Confined Photonic System

Here is the English translation of the Abstract, preserving the academic tone, rigor, ontology, and conceptual structure of the Manuscript v37. ABSTRACT (English Version) This manuscript presents the complete formulation of the Photonic-Conjugated Model (PCM), a physical–mathematical ontology that reconstructs the structure of matter, the fundamental interactions, and the genesis of particles from confined electromagnetic fields. The PCM is built upon the postulate that every physical entity — photons, leptons, hadrons, nuclei, and neutrinos — emerges as a topological state of the Fundamental Photonic Mesh, mediated by the Critical Radius r*, understood as the minimal unit of curvature and coupling of physical space. Toroidal topology, helical torsion, and electromagnetic confinement constitute the ontological pillars that replace the formalism of point-like particles, eliminate ultraviolet divergences, and render renormalization procedures unnecessary. The manuscript demonstrates that processes such as Breit–Wheeler, the emergence of electric charge, leptonic and hadronic decays, the formation of protons and neutrons, and the structuring of the atomic nucleus are manifestations of a single geometric mechanism: the topological saturation of the r* mesh followed by the stabilization of conjugated photonic modes. The detailed analysis of the Tau (τ⁻) reveals its nature as a multi-tubular photonic super-mode, whose collapse naturally explains both leptonic decays and the direct generation of pions. The manuscript then presents a framework for the inverse topological problem (Functional EM + Decay Sector → Field Reconstruction), offering guidelines for algorithms capable of inferring internal particle structure from experimental data. Beyond theoretical foundations, the PCM establishes formal convergence with QED and the Standard Model in low-energy regimes, while providing a continuous ontology in which those models become effective interpretations of a single underlying substrate. The manuscript introduces new experimental predictions, topological diagrams, criteria for photonic-toroidal stability, EM characterization of nuclei, a non-virtual interpretation of mediated forces, and identifies the fundamental granularity r* as a physically real limit of field dynamics. The result is a unified theory of simple structure and high explanatory power, in which matter is not added to the electromagnetic field but is the electromagnetic field itself in a state of topological confinement. The PCM therefore offers a coherent and finite mathematical pathway to understand particle genesis, charge quantization, nuclear stability, and the emergence of quantum mechanics from first geometric principles.