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

Paper and reproducible code for a coherence-gated mechanism that induces an SU(2) gauge structure from local internal-frame redundancy on a scalar-coherent domain (Omega_coh). Coherence gating is implemented as a strict domain-of-definition restriction for gauge observables, rather than as a smooth multiplicative weight, which can otherwise spoil the inhomogeneous gauge-connection transformation law. On coherent domains, a smooth rank-2 projector and local orthonormal frames yield the standard Wilczek–Zee SU(2) connection with exact gauge covariance, and the associated curvature admits a compact projector-commutator form; an explicit nonzero-curvature example is included.

Beyond the geometric existence of the gauge structure, the manuscript provides an explicit kernel-to-normalization interface in a tractable quadratic “two-leg” benchmark. Schur-complement elimination of heavy locking modes yields a canonical light-sector kernel and a dimensionless projector weight (benchmark value approximately 0.296). The matching-scale inverse coupling is fixed by the ratio of this projector weight to a positive stiffness parameter tau0, which is defined by auxiliary two-form (BF-type) elimination on the coherent domain. In the benchmark kernel, tau0 is related to an averaged heavy-mode compliance tau_sus by a fixed trace and transverse bookkeeping identity, separating the geometric necessity of the gauge field from its microphysical stiffness input.

A companion notebook reproduces the benchmark two-leg reduction, canonical normalization, projector-weight calculation, the tau_sus-to-tau0 normalization 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.