PROBABILITY FIELD THEORY Structural Unification: Derivation of Planck Constant (h), Fine-Structure Constant (α), Strong Coupling Constant (αs), and Hubble Tension (Ho) via γ and A086

Announcement: Discovery of the endogenous self-regulation of the fine-structure constant (α). Location: Section 3.5.1, Page 34, Equation 14.

Announcement: Resolution of the Hubble Tension via Nodal Probability Equilibrium. Location: Section 3.8, Page 48-56.

10.5281/zenodo.17425185 

Abstract. Modern physics faces a structural tension between quantum randomness and determinism. This work introduces the Equilibrium Principle (EP), a fundamental framework establishing probability as the physical magnitude governing the universe's structural stability. The constant A086 is the structural resistance factor that measures how much information the system can absorb before collapsing or undergoing transformation. It acts as the universal homeostatic regulator where informational entropy (γ) and probabilistic intensity converge; within this state, space and time function as iterative variables of a system calculating its own stability. It is demonstrated that every random physical phenomenon is governed by a convergence domain, that seeds a probability field within the architecture of space-time, where randomness and causality are two sides of the same coin. All natural probability is inherently self-regulated in an endogenous manner, manifesting as an equilibrium solution of its own field. The Entanglement Theorem (PE) demonstrates this property for the Planck constant (h), the fine-structure constant (α), and the Hubble constant (H0), establishing that these magnitudes are not arbitrary parameters but intrinsic equilibrium solutions where the realization function (FA) and the field's structural resistance (FA´) converge. By normalizing energy to a unit manifold, the EP demonstrates that energy density is the physical manifestation of structural probability intensity, postulating Bounded Occurrence as a universal constraint where no event with positive probability remains indefinitely unrealized. Within this framework, α ≈ 0.007297352569 is derived from the intersection of the informational limit γ ≈ 0.5772 and the continuous-discrete structural approximation threshold at Zmax ≈ 117.97, identifying Oganesson (Z = 118) as the empirical limit of unstable atomic organization. The theory identifies Plutonium (Z = 94) as the symmetry node coinciding with the final natural element. Similarly, αs ≈ 0.1175 is obtained as a pure structural probability at the electroweak scale, defined by the ratio between saturation energy and the gluonic manifold (n = 8). The Structural Consistency Criterion (SCC) demonstrates that gauge field unification and the MSSM configuration are necessary consequences of probabilistic stability. The framework precludes the existence of element Z =119, identifying it as a state beyond the system's derived structural stability limit. Accelerator synthesis is physically impossible: the force-brute approach of high-energy collision inevitably dissipates into vacuum distortion before structural stability can be achieved, marking the end of the technological collision paradigm. This theory demonstrates why the synthesis of Z =119 is impossible; this element does not exist and, therefore, the burden of proof does not lie in demonstrating the non-existence of the non-existent. Such responsibility belongs to the theoretical framework that argues for its possibility and to the experimental praxis that must prove it with facts. The numerical equivalence between γ and the time-dilation factor at a black hole's photon sphere (1/√3) unifies quantum equilibrium with general relativity. The observed vacuum energy density (ρΛ ≈ 10-9J/m3) is derived directly from the system´s unification cycle (nE/dc3), validating the model’s predictive power across cosmological scales. The architecture of the cosmos—from galactic rotation curves to subatomic couplings—emerges naturally from the physical conservation of probabilistic coherence. This work demonstrates that the Hubble Tension as a dynamic nodal transition between the early symmetry equilibrium point (∣ψp∣ = 0) and the structural equilibrium limit (∣ψp∣ = γ ≈ 0.5772), manifesting the evolutionary self-regulation of the universe: A = (FA = 0.5 /FA = γ) = 0.5/0.5772 = √3/2 = 0.8660. This framework links the 10-36 m/s2 background acceleration to the 70.43 km/s/Mpc Nodal Attractor, resolving the Hubble Tension through the field's physical probability density.

Keywords: Probability as a physical magnitude; Entanglement Theorem; Probability equilibrium; Euler-Mascheroni constant; Fine-structure constant; Hubble Tension