{"id": "c147", "title": "C147 — A local affine model has two selector freedoms", "filename": "490d_C147_529_Mirror_Bounded_Step_20260923.md", "role": "Research action", "step": 147, "sha256": "12d1e7e7ac9e9ac109aff218e7a37f5eca1c41a0c5cd8423d881cde68f8d1881", "bytes": 2500, "origins": ["C01–C479/reference/490d_C01_C265_Complete_Window_Archive_20260923.zip!/workspace/mirror_C136_C155_529_Square_Batch_20260923/C147/490d_C147_529_Mirror_Bounded_Step_20260923.md"], "download": "/sources/12d1e7e7ac9e9ac109aff218e7a37f5eca1c41a0c5cd8423d881cde68f8d1881.md", "format": "md", "derived": false, "tags": ["Regular", "Cumulative", "Mirror / 529"], "excerpt": "C147 — A local affine model has two selector freedoms\n\n23 September 2026 · Bounded step 12 of 20 (C136–C155).\n\nEight independent affine equations organize the ten local coordinates; two numerical freedoms remain before source restrictions. They can be represented by X and M, or equivalently d and j within the admitted ", "content": "# C147 — A local affine model has two selector freedoms\n\n23 September 2026 · Bounded step 12 of 20 (C136–C155).\n\n**Eight independent affine equations organize the ten local coordinates; two numerical freedoms remain before source restrictions.** They can be represented by X and M, or equivalently d and j within the admitted finite product.\n\n| Retained equation | Role |\n|---|---|\n| A-X=3K | Noah first leg |\n| A-Z=10K | Noah total |\n| D+X=17K | SP 17K diagonal |\n| D-b=868 | Cumulative/native separation |\n| b+q=11K | Creation–Conquest span |\n| z+q=8K | Generated 8K preimage |\n| M-f=190 | MT profile difference |\n| U+M=17K | MT 17K diagonal |\n\nExact rational elimination gives coefficient rank 8 and augmented rank 8. Imposing X−M=2K increases the rank to 9. Fixing P6's X=3709 as well gives rank 10 and forces M=2651, outside the retained alternate MT field.\n\nThe model explains why one additional alignment equation can simultaneously enforce several exact partitions. **Field membership and endpoint type are extra conditions**, not consequences of matrix rank. Its variables also include generated z, so rank does not confer historical status on that point.\n\nThese ranks concern only this ten-variable local comparison system. The frozen 208-node historical graph and its inherited rank are unchanged. The eight equations summarize retained relationships; their linear independence does not mean eight independent historical attestations.\n\n## Source and scope control\n\nAll numerical bases in this packet stand for paired coordinates: BC base B is (B+1)t/Bn BC; reflected AD base A is AD At/(A+1)n. Thus a cross-Mirror same-season span is B+A, after the civil no-year-zero subtraction. AD stations are reflected source events, not historical AD occurrences. K=529 throughout.\n\nRegular Gears remain restricted to Noah/Shem/Flood. Creation and Conquest are fixed source-field selections. C133–C135 corrections remain controlling. The C127 graph and canonical controls are frozen; source-field admission is distinguished from an existing graph node and from a generated comparison coordinate. No wider N01/N03 expansion or missing N03 Shem join is repaired. Original Reports 01–10 remain previously verified references; interrupted original Reports 11–25 remain unestablished. Check counts are computational assertions, not independent historical witnesses.\n\nEvidence: `CERTIFICATE.json`; **53 passing assertions** in `RESULTS.json`. The assertion list identifies the actual tests.\n"}