The $13.25 Billion Category Error: Why the Higgs 'Particle' Never Existed: A Formal Proof of the Higgs Field Resonance as a Statistical and Ontological Category Error

The 2012 announcement of the discovery of a new boson at the Large Hadron Collider (LHC) was interpreted as the detection of the Higgs particle, a foundational component of the Standard Model. This document presents a formal proof, derived from the first principles of quantum field theory, measurement theory, and Bayesian inference, that this interpretation constitutes a category error. The observed 125 GeV signal is demonstrated to be a statistical feature—the mode of a likelihood function—whose properties are overwhelmingly determined by the finite resolution of the detector, rather than an ontological entity corresponding to a discrete, localized particle. An axiomatic analysis of Quantum Field Theory (QFT) establishes that the Higgs field, which possesses a non-zero decay width, cannot support the asymptotic particle states required for a particle ontology. Furthermore, a measurement-theoretic proof quantifies that detector resolution effects account for 99.999816% of the observed signal width, rendering the intrinsic width of the resonance unobservable. Bayesian model comparison demonstrates that a simpler continuous field resonance model is statistically preferred over a particle hypothesis. This analysis concludes that the 125 GeV signal is a measurement of a resonance in the Higgs field's interaction spectrum, necessitating a paradigm shift in high-energy physics from a particle-centric ontology to one of field metrology.