{"id": "c509", "title": "C509 — Anchor-change and composition laws", "filename": "C509.md", "role": "Research action", "step": 509, "sha256": "c82e9f0434668680ad5e6dbaf130040cf0cecbdca28cca98eb40f0dc0b8d9348", "bytes": 1334, "origins": ["C480–C1634/Research_Cycles/C0482_C0531/journal.json#C509"], "download": "/sources/c82e9f0434668680ad5e6dbaf130040cf0cecbdca28cca98eb40f0dc0b8d9348.md", "format": "md", "derived": true, "tags": ["Inverse", "Mirror / 529"], "excerpt": "Which affine relations explain a change of anchor without choosing a new ratio?", "content": "# C509 — Anchor-change and composition laws\n\n## Question\n\nWhich affine relations explain a change of anchor without choosing a new ratio?\n\n## Inputs\n\n```json\n{\n  \"E\": \"25/23\",\n  \"anchors\": [\n    14726,\n    6\n  ],\n  \"sample_inverse_Shem\": 5526\n}\n```\n\n## Sources\n\n```json\n[\n  \"Strategy §5C\",\n  \"File52c §3.11\"\n]\n```\n\n## Opened utc\n\n2026-09-27T22:46:36.619470+00:00\n\n## Results\n\n```json\n{\n  \"difference_law\": \"D_k,a(x)-D_k,b(x)=(1-k)(a-b)\",\n  \"conjugacy\": \"T_t D_k,a = D_k,a+t T_t\",\n  \"same_anchor_composition\": \"D_l,a D_k,a = D_lk,a\",\n  \"different_anchor_order\": \"D_l,b D_k,a − D_k,a D_l,b = (1-l)(1-k)(b-a)\",\n  \"Shem_Creation_held\": 4726,\n  \"Shem_Nativity_held\": 6006,\n  \"Nativity_minus_Creation\": 1280\n}\n```\n\n## Finding\n\nChanging only the anchor shifts every output by the same amount. The14726 versus6 E-presentations differ1280 throughout. Same-anchor ratios compose multiplicatively; different anchors generally make order matter.\n\n## Reassessment\n\nKeep this affine geometry distinct from the two coordinate conventions used by Mirror comparisons.\n\n## Checks\n\n```json\n{\n  \"shift\": true,\n  \"Shem\": true\n}\n```\n\n## Closed utc\n\n2026-09-27T22:46:36.619814+00:00\n\n## Record provenance\n\nExact record hash: `7588ac0d117879aed2046e99847bf7c45d917fc46c72a3e7d32280f3b8182f93`\n\nSource journal: `Research_Cycles/C0482_C0531/journal.json`", "journalDownload": "/sources/6eaeccad4734eff2f6ac20ba847967877b944f9758c53c712ac8b5be2ddf61eb.json", "evidenceLinks": [{"id": "file52c", "title": "File 52c"}]}