{"id": "c594", "title": "C594 — Derive grid translation and carrier laws", "filename": "C594.md", "role": "Research action", "step": 594, "sha256": "1b9cc49d50803e4bfb1840893e2bb2dbe4ce978f4d5c748b815338d5151c9eb4", "bytes": 1520, "origins": ["C480–C1634/Research_Cycles/C0532_C0631/journal.json#C594"], "download": "/sources/1b9cc49d50803e4bfb1840893e2bb2dbe4ce978f4d5c748b815338d5151c9eb4.md", "format": "md", "derived": true, "tags": [], "excerpt": "Which operations commute, and why do companion rails converge?", "content": "# C594 — Derive grid translation and carrier laws\n\n## Question\n\nWhich operations commute, and why do companion rails converge?\n\n## Inputs\n\n```json\n{\n  \"rows\": 49,\n  \"carriers\": [\n    70,\n    72\n  ],\n  \"civil_translation\": 110\n}\n```\n\n## Sources\n\n```json\n[\n  \"File68 Appendix C; C593\"\n]\n```\n\n## Opened utc\n\n2026-09-28T00:23:08.448006+00:00\n\n## Results\n\n```json\n{\n  \"BC_carrier_gaps\": [\n    98,\n    96,\n    94,\n    92,\n    90,\n    88,\n    86,\n    84,\n    82,\n    80,\n    78,\n    76,\n    74,\n    72,\n    70,\n    68,\n    66,\n    64,\n    62,\n    60,\n    58,\n    56,\n    54,\n    52,\n    50,\n    48,\n    46,\n    44,\n    42,\n    40,\n    38,\n    36,\n    34,\n    32,\n    30,\n    28,\n    26,\n    24,\n    22,\n    20,\n    18,\n    16,\n    14,\n    12,\n    10,\n    8,\n    6,\n    4,\n    2,\n    0\n  ],\n  \"commutation_instances\": 98,\n  \"gap_law\": \"2(49−j)\"\n}\n```\n\n## Finding\n\nRow progression and fixed civil translation commute. Carrier substitution preserves row incidence and common terminal while its metric displacement shrinks from98 to0 according to remaining count. The terminal convergence is generated, not an independent target.\n\n## Reassessment\n\nCheck how the fixed-coordinate Cainan attribution overlay changes names.\n\n## Checks\n\n```json\n{\n  \"commutation\": true,\n  \"convergence\": true,\n  \"step\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T00:23:08.448318+00:00\n\n## Record provenance\n\nExact record hash: `fac98fabcb945b6ef73b6143386560940312f213c87892a1c2911c6c459b7415`\n\nSource journal: `Research_Cycles/C0532_C0631/journal.json`", "journalDownload": "/sources/7a2e1117efc741218b68e2db8bb20eadd33cab34e00384e9b903708031da1d2d.json", "evidenceLinks": [{"id": "d-2fb72e6c1267ac3e", "title": "File 68"}]}