Non-Abelian Gauge Structure from Coherence-Gated Internal Symmetries: A Projection Mechanism and a Kernel-to-Coupling Map

Published in AIP Advances (2026). The manuscript presents an effective-theory framework in which, on a scalar-coherent domain Ωcoh where a smooth rank-2 projector exists, local internal-frame redundancy induces the standard Wilczek–Zee SU(2) connection with exact gauge covariance. “Coherence gating” is implemented as a strict domain-of-definition restriction for gauge observables (not a smooth multiplicative weight), preserving the inhomogeneous connection transformation law; curvature admits a compact projector-commutator form, and an explicit nonzero-curvature example is included. Beyond the geometric construction, the paper provides a concrete kernel-to-normalization interface in a quadratic two-leg benchmark. Schur-complement elimination of heavy locking modes yields a dimensionless projector response fraction (ωeff≈0.296 in the benchmark), and the matching-scale inverse coupling is fixed by g−2(Λ)=ωeff/τ0 with τ0>0 defined via auxiliary two-form (BF-type) elimination onΩcoh. The revision also clarifies boundary/applicability statements near ∂Ωcoh, the non-topological role of the BF-type normalization, and the treatment of anisotropy via trace-ratio definitions (so fT need not equal 2/3 outside isotropic settings). The companion notebook reproduces the benchmark reduction, normalization steps, projector-weight calculation, the τsus ⁣→ ⁣τ0 bridge, and sensitivity scans. All reported benchmark values are derived directly from the stated parameter set; no numerical fitting or parameter tuning is performed. The notebook runs in a standard Google Colab or local Jupyter environment and regenerates the figures and tables associated with the benchmark analysis. This is the peer-reviewed accepted manuscript and includes the companion notebook. The final published version may differ after copyediting and typesetting.