{"id": "c526", "title": "C526 — The forwarded axis joins the529 grammar", "filename": "C526.md", "role": "Research action", "step": 526, "sha256": "b1a9d7c610f9b74c7278a6cf46b5cec81eba8c9b02943b1af18445c921a131c2", "bytes": 1950, "origins": ["C480–C1634/Research_Cycles/C0482_C0531/journal.json#C526"], "download": "/sources/b1a9d7c610f9b74c7278a6cf46b5cec81eba8c9b02943b1af18445c921a131c2.md", "format": "md", "derived": true, "tags": ["Mirror / 529"], "excerpt": "What does the existing three-axis diagram’s forwarded family share with the studied ladders?", "content": "# C526 — The forwarded axis joins the529 grammar\n\n## Question\n\nWhat does the existing three-axis diagram’s forwarded family share with the studied ladders?\n\n## Inputs\n\n```json\n{\n  \"forwarded_shift_magnitudes\": [\n    4232,\n    8464,\n    12696\n  ],\n  \"scope\": \"duration algebra only; existing source-authorized forwardings keep their own endpoint domains\"\n}\n```\n\n## Sources\n\n```json\n[\n  \"Chronology_Three_Axis_Mirrors.png supplied schematic\",\n  \"C505–C507; inherited C480 controls\"\n]\n```\n\n## Opened utc\n\n2026-09-27T22:53:47.842209+00:00\n\n## Results\n\n```json\n{\n  \"ladders\": [\n    {\n      \"source_shift\": 4232,\n      \"529_coefficient\": 8,\n      \"first_E\": 4600,\n      \"second_E\": 5000,\n      \"translation_dilation_difference\": 368\n    },\n    {\n      \"source_shift\": 8464,\n      \"529_coefficient\": 16,\n      \"first_E\": 9200,\n      \"second_E\": 10000,\n      \"translation_dilation_difference\": 736\n    },\n    {\n      \"source_shift\": 12696,\n      \"529_coefficient\": 24,\n      \"first_E\": 13800,\n      \"second_E\": 15000,\n      \"translation_dilation_difference\": 1104\n    }\n  ],\n  \"operator_relation\": \"D_E,a T_t = T_(E*t) D_E,a\",\n  \"shared_middle_duration\": \"8464 ->9200 ->10000\"\n}\n```\n\n## Finding\n\nThe diagram’s8,16,24 multiples of529 become4600/9200/13800, then5000/10000/15000. The middle ladder shares the9200→10000 duration used by the SP rectangle and Shem partition. This connects all three schematic families at the operator level; identical durations do not identify their source nodes or license new forwardings.\n\n## Reassessment\n\nUse the proven interfaces to replace a merely spatial reading of the axes with a map of actual operations.\n\n## Checks\n\n```json\n{\n  \"coefficients\": true,\n  \"first\": true,\n  \"second\": true\n}\n```\n\n## Closed utc\n\n2026-09-27T22:53:47.842480+00:00\n\n## Record provenance\n\nExact record hash: `6fa98efea2e8df1c8aa277bd2566ff2c354e7f81c46617fe5a1fa88da4d398d1`\n\nSource journal: `Research_Cycles/C0482_C0531/journal.json`", "journalDownload": "/sources/6eaeccad4734eff2f6ac20ba847967877b944f9758c53c712ac8b5be2ddf61eb.json"}