C170 — Sourced counterexamples show why the common alignment matters
23 September 2026 · Step 15 of 50, continuing C155.
Exact squares and exact 13K Creation spans are not unconditionally equivalent across all admitted endpoint selections. Two adjacent native Creation/Conquest choices provide concrete counterexamples while preserving 11K.
| Choice | b | q | D | X | δ | η | b+f |
|---|---|---|---|---|---|---|---|
| Aligned N04 | 4417 | 1402 | 5285 | 3708 | 0 | 0 | 6877 |
| Same square, next native pair | 4416 | 1403 | 5285 | 3708 | 0 | 1 | 6876 |
| Aligned P6 | 4416 | 1403 | 5284 | 3709 | 1 | 0 | 6876 |
| Same square, previous native pair | 4417 | 1402 | 5284 | 3709 | 1 | -1 | 6877 |
All four comparisons use source-admitted fields. In the second row, the square is exact but the Creation span is 6876. In the fourth, the Creation span is 6877 but the square retains its one-year residual. Both deviations arise from changing the native-member alignment η, not from inventing an event or changing the Mirror axis.
The original equivalence remains valid on its stated α=β=η=γ=ρ=0 family. These negative controls identify its boundary and prevent it from being generalized solely on the basis that all selected endpoints are individually sourced.
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. 25 assertions passed; see RESULTS.json and CERTIFICATE.json. Assertions, selected field combinations and inherited identities are not independent historical witness counts.