Ab-initio Electroweak Normalization and Mixing from a Coherent Pre-Geometric Background

This paper develops an ab-initio electroweak normalization in which the SU(2)_L and U(1)_Z  gauge couplings—and therefore the electromagnetic coupling e and fine-structure constant α—are fixed by a coherent pre-geometric background rather than calibrated to Standard Model electroweak data. A single background stiffness τ(ρ₀), together with fixed projection weights selecting the weak and Cartan directions, defines the neutral kinetic structure. The photon arises as the unique massless neutral mode, and its coupling is extracted without introducing electroweak fit inputs.

Using these UV “boxed” boundary conditions at the coherence/matching scale Λ_q, we evolve the couplings to M_Z (and to the Thomson limit) with a two-loop EFT renormalization group including threshold matching and quantified internal theory bands. For the canonical product-UV (isotropic) ledger (ω_L,ω_Z)=(1,1) with τ(ρ₀)≈0.178, the baseline prediction is α⁻¹(M_Z)≈140.8 and sin²θ_W(M_Z)≈0.258, which motivates a refinement: the realized coherent vacuum cannot be isotropic.

A diagnostic inversion identifies the required deformation of the neutral stiffness kernel, and Appendix J exhibits a concrete microscopic mechanism—coherent coupled dynamics of the morton x-pair—that naturally generates the needed anisotropy and yields UV handles consistent with the observed electroweak normalization α⁻¹(M_Z)≈127, sin²θ_W(M_Z)≈0.231 in the Scenario-B closure. The paper also includes a first-principles lattice computation of vacuum polarization in an internal S[θ,Z] current theory (a controlled analogue used for internal consistency/closure, not a claim of full QCD reproduction). Code, run manifests, and data products used to generate figures and tables are provided in the accompanying repository.

Revision note: 

Corrected Appendix J.11 scalar-wall closure to derive C_parent directly from the scalar potential declared in J.9. Updated the stationary scale and displacement outputs accordingly. The electroweak kernel, anisotropy mechanism, and RG results are unchanged.