CONFINEMENT OF THE ER-STRING BARYON: LINEAR TENSION FROM RYU–TAKAYANAGI INVARIANCE, TOPOLOGICAL B₃ BRAID LOCK, THE ELECTRONIC BOUNDARY PLUG, AND PRE-RUPTURE INTER-BRANE SPACING (XX v6)

Abstract

In the FCD-RBv6 pregeometric framework, hadronic confinement and baryon structural integrity are derived from the dual elastodynamic and topological constraints of trans-brane Einstein–Rosen (ER) bridges regularized at the Compton floor R₀ = ℏ/(m_const c) ≈ 0.6308 fm. Five core foundations are formalized: (1) The Dual Origin of Confinement: standard quantum chromodynamics (QCD) conflates two independent pregeometric mechanisms: dynamical linear confinement governed by holographic Ryu–Takayanagi invariance (dS_ent = 0, fixing σ₀ = 2(m_const c²)²/(ℏc) ≈ 0.99 GeV/fm and √σ₀ ≈ 442 MeV across mesons and baryons), and topological confinement governed by the non-abelian Artin braid group B₃; (2) Topological Stability & The Electronic Plug: absolute proton stability (τ_p > 10³⁴ yr) is guaranteed by the central braid lock Δ² = (σ₁σ₂)³ in the 5D bulk, reinforced at the visible 4D boundary by the electronic Rayleigh surface acoustic plug (-0.511 MeV) sealing Mouth A against negative bulk pressure; (3) Structural Decoupling of the Y-Gate: the tri-coordinated Y-gate is strictly an active thermodynamic manifold during primordial baryogenesis (and during TOV collapse); in bound nucleons, Mouth C is dormant and the triple junction acts as an internal kinematic pivot, not a bulk drain; (4) Braid-Invariant Beta Decay: weak transitions (ABB → AAB) execute an elastic snap-through mass redistribution in the quartic double-well potential without strand breakage or loss of the Δ² lock, emitting the excess kinetic energy as an antineutrino shear wave into the bulk; and (5) The Universal Inter-Brane Distance (d_bulk): derived dynamically as the maximal pre-rupture elongation sustained by relativistic rotation before reaching the 625 MeV pair-production threshold. In baryonic matter, d_bulk is locked to R₀ (metric scaffolding), while in cosmic voids it relaxes elastically, driving dynamical dark energy w(z) = -1 + ξ(z). All gravitational interactions remain mediated strictly by adiabatic bulk phase-space depletion (dS = 0).