Entropy–Order Balance VIII: Cross-Domain Consequences, the Yang–Mills Mass Gap, and a Complete Fundamental-Physics Audit

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–VII established the complete physical and mathematical architecture of the framework. This paper serves as the capstone of the series, systematically combining the machinery of the prior papers to resolve a broad slate of historically intractable cross-domain problems — including an unconditional proof of the Yang–Mills mass gap.

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 resolves fifty fundamental physics problems spanning quantum gravity, particle physics, cosmology, and foundations:

• An unconditional proof of the 4D SU(N) Yang–Mills mass gap (m > 0). Derived asymptotic freedom (b₃ = −11N/(48π²) < 0, Part VI) controls the flowed coupling at a single finite flow time s₀, enabling sectorwise Bakry–Émery coercivity on the ordered region where field strengths are O(g(s₀)). The Bogomolny barrier and a quantitative Sard estimate make the inter-sector transition tube exponentially small; coarea-barrier promotion converts the sectorwise log-Sobolev inequality to a global LSI with ρ ≥ c/s₀. The Martinelli–Cesi exponential clustering theorem connects the gradient LSI to the Osterwalder–Schrader spectral gap. Mosco convergence transfers the lattice spectral gap to the continuum, and a bridge theorem (compact-interval Källén–Lehmann contradiction) establishes m > 0.

• CPT symmetry and the spin-statistics connection, derived via the Jost theorem from the framework's emergent Lorentzian signature and spectrum condition

• The arrow of time as a channel-theoretic theorem, with the Past Hypothesis selected by theory-space stability at the cosmological bounce, and the problem of time resolved via the semigroup structure of the EOB contraction

• Thermodynamic emergence (all four laws), with temperature identified as the s⁻¹ scaling of the contraction rate

• A massless graviton (m_g = 0), the equivalence principle, speed of gravity v_g = c, cosmic censorship, and black hole no-hair — all from exact diffeomorphism invariance. Non-perturbative quantum gravity via the finite-resolution ordering cost K_s

• Bell nonlocality, wavefunction ontology, and the measurement problem resolved via barrier dominance and channel non-sufficiency

• Proton stability, BSM exclusion (including supersymmetry and extra dimensions), charge quantization, and gauge coupling non-unification from the no-alternative theorem

• Boltzmann brain suppression from barrier dominance at the observer scale

• Baryogenesis via derived Sakharov conditions, with a quantitative estimate η_B ≈ 10⁻¹⁰ consistent with observation

• The strong CP problem resolved (θ̄ = 0 from viability-face structure) and neutrino masses derived (normal hierarchy, δ_CP = 270° ± 14°, Σm_ν ≈ 0.06 eV)

• Fine-tuning dissolved by the unique theory-space maximizer

• Inflation derived (Starobinsky potential, n_s ≈ 0.964, r ≈ 3.5 × 10⁻³), dark matter identified (sterile neutrino, m ~ 7 keV), and the cosmological measure problem dissolved

• Spatial topology S³ from Λ > 0 and mode-counting maximization

An ancillary Python script (11 sections, 504 lines) provides a complete empirical ledger and sensitivity analysis, verifying all 21 quantitative predictions against PDG 2024 data and demonstrating structural robustness. The falsification ledger identifies 17 untested predictions with specific experiments and timelines, including the c⋆ bridge test connecting laboratory decoherence to the cosmological constant. With this paper, the EOB program resolves 50 of 50 fundamental physics problems from seven operational axioms with zero free parameters.

Parts I–VII (companion papers) derive the axiomatic framework, gravity, quantum mechanics, the Standard Model, strong-field physics, absolute coupling constants, and the underlying mathematical theorems from which these results follow.