The Volovik / 3He-A Substrate Audit Emergent Cone Invariance and Substrate-Arm Texture Inertia under Fixed-Metric Substrate Rescaling Paper II of the VFT Admissibility Programme

We perform the second admissibility audit of the VFT programme, with the same method- ological discipline as Paper I but on a structurally disjoint model: the superfluid Weyl phase 3He-A of liquid helium-3, in the Jannes–Volovik emergent-tetrad formulation. The audit object is the Anderson–Toulouse–Chechetkin (ATC) continuous double-quantum vortex texture and its translation moduli inertia Mv. We introduce a one-parameter sub- strate rescaling (∆0,pF,vF) →(λ∆0,λpF,vF) that, by construction, leaves the emergent quasi-relativistic metric gµν eff = diag(−1,c2 ⊥,c2 ⊥,c2 ∥) with c∥= vF and c⊥= ∆0/pF invariant. Three results are reported. (i) Test T1a (rigorous): the BCS coherence length transforms algebraically as ξ= ℏvF/(π∆0) →ξ/λ, verified to machine precision over eight grid points in λ ∈[0.5,4] (maximum relative deviation from the analytic scaling below 4 ×10−16). The substrate arm is therefore non-invariant under the variation that fixes the emergent metric, independently of any further assumption. (ii) Test T1b (weak-coupling comple- tion): under the parametric estimate ξd →ξd/λ, the Kopnin translation mass scales as Mv ∼ρξξd →Mv/λ2, withthesamemachine-precisionagreement. (iii)Robustness against the dipole-length hypothesis: writing the uncertain dipole-length response as ξd →ξdλ−q , the mass scales as Mv →Mvλ−(1+q), so inertia invariance under T1 requires the special compensating value q=−1 (ξd →λξd). For all other q tested (q ∈{0, 0.5, 1, 1.5}) the mass is non-invariant on the entire λ-grid. The Outcome A classification therefore does not rely on the weak-coupling assumption. The topological-protection column carries two integer-protected invariants: the ATC skyrmion number BATC ∈π2(S2) and the Weyl-point momentum-space charge N3 ∈Z, both invariant under the substrate rescaling. The audit returns Outcome A (structured scaffolding dependence): the substrate coherence length is rigorously non-invariant under T1a, and within the Kopnin-type inertia realisation this induces non-invariance of Mv unless a compensating ξd-scaling is imposed. 3He-A internalises the auxiliary structure that Skyrme keeps external, but does not eliminate scaffolding dependence; it relocates it from external auxiliary metric to substrate constants. The emergent cone is blind to a substrate deformation that the texture inertia sees.