{"id": "c494", "title": "C494 — The exact residual conservation law", "filename": "C494.md", "role": "Research action", "step": 494, "sha256": "3ce2cb71e0db34fab2bb78bd51196da841f87ca047603d1a9a7c98baf88e0a11", "bytes": 1682, "origins": ["C480–C1634/Research_Cycles/C0482_C0531/journal.json#C494"], "download": "/sources/3ce2cb71e0db34fab2bb78bd51196da841f87ca047603d1a9a7c98baf88e0a11.md", "format": "md", "derived": true, "tags": ["Rounded"], "excerpt": "Which declared endpoint changes preserve the weighted anchor?", "content": "# C494 — The exact residual conservation law\n\n## Question\n\nWhich declared endpoint changes preserve the weighted anchor?\n\n## Inputs\n\n```json\n{\n  \"rounded\": [\n    14006,\n    4106\n  ],\n  \"actual_completion\": [\n    14004,\n    4114\n  ],\n  \"strict_comparison\": [\n    14006,\n    4112\n  ],\n  \"Year6_pair\": [\n    14006,\n    4116\n  ]\n}\n```\n\n## Sources\n\n```json\n[\n  \"File51a §§3,16\",\n  \"File22 §§5.1,7.1\",\n  \"File52c §3.14\"\n]\n```\n\n## Opened utc\n\n2026-09-27T22:42:02.281825+00:00\n\n## Results\n\n```json\n{\n  \"states\": {\n    \"rounded\": {\n      \"weighted_point\": 12026,\n      \"shift_from_12026\": 0\n    },\n    \"actual_completion\": {\n      \"weighted_point\": 12026,\n      \"shift_from_12026\": 0\n    },\n    \"strict_comparison\": {\n      \"weighted_point\": \"60136/5\",\n      \"shift_from_12026\": \"6/5\"\n    },\n    \"Year6_pair\": {\n      \"weighted_point\": 12028,\n      \"shift_from_12026\": 2\n    }\n  },\n  \"kernel\": \"4 delta_C + delta_R = 0\",\n  \"selected_vector\": [\n    -2,\n    8\n  ],\n  \"general_integer_kernel\": \"t*(1,-4)\"\n}\n```\n\n## Finding\n\nThe actual completion selection lies exactly in the kernel. Strict and Year6 alternatives give shifts6/5 and2. The conserved anchor is therefore a precise relation between selected states, not invariance under every actual/rounded convention.\n\n## Reassessment\n\nFormalize the rounded path evaluator so convergence and nonconvergence can be explained by one rule.\n\n## Checks\n\n```json\n{\n  \"completion\": true,\n  \"strict\": true,\n  \"year6\": true\n}\n```\n\n## Closed utc\n\n2026-09-27T22:42:02.282051+00:00\n\n## Record provenance\n\nExact record hash: `6046d8b0bd0ffcab38d96bd1834e20f236c87b3bf140ab959f4be75644722ebb`\n\nSource journal: `Research_Cycles/C0482_C0531/journal.json`", "journalDownload": "/sources/6eaeccad4734eff2f6ac20ba847967877b944f9758c53c712ac8b5be2ddf61eb.json", "evidenceLinks": [{"id": "file52c", "title": "File 52c"}, {"id": "d-d8aa38afb2a2df8f", "title": "File 51a"}, {"id": "d-1c77fd504afbf59b", "title": "File 22"}]}