The Confinement Scale from the Electron Mass and the Fine-Structure Constant: Mutual Entanglement as Channelized Strain

Abstract

The scale of QCD confinement is an input to the Standard Model, traceable to the measured strong coupling and unrelated to any electromagnetic quantity. This paper derives it from the electron mass and the fine-structure constant alone, σ=N_ch m_e^2 c^3/(ħα^2), where N_ch is an integer supplied by the interface lattice of dual-domain cosmology. The mechanism distinguishes global entanglement, which dilutes radially and is α-suppressed at the interface, from mutual entanglement, a two-ended connection channelized into a tube that escapes that dilution at both ends. Its arity fixes N_ch=12·C(3,2)=36, hence √σ=420 MeV, inside both the lattice static-potential and Regge-slope ranges, with no hadronic datum entering. Solving the ultrarelativistic three-body Y-junction problem gives K = 5.3384 ± 0.0006 and the closed relation μ=K√(N_ch )/2α, placing the spin-independent baryon mass 3.3% high and the nucleon mass 3.8% high after the observed N–Δ splitting. Restoring the short-range term omitted from the Hamiltonian closes the ground-state residual to +0.07%. A pre-registered test of the radial spectrum fails, and the rescue proposed for it is computed and excluded; the failure lies in the Hamiltonian, not in the postulates. Three inputs remain postulates: the α^(-2) concentration factor, the projection rule Mc^2=⟨V⟩, and the arity-indexing postulate. The central claim survives them: the global/mutual distinction supplies a geometric reason why the strong energy scale exceeds the electromagnetic by a factor of order α^(-1). Keywords: confinement scale; string tension; proton–electron mass ratio; dual-domain cosmology; mutual entanglement; flux tube; fine-structure constant; Regge slope