Universal Mass Gap Formula ∆m = m0 ln K: Spontaneous Kubo-Martin-Schwinger State Emergence with Maximal Quantum Chaos

Abstract

We demonstrate that quark confinement and a non-zero quantized mass gap naturally emerge from deterministic, exactly solvable chaotic dynamics. Crucially, the fluctuation spectrum is natively quantized by discrete Lyapunov exponents λL = lnK, yielding a universal logarithmic mass gap formula: ∆m(K) = m0 lnK (K = 2,3,...) For prime topological degrees K (K = 3, 5, 7, 11, . . . ), this formula reproduces experimental hadron spectroscopy data—spanning light mesons, heavy quarkonia (charmonium and bottomonium), and Lattice QCD glueball spectra—with extraordinary precision within 0.5% relative error (Figs. 1–4). In contrast, composite branch scales (e.g., K = 4, 9) systematically exhibit downward mass shifts due to sub-branch prime factorization decay channels. As a benchmark prediction for light meson spectroscopy, we determine the K = 11 prime mass gap at 2682.0 MeV. Furthermore, by evaluating Koopman-Perron-Frobenius spectral duality over Takenaka-Malmquist isometric bases, complex- time analytic continuation directly unveils an autonomous thermal Kubo-Martin-Schwinger (KMS) state at temperature T (K) = ħ ln K without requiring external heat baths. Full mathematical 2πkB proofs, including the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation and exact canonical commutation relations [aˆ,aˆ†] = 1, are provided in the Supplementary Material.