Abstract

This paper completes the algebraic unification of the atomic constituents -- electron, proton, and neutron -- within the Cognitional Mechanics (CM) framework. The three atomic substances are shown to be not ontological primitives but distinct spectral projection modes of the single algebra M₃(ℂ). The automorphism group Aut(M₃(ℂ)) ≅ SU(3)/ℤ₃ is derived internally from Axioms A1-A2 via the Skolem-Noether theorem, without external introduction of SU(3). The isospin symmetry SU(2)_isospin is uniquely identified as the SU(2)₁₂ subalgebra. The dimension n=3 is proved unique: n=2 cannot generate the required roots, while n≥4 violates the Redundancy Exclusion Axiom A4. The neutron is established as ontologically non-independent: it is the T₃=-1/2 projection of the SU(2)₁₂ isospin doublet, with no independent Tier-2 existence separate from the proton. The nucleon magnetic moment ratio is derived in two layers. The first-order prediction μₚ/|μₙ| = 1.4630 (residual 0.21% against experiment 1.4599) follows from the correction coefficient Φ₁Φ₂/n², derived from the structural identity [Tr_adj(H²)]²/Tr_adj(H⁴) = Φ₂, which holds for ALL traceless Cartan generators via the pure algebraic identity a⁴+b⁴+(a+b)⁴ = 2(a²+ab+b²)² combined with the A1 trace-zero condition. The second-order correction δ₁ = αs·4/39, with normalization constant Φ₃ = 13 uniquely forced by the CM Self-Containment principle and the internal structure of Axiom A2, reduces the residual to 0.006%, yielding μₚ/|μₙ| = 1.45999. No free parameters enter at any stage. The Standard Model gauge structure SU(3)×SU(2)×U(1) is subsumed as the Tier-3 image of M₃(ℂ)⊕ℂ under projection, not negated. Published on March 29, 2026 DOI: 10.5281/zenodo.19301842