# C104 — The extension separates new coordinates from recovered graph connections

22 September 2026 · Step 2 of the authorized ten-step Mirror continuation (C103–C112).

This audit treats each node centre as an unknown and each recorded duration/reflection as a linear equation. Source coordinates are used to check consistency but are not inserted as one-node constraints. Thus the calculation measures the recorded relation system, rather than declaring every known date an independent equation.

| Measure | C43 baseline | C103 extension |
| --- | --- | --- |
| Variables | 81 | 85 |
| Exact rank | 77 | 82 |
| Free coordinates | 4 | 3 |
| Connected components | 5 | 4 |

The seven new duration equations add **5 ranks** while adding four unknowns. Of the seven, **2 are dependent** in the declared admission order. Pivot selection changes with equation order; total rank does not. The certificate lists the independent and dependent admissions.

This is algebraic independence within the frozen typed graph. Source membership is a separate evidential condition: a numerical coordinate does not by itself identify Joseph or validate the chosen cumulative member. Neither the graph rank nor the number of new rows counts independent historical witnesses.

**Validation.** 7 exact arithmetic/structural checks passed. The 13 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.** Attach the selected Kohath records and the original Joseph +110 source equations, then distinguish interval placement from source identity.