A Pre-declared Inertial Audit of the Coupled SkyrmeSubstrate Conguration Paper IV of the Verarmungsfeldtheorie series

We report the result of a pre-registered inertial audit of the coupled (U,χ) static congura- tion constructed in Paper III of the present series. The audit evaluates the rigid-translation moduli inertia Gcoupled XX on the archived Paper-III branch and compares the dimensionless ratio R(α) = Gcoupled XX /Ecoupled against the Paper-I at anchor R(0) = 1.0000446 on the pre-declared coupling grid A= {0.05,0.10,0.15,0.20,0.25,0.28}at mχ = 1. The primary observable is δmax = maxα|R(α)/R(0)−1|. We nd δmax = 0.2611423 at α⋆ = 0.28, placing the coupled branch in Outcome B: partial inertial preservation under the frozen Protocol Note v0.1. The drift is mechanistically driven by the conformal A2-weighting of the Skyrme contribution to the moduli inertia, an eect predicted on structural grounds by the frozen Structural Pre-Numerical Expectation Note v0.1 before any numerical evaluation. The drift is monotone across the branch and predominantly accelerated in coupling; the classication is stable under the D1, D2, D3, D5, D6 admissibility lters, with the D3 mesh stability check veried via an auxiliary branch-preserving regrid procedure. D4 is directly veried at the multi-seed probe points α= 0.10 and α= 0.20 with relative spreads ∼10−12; a full-grid D4 extension was not performed and is documented as a coverage limitation. The static internalisation of the Paper-I sectoral imbalance documented in Paper III therefore moderates, but does not remove, the inertial obstruction. The minimal scalar-conformal synthesis is not inertially closed; the minimal path remains open for the controlled robustness probes permitted under Outcome B, and explicitly does not justify ontological escalation at this stage.