The Standard Genetic Code as a Dissipative Optimum: A No-Fit-to-the-SGC Framework from S³-MEP

This preprint derives a geometric framework for the architecture and error-robustness of the Standard Genetic Code (SGC) from the S³-MEP (Maximum Entropy Production) framework, with no parameters fitted to the SGC. Eight exact integers — 4 bases, codon length 3, 64 codons, 20 amino acids, 3 stop codons, 61 sense codons, mean degeneracy 3.05, and the NLO bound ≤22 — are derived from the spatial dimension D=3 and the gauge fiber dimension K=7 of the S³-MEP framework (companion paper: DOI 10.5281/zenodo.18878097). Two independent routes yield N_AA = 20: the chiral tangent-space relation 2(D+K) = 20 and the coding-theoretic relation |Σ|(|Σ|+1) = 4×5 = 20. Their equality is equivalent to the algebraic identity K = (D²+D+2)/2 = 7, independently derived from Hurwitz–Cartan octonion completion. The wobble degeneracy at codon position 3 admits a geometric interpretation through the Hopf fibration S¹ → S³ → S². The fiber S¹ has zero intrinsic curvature (minimal information by the Čencov–Fisher–Rao theorem), while the base S² has positive curvature (maximal information). Positions 1–2 are associated with the base; position 3 with the fiber. The Klein four-group V₄ ⊂ Center(Isom(S³)), acting on the four basis vectors of H₁ = V^L_{1/2} ⊗ V^R_{1/2}, generates all three biological classifications of nucleotide bases: purine/pyrimidine (right isospin σ_R), amino/keto (left isospin σ_L), and Watson–Crick complementarity (antipodal map σ_L σ_R). Statistical optimality is confirmed by permutation tests on S₂₀ with 26 published physicochemical descriptors (none fitted to the SGC) and four parameter-free error channels. At the strongest explored PCA projection (5 principal components, 88% variance), Fisher's combined p-value is 5.99 × 10⁻⁹ under a channel-independence approximation — exceeding the significance of the Freeland & Hurst (1998) benchmark. The formula N_AA = |Σ|(|Σ|+1) retrodicts the ancestral code: |Σ|=2 → 6 AA (doublet phase), |Σ|=3 → 12 AA (early triplet), consistent with 10 independent phylogenetic reconstructions and the Trifonov (2004) chronological ranking, which exhibits phase boundaries at exactly the predicted positions (ranks 6 and 12). Keywords: genetic code, maximum entropy production, S³ geometry, Hopf fibration, wobble, amino acids, error minimization, permutation test, Fisher information, Klein group, dissipative structure, MaxCal