{"id": "c665", "title": "C665 — Derive the native core from carrier and flank", "filename": "C665.md", "role": "Research action", "step": 665, "sha256": "9021973540f50eba08266716eedf5bd35ee220650953e0b253d43a76aa759dd3", "bytes": 1052, "origins": ["C480–C1634/Research_Cycles/C0632_C0731/journal.json#C665"], "download": "/sources/9021973540f50eba08266716eedf5bd35ee220650953e0b253d43a76aa759dd3.md", "format": "md", "derived": true, "tags": [], "excerpt": "What minimal source inputs generate the720/30 family?", "content": "# C665 — Derive the native core from carrier and flank\n\n## Question\n\nWhat minimal source inputs generate the720/30 family?\n\n## Inputs\n\n```json\n{\n  \"carrier\": 720,\n  \"flank\": 30\n}\n```\n\n## Sources\n\n```json\n[\n  \"Supplement A §§1.1–1.2\"\n]\n```\n\n## Opened utc\n\n2026-09-28T01:08:30.974042+00:00\n\n## Results\n\n```json\n{\n  \"core\": 690,\n  \"flank_coefficients\": {\n    \"core\": 23,\n    \"carrier\": 24,\n    \"native_bracket\": 25,\n    \"expanded_core\": 25\n  }\n}\n```\n\n## Finding\n\nThe crossed core690 is23 flanks of30. The carrier is24 flanks, and both the native two-flank bracket and E-expanded core are25 flanks. Their shared750 is forced by core=23×flank, while their component roles differ.\n\n## Reassessment\n\nGenerate all native, P and E core/flank/bracket states together.\n\n## Checks\n\n```json\n{\n  \"core\": true,\n  \"forced_equality\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T01:08:30.976261+00:00\n\n## Record provenance\n\nExact record hash: `1aeb72d2ecd8dc9dd6ded191817336a2590dc2700aed7b90d530052f84cb6a71`\n\nSource journal: `Research_Cycles/C0632_C0731/journal.json`", "journalDownload": "/sources/f0643e934c6a7443706351fa40040684d915ed0ae25c0f9188a4c4dba12814ff.json"}