# C204 — The aligned coordinates reduce to K,190 and two finite selectors

23 September 2026 · Step 49 of 50, continuing C155.

**The whole aligned configuration can be written with K=529, H=190 and two source selectors s,j.** This compact form exposes the529 coefficients without concealing the source restrictions.

| Coordinate | Expression |
|---|---|
| A | 10K+s |
| D | 10K−s |
| X | 7K+s |
| Z | s |
| U | 12K−j |
| M | 5K+j |
| f | 5K−H+j |
| b | 8K+H−s |
| q | 3K−H+s |
| z generated | 5K+H−s |

The five-row family has s=2,…,6 and j=0,…,5; δ=s−j. The exact common core is s=j=2,…,5. Allowing the sourced sixth11K/17K row adds s=7, but its A=5297 is outside the cumulative source field. The gap D−b=2K−H=868 is built into this selected alignment.

This is a reduced coordinate grammar, not an independent derivation of K or the source dates. It combines the conditional equations established in this batch. The explicit domains prevent the attractive integer coefficients from licensing missing endpoints, extra Gears or a global source-preserving action.

## Evidence and scope

K=529. Positive BC base B denotes (B+1)t/Bn BC; reflected AD base A denotes AD At/(A+1)n. Their same-season civil span is B+A, after the no-year-zero correction. AD source projections are not historical AD occurrences. Generated coordinates and interval midpoints do not acquire event identity from numerical coincidence.

Regular Gears remain confined to Noah/Shem/Flood. Creation and Conquest use fixed source-field members; no fourth Gear is admitted. File_18/File_09 and the C127 graph are unchanged. C133–C155 source corrections remain controlling, with the C10 ancestry of the next-Flood-Gear rule now explicit. No historical campaign is rerun, no quarantined primer is reopened, and no N01/N03 expansion or missing Shem join is repaired. Original Reports 01–10 remain previously verified; interrupted original Reports 11–25 remain unestablished.

Sources: controlling File_18 §§2–3, 6A–6D; File_09 paired Mirror rules; selectively retained C05, C08, C10, C123, C128 and C133–C155 evidence. Specific dependencies are named in the body/certificate. **80 assertions passed**; see `RESULTS.json` and `CERTIFICATE.json`. Assertions, selected field combinations and inherited identities are not independent historical witness counts.