{"id": "c525", "title": "C525 — Freeze a compact construction grammar", "filename": "C525.md", "role": "Research action", "step": 525, "sha256": "11d08ef1a672c786700659ae48be36e9b05322534fbc2886c91c745efff6e256", "bytes": 2833, "origins": ["C480–C1634/Research_Cycles/C0482_C0531/journal.json#C525"], "download": "/sources/11d08ef1a672c786700659ae48be36e9b05322534fbc2886c91c745efff6e256.md", "format": "md", "derived": true, "tags": ["Regular", "Cumulative", "Rounded", "Calendar Keys", "Mirror / 529"], "excerpt": "Which operation types are actually needed for the completed family reconstructions?", "content": "# C525 — Freeze a compact construction grammar\n\n## Question\n\nWhich operation types are actually needed for the completed family reconstructions?\n\n## Inputs\n\n```json\n{\n  \"evidence_range\": \"C482–C524\",\n  \"source_objects\": \"ordered biographies plus tradition, frame, phase, node role and coordinate chart\"\n}\n```\n\n## Sources\n\n```json\n[\n  \"Strategy §§1,5B–5G\",\n  \"completed sequential ledger\"\n]\n```\n\n## Opened utc\n\n2026-09-27T22:53:15.913084+00:00\n\n## Results\n\n```json\n{\n  \"operations\": [\n    {\n      \"operation\": \"row change\",\n      \"domain\": \"compatible biography or admitted insertion\",\n      \"example\": \"(b,r)->(b+d,r−d); Cainan130/330\"\n    },\n    {\n      \"operation\": \"chronological projection\",\n      \"domain\": \"ordered source rows and supplied terminal anchor\",\n      \"example\": \"regular sums begetting intervals; cumulative sums lifespans\"\n    },\n    {\n      \"operation\": \"round with residual\",\n      \"domain\": \"declared begetting or lifespan list\",\n      \"example\": \"nearest5 with retained exact residual\"\n    },\n    {\n      \"operation\": \"evaluate reversed path\",\n      \"domain\": \"source-admitted integer spans with retained segmentation\",\n      \"example\": \"a+sum I(s_i)\"\n    },\n    {\n      \"operation\": \"anchored dilation\",\n      \"domain\": \"declared linear coordinate chart, source nodes and held anchor\",\n      \"example\": \"a+k(x−a), with supplied E/P/J\"\n    },\n    {\n      \"operation\": \"scoped translation/state switch\",\n      \"domain\": \"source-authorized affected nodes or finite switch field\",\n      \"example\": \"native/equalized frame or OFF->ON once\"\n    },\n    {\n      \"operation\": \"reflection\",\n      \"domain\": \"declared comparison chart and source roles\",\n      \"example\": \"q->−q for Rounded Mirror away from origin\"\n    }\n  ],\n  \"relations\": [\n    \"L=b+r and cumulative repartition conservation\",\n    \"weighted residual4deltaC+deltaR=0 in its selected state\",\n    \"calendar d*K_d=8400/23\",\n    \"affine composition/conjugacy and pivot congruences\",\n    \"path concatenation retains segments; general additivity after forgetting them is rejected\"\n  ]\n}\n```\n\n## Finding\n\nSeven operation types suffice to express the reconstructed examples. Inputs still include source rows, admitted partitions, anchors and state selections. This is a useful candidate grammar; neither an unrestricted transformation group nor a proven globally smallest presentation is claimed.\n\n## Reassessment\n\nMap these operations onto the three family axes and their Mirrors as an explanatory topology.\n\n## Checks\n\n```json\n{\n  \"no_free_anchor_operation\": true,\n  \"finite_insertions_preserved\": true,\n  \"count\": true\n}\n```\n\n## Closed utc\n\n2026-09-27T22:53:15.913368+00:00\n\n## Record provenance\n\nExact record hash: `8bf0380daa7ca26a08526ac3eaa31f15e87e78f3ff7c5393636001e8027a6f0d`\n\nSource journal: `Research_Cycles/C0482_C0531/journal.json`", "journalDownload": "/sources/6eaeccad4734eff2f6ac20ba847967877b944f9758c53c712ac8b5be2ddf61eb.json"}