Computer-Assisted Existence and Linear Nonnegativity of a Monopole in an Extended U(2) Gauge–Higgs Model

We study a fixed classical U(2) gauge–Higgs model with an adjoint scalar, a determinant-charged scalar, a complex spin-two scalar, and a positive-mass fundamental probe with zero background. At specified nonzero mixing coupling, we present computer-assisted arguments for two separately assessable results. First, continuous residual and coercivity estimates locate a unique radial stationary point in a specified weighted Sobolev ball about an explicitly defined trial. An origin bootstrap and full-field substitution give a smooth finite-energy static field carrying unit model magnetic charge. Second, errors in that same exact background are propagated into the complete perturbation problem. The analysis retains the translational zero mode, treats the massless channels in their proper sectors, controls the full low-angular-momentum blocks, and uses a uniform comparison for all higher angular momenta. A closed quadratic-form construction and a positive-resolvent argument define the Gauss-compatible self-adjoint realization without assuming a bounded zero-frequency inverse. This yields nonnegativity of the stated quadratic form and excludes normalizable growing modes in the specified space. The contribution is a quantitatively auditable combination of existence and full linear analysis for this coupled model, not a new general stability method. No nonlinear stability, open parameter region, production rate, or identification with observed electromagnetism is claimed. Author preprint v1. The work was submitted to the Journal of Mathematical Physics on 21 September 2026; this record does not claim journal acceptance or completed independent peer review. The scientific content is unchanged from the author manuscript of that date. This public version adds publication and licensing information, removes a stray caption punctuation mark, and clarifies that supporting data and U(2)-specific validation programs are available from the author upon reasonable research request. Only the article PDF is included in this record. No new computational replay or independent mathematical validation was performed for this public-version preparation.