{"id": "c563", "title": "C563 — Compress the double Adam square", "filename": "C563.md", "role": "Research action", "step": 563, "sha256": "76ad9616355a68066850e45d5ce1bd20e55c71280452498a5addbe6c1ec4b1e3", "bytes": 1220, "origins": ["C480–C1634/Research_Cycles/C0532_C0631/journal.json#C563"], "download": "/sources/76ad9616355a68066850e45d5ce1bd20e55c71280452498a5addbe6c1ec4b1e3.md", "format": "md", "derived": true, "tags": ["Calendar Keys"], "excerpt": "Do both110-squared constructions follow from a rigid translation?", "content": "# C563 — Compress the double Adam square\n\n## Question\n\nDo both110-squared constructions follow from a rigid translation?\n\n## Inputs\n\n```json\n{\n  \"base\": [\n    14006,\n    1906,\n    1796\n  ],\n  \"apparent_whole_year\": [\n    14036,\n    1936,\n    1826\n  ]\n}\n```\n\n## Sources\n\n```json\n[\n  \"File61 §§12.4–12.6\"\n]\n```\n\n## Opened utc\n\n2026-09-28T00:15:00.974870+00:00\n\n## Results\n\n```json\n{\n  \"differences\": [\n    [\n      12100,\n      12210,\n      110\n    ],\n    [\n      12100,\n      12210,\n      110\n    ]\n  ],\n  \"pair_translation\": [\n    30,\n    30,\n    30\n  ],\n  \"exact_phase_mismatch\": \"24199/2\",\n  \"square\": 12100\n}\n```\n\n## Finding\n\nThe two square/rectangle displays are the same12100/12210 geometry translated30. Substituting an exact-phase Joseph node alone yields12099.5 and breaks the square; no new head is fitted.\n\n## Reassessment\n\nDetermine how the Isaac macro partition relates to the calendar ratios.\n\n## Checks\n\n```json\n{\n  \"same_shape\": true,\n  \"translation\": true,\n  \"mismatch\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T00:15:00.975240+00:00\n\n## Record provenance\n\nExact record hash: `85bcaeadc456db00f32fa3ca3524cd88291d4d41b97cc312a3d72127954dca79`\n\nSource journal: `Research_Cycles/C0532_C0631/journal.json`", "journalDownload": "/sources/7a2e1117efc741218b68e2db8bb20eadd33cab34e00384e9b903708031da1d2d.json", "evidenceLinks": [{"id": "d-d580afd48d6e12d6", "title": "File 61"}]}