# C109 — The sourced 600-year Noah/Flood interval calibrates the free unit to 529

22 September 2026 · Step 7 of the authorized ten-step Mirror continuation (C103–C112).

The junction equations determine r, but leave k free. The apparent 12-fold row supplies a direct source calibration: its G1 Noah and G1 Flood are separated by 600 years. This is the same-Gear Noah/Flood interval from File_18, not a newly selected cross-Gear difference.

\[
N-F=12kr(r-1)=\frac{600}{529}k=600,
\qquad k=529.
\]

The resulting anchor difference is d=25. The source Flood coordinate 2456 then fixes the origin:

\[
\alpha=2456-12(529)\frac{25}{23}=-4444,
\qquad b=\alpha+25=-4419.
\]

| Reconstructed target row | First | Second | Third |
| --- | --- | --- | --- |
| Ordinary 11 | 1400 | 1906 | 2456 |
| Apparent 12 | 1904 | 2456 | 3056 |
| Ordinary 13 | 2458 | 3056 | 3706 |

The apparent first target is 1904, which agrees with the original Joseph closing source identity 1794+110. This source identification remains a separate requirement from the geometric reconstruction.

The 600-year interval is common to all three allowed Gears, so it alone does not choose G1. With the absolute Flood coordinates, G2/G3 reconstruct apparent Creation −4442/−4440; these lie outside the held apparent field. G1 alone fits that field and recovers the closing −4444 member. Ordinary Creation is selected from its fixed field; no Creation Gear movement is used.

The result reduces the construction to two source junctions, the shared family/ratio shape, one 600-year scale calibration and one absolute source coordinate. These premises reuse the supplied model; the calculation is not an independent historical proof of the unit.

**Validation.** 10 exact arithmetic/structural checks passed. The 18 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.** Apply the symbolic junction equations to N04 while retaining its two explicit G2-versus-G1 residuals and the fixed apparent row.