# C228 — The 868 prefix becomes center gaps 434→664→914

23 September 2026 · Step 23 of 60, continuing C205.

With Creation fixed, the expanding cumulative left boundary makes the old 868 prefix grow to 1328 and 1828. The corresponding center offsets are 434, 664 and 914, gaining 230 and 250.

| p | Prefix widths | Half-prefix / center offsets |
|---|---|---|
| 3 | [Fraction(868, 1), Fraction(1328, 1), Fraction(1828, 1)] | [Fraction(434, 1), Fraction(664, 1), Fraction(914, 1)] |
| 5 | [Fraction(868, 1), Fraction(1328, 1), Fraction(1828, 1)] | [Fraction(434, 1), Fraction(664, 1), Fraction(914, 1)] |

The full prefix gains 460 and 500 come from the ten-unit cumulative coefficient multiplied by the carrier gains 46 and 50. They are not an independently held Cainan or biographical offset in this operation. A familiar number must retain the role supplied by these endpoints.

## Evidence and scope

K=529 and r=25/23. BC base B means (B+1)t/Bn BC; reflected AD base A means AD At/(A+1)n. Their civil span is B+A in both seasonal components, with no year zero. Signed paired centers are −B and +A; the center model uses components ±1/4 and restores this separation after dilation. An interval center is geometry, not an event or a proposed universal Mirror axis.

Regular Gears are restricted to Noah/Shem/Flood. Creation and Conquest retain fixed source-field members; no fourth Gear is admitted. Generated coordinates, source-field membership and stored graph incidence are distinct. File_18/File_09 and the frozen C127 graph are unchanged. Earlier N01/N03 qualifications, the missing Shem join, closed primers and unestablished original Reports 11–25 remain unchanged. This packet selectively uses prior evidence; it does not rerun completed campaigns. Assertions and alternative placements are not independent historical witness counts.

**6 step-specific checks and 19 frozen-input checks passed.** Exact inputs, results and predecessor hashes are in the accompanying JSON records; calculation code is in the evidence archive. Source dependencies are identified in the body and frozen in `sources/`.