Atomic Microcosmos without "the subatomics": Algebraic Unification of Electron, Proton, and Neutron from M3(C) Structure

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 Trₐdj (H²) ²/Trₐdj (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.