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