{"id": "c572", "title": "C572 — Close the Actual-to-Rounded cumulative square", "filename": "C572.md", "role": "Research action", "step": 572, "sha256": "54c3c04fa64e414d9067f5ba7ec42c61e868e4c7069c508d8dad38ab9aa62a78", "bytes": 1219, "origins": ["C480–C1634/Research_Cycles/C0532_C0631/journal.json#C572"], "download": "/sources/54c3c04fa64e414d9067f5ba7ec42c61e868e4c7069c508d8dad38ab9aa62a78.md", "format": "md", "derived": true, "tags": ["Regular", "Cumulative", "Rounded"], "excerpt": "Does the J image followed by the source pair adjustment recover both Rounded endpoints?", "content": "# C572 — Close the Actual-to-Rounded cumulative square\n\n## Question\n\nDoes the J image followed by the source pair adjustment recover both Rounded endpoints?\n\n## Inputs\n\n```json\n{\n  \"Actual\": [\n    14004,\n    1446\n  ],\n  \"Rounded\": [\n    14006,\n    1406\n  ],\n  \"pair_translation\": 2\n}\n```\n\n## Sources\n\n```json\n[\n  \"File63 §9.7; File51a; latest File52c\"\n]\n```\n\n## Opened utc\n\n2026-09-28T00:17:33.798912+00:00\n\n## Results\n\n```json\n{\n  \"Actual_span\": 12558,\n  \"J_pair\": [\n    14004,\n    1404\n  ],\n  \"translated_pair\": [\n    14006,\n    1406\n  ],\n  \"span_gain\": 42,\n  \"endpoint_change\": [\n    2,\n    -40\n  ]\n}\n```\n\n## Finding\n\nThe Actual Creation–Exodus pair maps by anchored J to14004/1404, then by a declared+2 pair translation to Rounded Creation–Conquest14006/1406. This is an exact interface between differently typed endpoint pairs.\n\n## Reassessment\n\nRelate this pair interface to the separate12026 regular/cumulative bridge.\n\n## Checks\n\n```json\n{\n  \"endpoints\": true,\n  \"span_gain\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T00:17:33.799187+00:00\n\n## Record provenance\n\nExact record hash: `aa16643fa36d3d74a12b53518ee1c1a8f7d239b1c2aeec8ae1d3633d309d8f7b`\n\nSource journal: `Research_Cycles/C0532_C0631/journal.json`", "journalDownload": "/sources/7a2e1117efc741218b68e2db8bb20eadd33cab34e00384e9b903708031da1d2d.json", "evidenceLinks": [{"id": "d-180803601a2db301", "title": "File 63"}, {"id": "file52c", "title": "File 52c"}, {"id": "d-d8aa38afb2a2df8f", "title": "File 51a"}]}