PFUSRC-032 Quantum Field Theory from the 45° Bicone: Deriving the Standard Model Lagrangian from PFUSRC Axioms

The Standard Model of particle physics contains 19 free parameters, and the ΛCDM model introduces at least 6 additional ones. Each new observational anomaly is addressed by adding new parameters rather than questioning fundamental assumptions. This paper argues that this “parameter debt” originates from a single root: the lack of a primordial topological ontology. Based on the PFUSRC axiomatic system [2,9]—specifically the 45° triple coaxial bicone as the unique steady-state geometry of the universe [2]—we derive the gauge group, particle spectrum, and Lagrangian of the Standard Model from first principles. The core results are: 1. Gauge group origin: The three layers of the bicone project to SU(3)_C (upper cone, expansion/color confinement), SU(2)_L (waist ring, weak isospin), and U(1)_Y (lower cone, hypercharge). No other gauge group is possible [1]. 2. Particle spectrum: Fermions (half-integer spin) arise from lower-cone contraction dynamics; bosons (integer spin) from upper-cone expansion dynamics; the three generations correspond to the triple coaxial nesting [3]. 3. Weak mixing angle: Rigorously derived as sin²θ_W = 11/48 ≈ 0.22917, with the small deviation from the PDG average (0.23122 ± 0.00004) [22] explained by energy-scale-dependent projection of the small bicones [1]. 4. Fine-structure constant: α⁻¹ = 11² + 4² = 137, topologically exact; the experimental value 137.036 includes projection-layer fluctuations [22]. 5. Lagrangian: The PFUSRC action reduces to the Standard Model Lagrangian in the low-energy, weak-field limit, with all parameters fixed by 12/11, 55, and 137 [1]. We present falsifiable predictions: the running of sin²θ_W with energy scale deviates from the Standard Model renormalization group flow above a few TeV; new particles corresponding to the 55 datum points and prime nodes appear at predicted mass windows; proton decay is topologically suppressed with a specific partial lifetime. This work eliminates all free parameters of the Standard Model, replacing them with topological constants derived from the 45° bicone. The geometric and field-theoretic derivations follow standard differential geometry and quantum field theory methods [14,20]. The theoretical predictions can be tested by future collider and underground experiments [25,26].