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.