Physical Constants as Scalar Projections of Stable Coupling Channels in PJM–GTWSSF–USC–GTCW Ontological and Formal Annex to the White Book

Physical Constants as Scalar Projections of Stable Coupling Channels in the PJM GTSFC USC GTCW Framework This work is an ontological and formal annex to the PJM GTSFC USC GTCW research programme, developed as an attempt to formulate a possible relational and informational layer of physical description. The document does not reject the Standard Model or the established achievements of classical, relativistic, quantum, nuclear, particle, cosmological and high-energy experimental physics. The adopted perspective treats this heritage as the foundation for a further question: whether beneath the layer of observable scalar values, parameters, constants, masses, couplings and amplitudes there may exist a deeper structure of relational physical compatibility. The starting point of the work is the assumption that numerical values used in physics are tools of the observer's description, not the primitive mechanism of nature itself. Physical constants, masses, couplings and effective parameters are interpreted here as observable projections of stable coupling relations. This means that number is not rejected as a scientific tool, but is placed in a broader context: as the result of a projection of relations between geometry, topology, phase, chirality, spin, curvature, energy, momentum and the structure of interaction channels. The Standard Model describes the effective values of these relations with remarkable precision and remains the basic reference layer of particle physics. This annex does not question that effectiveness. It asks, however, whether the observable parameters of the Standard Model may be treated not as ultimate input data, but as scalar traces of a deeper condition of relational stability. In this sense, the USC formalism does not replace known physics, but proposes an additional level of interpretation: a relational and informational level in which the stability of a physical object follows from the closure condition of its coupling parameters. The work develops a conceptual and mathematical-physical apparatus including the projection operator of constants, the relational closure defect, the coupling and interlocking operator of relations, the relational space, formalization through POVM measures, the Fisher Bures metric, dagger monoidal categories, holonomy, connections, the renormalization flow of projections and the interpretation of selected physical constants such as the fine structure constant, the Fermi constant, the Boltzmann constant, the gravitational constant, the Planck constant and the speed of light. The aim is not to assign new numerical values to these quantities, but to indicate that their physical meaning may be understood as a scalar projection of stable coupling channels. A particularly important distinction is made between a mathematical constant and its physical occurrence. A mathematical constant, such as pi, remains an invariant of mathematical definition. What may vary is the physical realization of geometry, in which relations between circumference, radius, curvature, surface and volume are projected by the structure of space, boundary conditions or the method of measurement. Similarly, physical constants are not treated in this work as primitive numbers of nature, but as observable traces of deeper compatibility relations. The annex is programmatic, formal and ontological in character. Its purpose is to organize a language in which physical scalar values are treated as traces of stable relational and informational channels, rather than as the final explanatory level of nature. The work provides a foundation for a subsequent technical and numerical development in which the photon electron channel will be treated as a surface mode of electromagnetic information transfer, while the neutrino nucleon channel will be treated as a deep mode of weak nuclear information transfer. In this sense, the document serves as the ontological foundation for further quantitative, calibration and falsification analyses within the PJM GTSFC USC GTCW programme.