Integrated Topological-Amplitude-Gauge Field

What is the smallest field structure capable of sustaining topological identity, amplitude–phase flow, gauge closure, shell organization, and composite binding without collapsing into a single scalar? This work answers that question by constructing an integrated three-sector field Ψ=(U,χ,Aμ), where U∈SU(2) carries topological identity, χ=ρeiθ governs shell currents, and Aμ provides gauge-mediated closure. The paper delivers a complete formal framework: action, Euler–Lagrange equations, topological baryon current, explicit DIFT functionals (coherence, informational impedance, dynamostasis), dimensionless reduction, and linear stability analysis. But the centerpiece is a first-of-its-kind three-dimensional validation on a validated DIFT carrier: H1 (Real-time persistence): A shell-bound χ sector remains dynamically dominant for >90% of the evolution, with final ηshell≈0.9946, ηedge≈0.0018, and exact mass conservation. H2 (Reduced-mode stability): Projected Hessian analysis reveals no negative eigenvalue in a physically interpretable 9‑dimensional fluctuation basis. H3 (Computational trajectory): A continuous homotopy from weak to strong coupling yields explicit terminal observables: E∗=−62.63, R∗=4.51, rshell,∗=5.07, and ω∗=3.13. This is not a claim of particle physics or full quantum theory. It is a rigorous, reviewer‑safe demonstration that a shell‑bearing regime can be dynamically persistent, modally stable (in a reduced sector), and connected to well‑defined observables — turning a conceptual DIFT extension into a computationally testable substrate for further research. Keywords: DIFT, topological field theory, Skyrme model, gauge fields, shell persistence, reduced‑mode stability, computational trajectoryDOI: 10.5281/zenodo.19736041