{"id": "c1250", "title": "C1250 — Determine the arithmetic freedom in the430/490 bridge", "filename": "C1250.md", "role": "Research action", "step": 1250, "sha256": "5690859ebe49a2210594979f8cec08e8ab37177193397483430dc8d3a43c9940", "bytes": 1162, "origins": ["C480–C1634/Research_Cycles/C1132_C1431_Recovered/journal.json#C1250"], "download": "/sources/5690859ebe49a2210594979f8cec08e8ab37177193397483430dc8d3a43c9940.md", "format": "md", "derived": true, "tags": [], "excerpt": "Does the integer bridge430m−490n=130 have only the source solution?", "content": "# C1250 — Determine the arithmetic freedom in the430/490 bridge\n\n## Question\n\nDoes the integer bridge430m−490n=130 have only the source solution?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"C1238\",\n  \"File51a §7A.2\"\n]\n```\n\n## Opened utc\n\n2026-09-28T05:43:46.390359+00:00\n\n## Results\n\n```json\n{\n  \"bridge_family\": {\n    \"path\": \"model/Moses_cycle_bridge_integer_family.json\",\n    \"sha256\": \"5511afbe3ed58ac79ffe1d94b93293f8fab73e811d91fa86e0454fffd7af8275\",\n    \"bytes\": 587\n  }\n}\n```\n\n## Finding\n\nThe bridge has infinitely many positive integer solutions, with6/5 the smallest in this fixed430/490 equation. That arithmetic property is separate from the source path’s identification ofMoses.\n\n## Reassessment\n\nAssess the minimal source packet that regenerates the completeMosesfamily rather than just itscyclelabels.\n\n## Checks\n\n```json\n{\n  \"source_equation\": true,\n  \"step_homogeneous\": true,\n  \"examples\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T05:43:46.390729+00:00\n\n## Record provenance\n\nExact record hash: `0677fb515a567213d1cedea44caa1354604c9c1a595221eb22190378fe30c3e2`\n\nSource journal: `Research_Cycles/C1132_C1431_Recovered/journal.json`", "journalDownload": "/sources/6adb632ce171623c2bce60d7ed58ae319ccb379cf76b751c0a477c1742fd348c.json", "evidenceLinks": [{"id": "d-5511afbe3ed58ac7", "title": "model/Moses_cycle_bridge_integer_family.json"}, {"id": "d-d8aa38afb2a2df8f", "title": "File 51a"}]}