031da1d2d.json", "evidenceLinks": [{"id": "d-180803601a2db301", "title": "File 63"}]}