Rest Mass as Spectral Gap: Definitional Derivation of m0 from M3(C) Geometry

This paper provides a structural definition of rest mass m0 as the operational latency induced by the spectral gap of the minimal non-commutative algebra M3(C). Definition: m0 := κ·|λi - λ̄|, where λi are eigenvalues of normalized M ∈ M3(C), λ̄ is their arithmetic mean, and κ = ℏ/(c·ℓP) is the dimensional conversion factor with ℓP the minimal operational length scale derived from the metric structure axiom of Cognitional Mechanics. The spectral gap |λi - λ̄| is invariant under unitary conjugation, establishing it as a basis-independent structural quantity. Four fundamental forces contribute to m0 through different projections of this gap: non-commutative constraints (strong force) contribute ~99% to hadronic mass, diagonal trace components (electromagnetic) ~1%, eigenvalue transitions (weak force) <0.1%, and background modulation (gravity) provides uniform scaling. The necessity of three fermion generations follows from M3(C) minimality (n = 3 required for metric triangulation and spectral stability). Mass hierarchy corresponds to spectral excitations with characteristic scale δ = √(3/2). Numerical results: α⁻¹ = 137.0359 (relative error 0.004% vs CODATA); muon g-2 anomaly consistent with Cognitional Mechanics prediction; proposed ISS orbital test Δ(α⁻¹) = +0.0002. The Higgs mechanism is reinterpreted as explaining trace-component excitations (~1% of hadronic mass), with the 125 GeV resonance corresponding to Tr(F) ≠ 0 perturbations. The dominant 99% contribution arises from non-commutative operational constraints. This definition requires no new particles or extra dimensions and preserves all Standard Model predictions.