Confinement of the ER-String Baryon (XX v4)

Part XVIII established that the nucleon core is the relativistic rotational kinetic energy of a triply-truncated Einstein-Rosen (ER) bridge, giving a constituent mass m const = M p /3 ≈ 312.8 MeV. This paper closes the dynamical side of that picture by deriving the equation of state of the ER string and demonstrating that the same constituent mass fixes the confining tension with no free parameter. Confinement is found to have two logically distinct origins that standard Quantum Chromodynamics (QCD) merges but the ER-dipole model keeps separate: (1) Dynamical/linear confinement: the closed bridge is a maximally-entangled Thermofield Double (TFD) state whose throat area, and hence its tension, is held strictly constant by the holographic conservation of its entanglement entropy (S ent = A/4G N ). This forces a strictly linear potential V (r) = σr with σ = 2(m const c 2 ) 2 /ℏc ≈ 0.99 GeV/fm and √ σ = √ 2m const c 2 ≈ 442 MeV, in superb agreement (∼ 1%–5%) with lattice QCD. (2) Topological confinement: the three-strand baryon is a braid in the non-abelian Artin braid group B 3 , whose central full twist ∆ 2 = (σ 1 σ 2 ) 3 cannot relax continuously. This topological barrier guarantees absolute proton stability and fractional-charge confinement as braid invariants. We then use this unified framework to resolve three issues left open by earlier work: we clarify that the Y-gate is a white-hole baryogenesis feature and not a confinement mechanism, derive a braid-consistent mechanism for neutron beta decay, and explain the universal inter-brane distance as the maximal pre-rupture elongation reached by relativistic rotation. We conclude by presenting seven falsifiable predictions.