C167 — The Creation prefix also depends on the 868 alignment

23 September 2026 · Step 12 of 50, continuing C155.

A square's δ alone does not determine the Creation-to-Flood span when native Creation is independently selected. Define η=D−b−868 and ρ=M−f−190. Exact subtraction gives

The earlier 13K−δ formula is recovered when α=η=ρ=0. In particular, η records the source-field alignment identified in C156, rather than treating 868 as an automatic chronology-wide offset.

Keeping every square vertex fixed while selecting an adjacent admitted Creation member changes η and the Creation span, but leaves δ and the square unchanged. This shows where the linkage depends on the native-member pairing. It does not invalidate the earlier finite aligned family; it states the condition needed before extending its conclusion to other sourced endpoints.

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. 60 assertions passed; see RESULTS.json and CERTIFICATE.json. Assertions, selected field combinations and inherited identities are not independent historical witness counts.