# C108 — The two shared junctions force 25/23 within the 11/12/13 shape

22 September 2026 · Step 6 of the authorized ten-step Mirror continuation (C103–C112).

Let **k** be an unspecified positive base unit, **r>1** the common expansion ratio, α the apparent Creation anchor, and b the ordinary N02 Creation anchor. Write d=b−α. Retain the declared family labels 11, 12 and 13, but do not insert 529 or 25/23.

The same G1 Flood is reached by ordinary 11 at its third stage and apparent 12 at its second. The same G1 Noah is reached by ordinary 13 at its second stage and apparent 12 at its third:

```mermaid
flowchart TD
  A["Apparent Creation α"] -->|"12kr"| F["G1 Flood"]
  B["Ordinary Creation b"] -->|"11kr²"| F
  A -->|"12kr²"| N["G1 Noah"]
  B -->|"13kr"| N
```

Thus

\[
d+k(11r^2-12r)=0,\qquad d+k(13r-12r^2)=0.
\]

Subtracting eliminates the unknown anchor difference:

\[
kr(23r-25)=0.
\]

In the declared nondegenerate expansion domain, **r=25/23**, and either junction then gives **d/k=25/529**. The 23 and 25 arise directly as 11+12 and 12+13. The denominator 529 is 23² in the derived anchor ratio, not an inserted value of k.

This is a structural reconstruction conditional on the shared junction identities, the three family labels and one common ratio. It does not independently establish those premises or prove historical intention. The absolute unit k and the origin α remain free. The degenerate r=0 algebraic root is excluded by the expansion domain and cannot represent the ordered source intervals.

**Validation.** 8 exact arithmetic/structural checks passed. The 17 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); File_18 §§2.1.3, 3.1 and 6A (regular fields and cumulative source members); File_61 §11.2 (original backward Joseph +110); File_62 collateral-scope guards; C05 admitted apparent field; C43 frozen graph; C95 and C100–C102 named carrier rows; preceding current certificates. The forthcoming 529 × 4 × 2 cycle has not been explored. The declared phase model does not infer an unstated birthday or event month from an annual source row.

**Best next bounded step — High sufficient.** Calibrate the still-free unit with the same-Gear Noah-to-Flood 600-year source interval, then locate the reconstructed anchors in their fixed source fields.