{"id": "c513", "title": "C513 — One rule generates the14726 family", "filename": "C513.md", "role": "Research action", "step": 513, "sha256": "17fecfc08f569d946d3c31c43f7653a06d6c6f5f9d474ccde1dedef33e3fed29", "bytes": 2472, "origins": ["C480–C1634/Research_Cycles/C0482_C0531/journal.json#C513"], "download": "/sources/17fecfc08f569d946d3c31c43f7653a06d6c6f5f9d474ccde1dedef33e3fed29.md", "format": "md", "derived": true, "tags": ["Inverse"], "excerpt": "Can the complete set of Creation-held results be compressed into one affine formula?", "content": "# C513 — One rule generates the14726 family\n\n## Question\n\nCan the complete set of Creation-held results be compressed into one affine formula?\n\n## Inputs\n\n```json\n{\n  \"inverse_coordinates\": {\n    \"Mahalalel\": 1731,\n    \"Shem\": 5526,\n    \"Shelah\": 2421,\n    \"Eber\": 9321,\n    \"Terah\": 3226,\n    \"Abraham\": 2076,\n    \"Moses\": 1616,\n    \"Flood_countdown\": 8516,\n    \"Affliction_hub\": 1846\n  },\n  \"held_anchor\": 14726\n}\n```\n\n## Sources\n\n```json\n[\n  \"File52c §§3.7.3,3.11.4\",\n  \"C509,C512\"\n]\n```\n\n## Opened utc\n\n2026-09-27T22:48:23.882482+00:00\n\n## Results\n\n```json\n{\n  \"normal_form\": \"X=6+115k;14726=6+115*128;Creation-held result=125k−1274;Nativity-held result=125k+6\",\n  \"members\": {\n    \"Mahalalel\": {\n      \"k\": 15,\n      \"complement_k\": 113,\n      \"Creation_held\": 601,\n      \"Nativity_held\": 1881\n    },\n    \"Shem\": {\n      \"k\": 48,\n      \"complement_k\": 80,\n      \"Creation_held\": 4726,\n      \"Nativity_held\": 6006\n    },\n    \"Shelah\": {\n      \"k\": 21,\n      \"complement_k\": 107,\n      \"Creation_held\": 1351,\n      \"Nativity_held\": 2631\n    },\n    \"Eber\": {\n      \"k\": 81,\n      \"complement_k\": 47,\n      \"Creation_held\": 8851,\n      \"Nativity_held\": 10131\n    },\n    \"Terah\": {\n      \"k\": 28,\n      \"complement_k\": 100,\n      \"Creation_held\": 2226,\n      \"Nativity_held\": 3506\n    },\n    \"Abraham\": {\n      \"k\": 18,\n      \"complement_k\": 110,\n      \"Creation_held\": 976,\n      \"Nativity_held\": 2256\n    },\n    \"Moses\": {\n      \"k\": 14,\n      \"complement_k\": 114,\n      \"Creation_held\": 476,\n      \"Nativity_held\": 1756\n    },\n    \"Flood_countdown\": {\n      \"k\": 74,\n      \"complement_k\": 54,\n      \"Creation_held\": 7976,\n      \"Nativity_held\": 9256\n    },\n    \"Affliction_hub\": {\n      \"k\": 16,\n      \"complement_k\": 112,\n      \"Creation_held\": 726,\n      \"Nativity_held\": 2006\n    }\n  }\n}\n```\n\n## Finding\n\nNine outputs follow from one formula and the supplied member coefficients. The1280 anchor-change difference is uniform. This compresses the calculation, while the nine source selections and their k values remain inputs needing explanation.\n\n## Reassessment\n\nTest a whole three-node relation under the formula: the Abraham–affliction–Moses midpoint.\n\n## Checks\n\n```json\n{\n  \"integral_k\": true,\n  \"formula\": true,\n  \"shift\": true\n}\n```\n\n## Closed utc\n\n2026-09-27T22:48:23.882801+00:00\n\n## Record provenance\n\nExact record hash: `792c142e2edb2594537b5cae429bc1067f054069231af78c09516262886a34b1`\n\nSource journal: `Research_Cycles/C0482_C0531/journal.json`", "journalDownload": "/sources/6eaeccad4734eff2f6ac20ba847967877b944f9758c53c712ac8b5be2ddf61eb.json", "evidenceLinks": [{"id": "file52c", "title": "File 52c"}]}