Entropy–Order Balance IV: The Standard Model from Theory-Space Stability

Any finite-resolution description of a physical system incurs two costs: an information cost, quantifying microscopic complexity via relative entropy, and an ordering cost, quantifying geometric or structural organization. The Entropy–Order Balance (EOB) framework postulates that realized physical laws correspond to Lyapunov-stable equilibria of the total cost functional. Parts I–II derived gravity and quantum mechanics; Part III derived local quantum field theory and a unique theory-space selection mechanism. This paper evaluates that mechanism explicitly: the Standard Model emerges as the unique maximizer. Starting from the seven inputs established in Parts I–III — five operational axioms, Lyapunov stability, and dilation covariance, with no new axioms introduced — the paper derives: The gauge group SU(3) × SU(2) × U(1) as the unique global maximizer among all compact gauge groups with anomaly-free chiral fermion content, via exhaustive enumeration (129 candidates) combined with a monotonicity theorem covering all larger groups Three chiral generations from CP-violating efficiency: the Jarlskog invariant per angular parameter is uniquely maximized at N_g = 3, with the Horn majorization bound forcing O(N_g^{−4}) decay for N_g ≥ 4 A single Higgs doublet pinned to the electroweak metastability ridge β_λ(μ*) ≈ 0 Log-even Yukawa hierarchies with parameter-free predictions: |V_{us}| ≃ √(m_d/m_s) ≈ 0.224, |V_{ub}|/|V_{cb}| ≃ √(m_u/m_c) ≈ 0.085, and a leptonic CP phase δ_{CP} = 270° ± 14° A No-Alternative theorem: any non-decoupled beyond-Standard-Model extension strictly reduces the theory-space functional Cosmological consequences from the same viability-face structure: Bunch–Davies vacuum selection, slow-roll inflation with n_s ≈ 0.964 and r ≈ 3.5 × 10^{−3}, and the effective cosmological constant Λ_{eff} = cH₀² with full SM matter content An ancillary Python script provides independently reproducible Smith Normal Form certificates for all 129 candidate gauge groups. The total input count remains seven; the Standard Model is an output. Parts I–III (companion papers) derive the axiomatic framework, quantum mechanics, general relativity, local quantum field theory, and the theory-space selection mechanism from which these results follow.