C111 — Ratio, scale and origin require distinct bindings

22 September 2026 · Step 9 of the authorized ten-step Mirror continuation (C103–C112).

The reduced junction model has four continuous parameters: apparent origin α, anchor difference d, base unit k and common ratio r. Its assumptions have separate jobs:

The rank calculation is the exact Jacobian rank at the reconstructed solution. The explicit factorization in C108 and calibration in C109 also give uniqueness throughout the declared positive expansion domain; local rank alone would not establish that global statement.

Either junction alone is insufficient. In a formal unit model, the Flood junction admits r=13/12 with a positive anchor difference while missing the Noah junction; the Noah junction admits r=12/11 while missing the Flood junction. These are diagnostic parameter examples, not alternate sourced chronologies. Other source constraints are intentionally not imported into this reduced-model deletion test.

Even after all four numeric parameters are fixed, geometry supplies a coordinate rather than a person's identity. Calling the first apparent target Joseph still requires the original Kohath +110 source rule and its admitted member. That requirement cannot be replaced by matrix rank.

The full fixed-width graph has a different count: 104 variables and rank 101. Its three remaining freedoms occur only in the isolated C5/C6/C7 Creation–Conquest pairs. One already recorded source coordinate per pair raises a diagnostic pinned system to rank 104 without inconsistency. The stored relation graph remains unchanged at rank 101; these explicit source pins are reported separately. The selected junction construction is not left underdetermined by those unrelated graph components.

Validation. 9 exact arithmetic/structural checks passed. The 20 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. Synthesize the graph extension and the conditional ratio/scale reconstruction, publish the completed ten-step checkpoint, then await the user’s 529 × 4 × 2 cycle.