Part VI — Phenomenology

Abstract

Part VI confronts the Dual–Flux (DF) framework with particle-level phenomenology using only the structural ingredients fixed in Parts I–V. No new dynamical kernels or independent mass scales are introduced. All empirical inputs are limited to measured quantities—the charged-lepton masses, sin²θ_W(m_Z), G_F, and a single dimensionless hadronic slope ratio—while all additional coefficients remain O(1) projector weights fixed by DF sector geometry. Every observable discussed here follows from the present-surface geometry, the TDGL memory kernel, and the sector projectors acting on closed states.

We show first that the three gauge couplings at the electroweak scale {α, α₂, α₃} emerge from a single present-only scale α_*, determined by the DF–Foot lepton analysis, together with the short/long memory ratio w(μ) extracted from the weak mixing angle. A small, non-resonant 2π contribution of the long-memory kernel then reproduces the observed electromagnetic running from m_Z down to zero momentum. The same stiffness scale, combined with G_F, fixes m_W and m_Z at tree level, while the Higgs mass appears as a curvature eigenvalue of the scalar projector, requiring no new dimensionful input.

Mixing matrices arise from small inter-sector leakage on the present surface. The contrast between small CKM and large PMNS angles follows from the DF mass = memory hierarchy and neutrino quasi-degeneracy, while CP violation results from the product of torsion and leakage. This yields sharp no-go signatures: inverted CKM/PMNS hierarchies or vanishing lepton-sector CP phases would falsify DF at the interaction level.

Lifetimes and decay widths follow from the imaginary part of the TDGL kernel after present-closure. Unstable states correspond to differentiated coherons whose loops cannot be sustained by finite present-memory, providing a unified account of the observed hierarchy from stable neutrinos and electrons to rapidly decaying heavy quarks and broad W, Z resonances. Photon interference in double-slit setups is similarly described as linear propagation of non-anchored Φ⁺ flux on Σ_present, with the disappearance of fringes at large distances controlled solely by the finite depth of the present-memory functional, without any collapse postulate.

Overall, Part VI shows that DF can reproduce a broad set of couplings, mass relations, mixing patterns, lifetimes, and interference phenomena using only present-surface geometry, the TDGL memory kernel, and a small set of dimensionless anchors. This places the theory at a point where cosmological tests become the next natural and unavoidable step.