{"id": "c499", "title": "C499 — Where path evaluation is compatible with affine geometry", "filename": "C499.md", "role": "Research action", "step": 499, "sha256": "7770aedb07e1de5c307a28f95d3f11f1710308b35c92d777cee2e93833658fd5", "bytes": 1488, "origins": ["C480–C1634/Research_Cycles/C0482_C0531/journal.json#C499"], "download": "/sources/7770aedb07e1de5c307a28f95d3f11f1710308b35c92d777cee2e93833658fd5.md", "format": "md", "derived": true, "tags": ["Inverse", "Calendar Keys"], "excerpt": "Which operations commute with the path evaluator without losing segmentation?", "content": "# C499 — Where path evaluation is compatible with affine geometry\n\n## Question\n\nWhich operations commute with the path evaluator without losing segmentation?\n\n## Inputs\n\n```json\n{\n  \"parts\": [\n    1650,\n    1050\n  ],\n  \"anchor\": 1406,\n  \"test_translation\": 215,\n  \"decimal_scale\": 10\n}\n```\n\n## Sources\n\n```json\n[\n  \"File52c §1.2\",\n  \"Strategy §§5C–5F\",\n  \"C495\"\n]\n```\n\n## Opened utc\n\n2026-09-27T22:43:19.757713+00:00\n\n## Results\n\n```json\n{\n  \"translated_endpoint\": 12241,\n  \"scaled_endpoint\": 120260,\n  \"original_endpoint\": 12026,\n  \"whole_span_inverse\": 7200,\n  \"segmented_inverse_sum\": 10620,\n  \"general_rules\": [\n    \"all dates and anchor translated together: V shifts by same t\",\n    \"all durations and anchor scaled by10^k: V scales by10^k\",\n    \"I(s+t) need not equal I(s)+I(t)\"\n  ]\n}\n```\n\n## Finding\n\nThe module respects a change of origin and decimal rescaling when the entire declared object moves. It does not respect erasing segmentation. These are mathematical compatibility rules, not permission to translate source chronologies outside their admitted domains.\n\n## Reassessment\n\nConnect the actual field to the three calendar Keys through their common measure.\n\n## Checks\n\n```json\n{\n  \"translation\": true,\n  \"scale\": true,\n  \"nonadditive\": true\n}\n```\n\n## Closed utc\n\n2026-09-27T22:43:19.757928+00:00\n\n## Record provenance\n\nExact record hash: `ce6d76fb4adda85cc41fc08521f6dbacb1b1aeffd236bf259317221b9aae69fa`\n\nSource journal: `Research_Cycles/C0482_C0531/journal.json`", "journalDownload": "/sources/6eaeccad4734eff2f6ac20ba847967877b944f9758c53c712ac8b5be2ddf61eb.json", "evidenceLinks": [{"id": "file52c", "title": "File 52c"}]}