From Particle Ontology to Spectral Invariance: ξ≡µα as the Algebraic Dissolution of Substructure and the Phlogiston Nature of Modern Particle Taxonomy

This paper establishes that particle ontology is logically unnecessary in fundamental physics. The dimensionless invariant ξ ≡ μα — product of the proton-to-electron mass ratio μ and the fine-structure constant α — cancels all particle-ontological prerequisites through dependence annihilation, yielding a purely spectral quantity. While μ and α individually presuppose particle ontology, their product ξ² = (μα) ² resides in the kernel of the scale-valuation map, constituting the unique minimal generator of scale-invariant spectral observables of M₃ (ℂ). This is not a numerical coincidence but a structural consequence of axioms A1 (non-commutativity) and A2 (metric completeness). The natural variable ξ² admits a closed-form six-term expansion derived exclusively from axioms A1–A3 of Cognitional Mechanics, with zero free parameters. The numerical value ξ² = 179. 5347. . . agrees with experiment to within 1. 73×10⁻¹³ (relative). Once ξ² is constructively realized from the algebra, retaining particle taxonomy as a primitive becomes structurally untenable: the declaration of phlogiston-equivalence is a logical necessity imposed by the algebra itself, not a philosophical preference. All gauge-invariant observables of the Standard Model reduce to spectral data of Spec (D) on the algebra AF = M₃ (ℂ) ⊕ ℂ. The surjective map ℰ: Sₛpec → TSM and the Reconstruction Lemma establish that ξ² is a complete gauge-invariant statistic for the observational content of the Standard Model. Asymptotic freedom, DGLAP phenomenology, and three-generation structure are accounted for as Tier-2 projections of M₃ (ℂ) without particle ontology. Particle ontology satisfies all three phlogiston-equivalence criteria and is structurally redundant.