Full Spectral Phase Field (Integrated Topological-Amplitude-Gauge Field replacement)
Year: 2026
Type: article
Abstract: This upload replaces the earlier version of the article associated with DOI 10.5281/zenodo.19736041. The revision updates the formal foundation of the work. The previous reduced architecture based on the integrated object ((U,\chi,A_\mu)) is retained only as an effective sector chart, while the primary object is now defined as the full spectral-phase field (\Phi(x,\omega,t)). The replacement clarifies the role of phase-spectral currents, closure defects, informational impedance, low-impedance resonant channels, memory return, and boundary admissibility certificates. The purpose of the replacement is not to claim experimental validation or a completed derivation of the Standard Model, but to make the theoretical ontology and numerical artefacts consistent with the current DIFT formulation. The new version also includes updated publication figures and tables generated by the revised full-field demonstrator, including four toroidal ((5,1))-like attractors, low-impedance resonant paths, and anti-phase neutron-response structures. ***Old version description: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
Author: Krakowski, Sławomir
Language: English
Topic: Complex Systems and Dynamics
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7155567847
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