C158 — Adding Conquest narrows the seven gap pairs to six
23 September 2026 · Step 3 of 50, continuing C155.
Six of the seven 868 pairs also support the retained 11K Creation→reflected-Conquest relation.
| D | b | Required q | Conquest admission |
|---|---|---|---|
| 5283 | 4415 | 1404 | yes |
| 5284 | 4416 | 1403 | yes |
| 5285 | 4417 | 1402 | yes |
| 5286 | 4418 | 1401 | yes |
| 5287 | 4419 | 1400 | yes |
| 5288 | 4420 | 1399 | yes |
| 5289 | 4421 | 1398 | no |
The native opening b4421 requires q1398, which is absent from the held Conquest field. The opposite native closing b4414 does admit q1405, but it never entered the 868 field intersection because its required D5282 is absent. These are separate boundary failures.
This refines the C155 source hierarchy: the familiar five Noah rows sit inside a six-row 868/11K intersection. The next step asks whether the sixth row lacks a Noah source or only fails a further cumulative requirement. The generated 8K preimage z=4232−q remains a comparison coordinate in every admitted Conquest row.
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. 22 assertions passed; see RESULTS.json and CERTIFICATE.json. Assertions, selected field combinations and inherited identities are not independent historical witness counts.