The Yuanzhi Field Theory — Paper II : Path Integral Quantization for Non-Associative Algebras and the Topological Origin of the Lepton Mass Spectrum

This paper provides the rigorous mathematical foundations for the Yuanzhi Field Theory, resolving the open technical gaps in the axiomatic framework of the companion work "The Silent Glacier." We first construct a rigorous path integral for the non-associative octonionic matrix model using Hida white noise analysis, circumventing the failure of the Trotter product formula. The physical state space is lifted to a Gelfand triple of Hida distributions, where the strictly associative Wick product defines interactions. Convergence is proven via the Kondratiev-Streit theorem with gauge fixing. Second, we resolve the cyclic cohomology paradox by lifting the non-associative Albert algebra J3(O) to the universal enveloping algebra U(e6) via the Tits-Kantor-Koecher construction. A refined cubic projection and form contraction define a legitimate 5D cyclic cocycle for anomaly inflow. Third, we derive the dimensionless constant α = 66/π² that governs the exponential relation between lepton mass and hyperbolic knot volume. Three independent paths—M-theory flux quantization, the dual Coxeter number of e6, and anomaly matching—converge on this value. We correct earlier Dynkin index misidentifications and establish the principal SU(2) embedding linking geometric volume to E6 gauge theory. Fourth, we compute lepton mass ratios including one-loop Reidemeister torsion and effective Vassiliev corrections. The muon-to-electron mass ratio matches experiment to 0.5%, and the tau-to-muon ratio agrees with observation for reasonable supersymmetric cancellation parameters. The emergent scale Λ ≈ 398 GeV aligns naturally with the electroweak scale. Fifth, we extend the framework to quarks, identifying weak doublets with hyperbolic links and deriving the CKM hierarchy and CP violation from volume differences and complex Chern-Simons invariants. An extended Epilogue addresses the ontological and meta-cognitive paradoxes arising at the boundaries of any final theory. This work establishes a falsifiable, quantitative bridge from exceptional algebraic structures to the observed particle spectrum.