C147 — A local affine model has two selector freedoms
23 September 2026 · Bounded step 12 of 20 (C136–C155).
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.
| Retained equation | Role |
|---|---|
| A-X=3K | Noah first leg |
| A-Z=10K | Noah total |
| D+X=17K | SP 17K diagonal |
| D-b=868 | Cumulative/native separation |
| b+q=11K | Creation–Conquest span |
| z+q=8K | Generated 8K preimage |
| M-f=190 | MT profile difference |
| U+M=17K | MT 17K diagonal |
Exact 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.
The 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.
These 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.
Source and scope control
All 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.
Regular 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.
Evidence: CERTIFICATE.json; 53 passing assertions in RESULTS.json. The assertion list identifies the actual tests.