# C81 — The source fixes the scale that ratio closure leaves free

22 September 2026 · Step 9 of the authorized ten-step Mirror continuation (C73–C82).

The closure equation in C80 cancels K. It therefore does not by itself recover 529. The same-Gear Noah–Flood span supplies the dimensional constraint:

\[
600=K(13r-11r^2),\qquad r=25/23,
\]
\[
13r-11r^2=600/529\quad\Rightarrow\quad K=529.
\]

The two-year Flood separation gives the equivalent expression

\[
2=K(13-11r^2),\qquad13-11r^2=2/529.
\]

The two calibration rows are proportional by 300; they provide one scalar constraint once these coefficients and r are held. They must not be counted as two independent scale determinations.

| Formal K | Closure residual | Implied Noah–Flood span | Implied Gear step | Matches source |
| --- | --- | --- | --- | --- |
| 529 | 0 | 600 | 2 | yes |
| 530 | 0 | 318000/529 | 1060/529 | no |

K=530 preserves the formal meeting of the two routes but changes both required source intervals. This single control distinguishes ratio consistency from chronological admission; it is not an alternative chronology or a new broad negative-case campaign.

The resulting 529 expression is a conditional reformulation of the already calibrated model. It uses the selected 11/13 family coefficients, the retained 25/23 ratio and source Noah/Flood relations. Repeated placements, exact phase checks and the equivalent two-year equation do not create additional independent witnesses. The original C22 calibration and source provenance remain controlling.

**Validation.** 7 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.** Publish the C73–C82 synthesis, retaining the six/three/two/one source domains and the new named 7200 landing.