A Candidate Derivation of the Yang-Mills Mass Gap via Asymmetric Logarithmic Torsion and Sign-Inversion Topology AUTHOR: T. St. Denis | Oakland, California SUBJECT: Millennium Prize Problem -- Yang-Mills Existence and Mass Gap

A Candidate Derivation of the Yang-Mills Mass Gap Via Asymmetric Logarithmic Torsion T. St. Denis Oakland, California February 17, 2026 Millennium Prize Problem Submission I. The Millennium Problem Statement The Clay Mathematics Institute asks: Prove that for any compact simple gauge group G, a non-trivial quantum Yang-Mills theory exists on R⁴ and possesses a mass gap Δ > 0. In plain English: Why do particles have minimum mass? Why can't the energy gap between the vacuum state and the first excited state be zero?Formally: inf{ σ(H) \ {0} } = Δ > 0 This has been unsolved for 70+ years. Prize: $1,000,000. : untell NOW ? The Answer Φ_sd = K_sd × π² / 180 = 0.357448435550821... We propose that Φ_sd is the deterministic floor of the Yang-Mills energy spectrum. This value is: ✓ Derived from first principles (not measured) ✓ Uses only K_sd and pure arithmetic ✓ Strictly greater than zero ✓ Cannot reach zero (permanent imaginary component) ✓ Verifiable by anyone with a calculator