{"id": "c1213", "title": "C1213 — Test row operations that translate by the five-year lattice", "filename": "C1213.md", "role": "Research action", "step": 1213, "sha256": "6c27c4540910261fcab2d2ff00dd2b6e8efab5fa69d805281440fab5930fa5bf", "bytes": 1180, "origins": ["C480–C1634/Research_Cycles/C1132_C1431_Recovered/journal.json#C1213"], "download": "/sources/6c27c4540910261fcab2d2ff00dd2b6e8efab5fa69d805281440fab5930fa5bf.md", "format": "md", "derived": true, "tags": ["Rounded"], "excerpt": "Which changes pass through nearest-five rounding without changing their amplitude?", "content": "# C1213 — Test row operations that translate by the five-year lattice\n\n## Question\n\nWhich changes pass through nearest-five rounding without changing their amplitude?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"C1182\",\n  \"C1199\",\n  \"prep/review1182_1201 pending independent review\"\n]\n```\n\n## Opened utc\n\n2026-09-28T05:29:06.281790+00:00\n\n## Results\n\n```json\n{\n  \"equivariance\": {\n    \"path\": \"model/round_lattice_equivariance.json\",\n    \"sha256\": \"cd4cba7a1d4f52780ea7a1406c86691f7f48b8dbaefa232792e71ca96049ced1\",\n    \"bytes\": 504\n  }\n}\n```\n\n## Finding\n\nAll translations by multiples of five pass through rounding exactly, including the century, half-century, forty and sixty changes. The signed carry notation uses an algebraic extension, not negative source durations.\n\n## Reassessment\n\nLocate the only whole-genealogy amplitudes outside that lattice.\n\n## Checks\n\n```json\n{\n  \"all_translation_cases\": true,\n  \"two_off_lattice\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T05:29:06.282246+00:00\n\n## Record provenance\n\nExact record hash: `d8888961095773dcd375ca4baa91c39f66218acc52b18322cd77ca1eb20e7ddb`\n\nSource journal: `Research_Cycles/C1132_C1431_Recovered/journal.json`", "journalDownload": "/sources/6adb632ce171623c2bce60d7ed58ae319ccb379cf76b751c0a477c1742fd348c.json", "evidenceLinks": [{"id": "d-cd4cba7a1d4f5278", "title": "model/round_lattice_equivariance.json"}]}