# C80 — The 11-fold and 13-fold routes close at the same lower Flood

22 September 2026 · Step 8 of the authorized ten-step Mirror continuation (C73–C82).

Two different source-qualified routes reach the lower Flood pair from the retained comparison:

1. Expand the Creation→Conquest 11-fold width twice by 25/23.
2. Take the old upper Flood of the 13-fold chain and apply the held-Noah 300/299 map.

| Branch | Conquest start of route1 | Upper Flood start of route2 | Shared lower Flood | Held MT Noah |
| --- | --- | --- | --- | --- |
| N02 | 1400 | 2458 | 2456 | 3056 |
| N04 | 1402 | 2460 | 2458 | 3058 |

Measure from the held Creation centre, let r be the expansion factor, and e=300/299. The two relative target coordinates are

\[
11Kr^2\quad\text{and}\quad13Kr+13Ke(1-r).
\]

Their equality reduces to

\[
253r^2+r-300=0
=(23r-25)(11r+12).
\]

The positive root is r=25/23; the other root −12/11 reverses order and is outside the declared positive expansion. This is a compact conditional closure equation for the retained 11/13-family placements and the 300/299 source map. It re-expresses their dependencies, rather than providing independent evidence for the chosen ratios.

The equality is at the specified sourced points. The two maps have different slopes, r² and e. Moving their corresponding inputs by one gives a residual 1225/6877, so they must not be presented as the same global affine operator or an unrestricted commuting transformation. Both seasonal components agree at the qualified meeting point under the existing phase lift.

**Validation.** 10 exact arithmetic/structural checks passed. The 15 frozen dependencies passed hash verification; all three generated outputs replayed byte for byte in isolation, and the original dependencies remained unchanged. This step reads completed certificates and does not execute their campaigns.

**Scope and provenance.** Controlling File_18 and File_09 remain unchanged. Regular Gears apply only to Noah/Shem/Flood; SP person companions only to Noah/Shem. Creation and Conquest fields remain fixed. Native LXX ON, explicitly derived OFF, independent Flood start/close, and paired suffix inversion at January AD 1 remain in force. No civil year zero, upstream Gear transport, primers, Rounded campaign, or localized −33 is introduced. These are new continuation reports, not recovered historical Reports 11–25. Evidence is conditional on the supplied project model, not a proof of literary intention or independent historical dating.

**Source locators.** File_09 §3 and Appendix A (paired Mirror and exact phase); File_18 §§2.1.3, 2.4, 3.1 and 6/6A (regular fields and cumulative collateral source); File_61 §11 and File_62 collateral-scope guards (original Joseph portion only); frozen C15/C16/C22/C43/C65/C72 certificates and C01/C05/C09 reports (retained source, phase and family dependencies). The declared phase model does not infer an unstated birthday or event month from an annual source row.

**Best next bounded step — High sufficient.** Separate this ratio closure from source calibration of the 529 scale and the two-year Gear interval.