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

In the Standard Model the confinement scale is an input, set by the measured strong coupling and unrelated to electromagnetism. This paper derives it, conditionally on three postulates, from the electron mass and the fine-structure constant alone, σ=N_ch m_e^2 c^3/(ħα^2), with N_ch an integer from the interface lattice of dual-domain cosmology. Global entanglement dilutes radially and is α-suppressed at the interface; mutual entanglement, channelized into a two-ended tube, escapes that suppression at both ends. Its arity fixes N_ch=12·C(3,2)=36, hence √σ=420 MeV, inside the Regge-slope range and 5% below the latest static-potential value, with no hadronic parameter.

The ultrarelativistic three-body Y-junction problem gives K=5.3384±0.0006 and μ=K√(N_ch )/2α, placing the spin-independent baryon mass 3.3% high, a consistency check rather than a determination. Rest mass is identified with the ground configuration's stored strain; energy conservation makes excited levels project in full. The closed-form meson excitations then agree with experiment to within 18%, and the radial spacing alone implies √σ=444 MeV. Two pre-registered baryon tests fail in opposite directions, the radial excitation 7% high and the first orbital band 12% low: the level-ordering problem of constituent-quark models, which no projection rule removes.

The three postulates are the α^(-2) concentration factor, the ground-state projection, and Part V's fiber-completeness postulate. The central claim rests on the first: the global/mutual distinction motivates geometrically, without yet deriving, why the strong scale exceeds the electromagnetic one 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