Contemporary nuclear physics accounts for radioactive decay and nuclear reactions through five independent theoretical frameworks, each with its own force carriers, coupling constants, and free parameters. Alpha decay is modeled via quantum mechanical tunneling through the Coulomb barrier. Beta decay is attributed to weak interaction mediated by W± bosons. Gamma decay is treated as electromagnetic radiation from excited nuclear states. Nuclear fission is described by the liquid drop model. Nuclear fusion is governed by strong force dynamics. No unified derivation from a single axiomatic structure has been achieved within the Standard Model. This paper derives all five phenomena from the axioms of Cognitional Mechanics (CM) and the algebraic structure of M₃(ℂ), the unique minimal noncommutative finite-dimensional C*-algebra, without free parameters. The central result is that all nuclear transitions are instances of spectral relaxation of the resonance coefficient κ toward the Iron Stability Attractor κ(Fe) = 6/13, established as the S4 closure node of the M₃(ℂ) automorphism structure. Alpha decay is derived as separation of the ⁴He Aut-invariant orbit unit. Beta decay is derived as SU(2)₁₂ isospin transition, with parity non-conservation following from the Tier structural non-alignment between the Tier-2 algebraic operation and the Tier-3 spatial symmetry. Gamma decay is derived as Cartan eigenvalue relaxation. Nuclear fusion is derived as two-domain spectral convergence toward κ(Fe) = 6/13. Nuclear fission is derived from the condition δt(x)/t → −1, under which entropy monotonicity becomes unsatisfiable within a single M₃(ℂ) domain. The half-life is established as a Tier-3 dimensional quantity structurally excluded from Tier-2 derivation. The Iron Stability Theorem κ(Fe) = 6/13 unifies all nuclear transitions under a single algebraic fixed point. Sonnet 4.6
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