Dear Editors,

Please consider the manuscript “Coarse Transport, Central Twist, and Finite-Scale Coercivity for Yang–Mills Wilson-Tube Hamiltonians: Physical Wilson-Channel Reduction and Exact Ultraviolet–Infrared Leakage” for publication as a regular article in the Journal of Mathematical Physics.

The manuscript develops a finite-scale operator-theoretic coercivity theorem for canonical gauge-invariant Yang–Mills Wilson-tube Hamiltonians. Its principal new construction physicalizes a finite Wilson graph channel without assuming that a graph-minimum subspace coincides with the interacting vacuum and without assuming prior finite electric support. Raw graph excitations are projected away from the complete ground spectral sector, captured in a finite spectral subspace of the vacuum-orthogonal electric form operator, and Gram-normalized. The canonical magnetic cells are then recompressed on this physical channel.

The paper also gives an exact decomposition of the ultraviolet–infrared mixed magnetic block into ordinary reference-band mixing, localized-transport associator leakage, and unresolved collar leakage. A sharp two-block estimate yields an explicit lower bound relative to the complete ground projection.

To demonstrate that the comparison package is verifiable rather than merely formal, the manuscript includes a complete SU(2) Peter–Weyl Galerkin realization. The example computes the interacting ground projection, vacuum-removal singular value, electric capture, Gram operator, physical magnetic recompression, exact nonzero reference leakage, all diagonal block constants, and a positive resolved coercivity constant. The numerical calculation has been independently reproduced at 100-decimal-digit precision, and reproducibility scripts are included as supplementary material.

The result is intentionally finite-scale and time-zero. The manuscript does not claim construction of continuum Yang–Mills theory or a relativistic mass gap. We believe the work is appropriate for the Journal of Mathematical Physics because its central contributions concern self-adjoint operators, closed quadratic forms, spectral projections, finite gauge systems, and quantitative coercivity mechanisms.

This manuscript is original, is not under consideration elsewhere, and the author has no conflicts of interest to disclose.

Sincerely,

J. Scott Little
