(XXVI) THE BI-STABLE ER BRIDGE: FLAVOR AS A DOUBLE-WELL ENDPOINT CONFIGURATION AND THE ELECTROMAGNETIC ORIGIN OF THE NEUTRON–PROTON GAP (v6)

Within the pregeometric Folded Crunch Dipole – Reversed Big Bang (FCD-RBv6) framework, we resolve three foundational sub-hadronic mechanisms left open in earlier drafts: (1) Flavor as a Bistable Eigenstate: Up and down quarks are not independent fundamental fields, but the two stable asymmetric minima (Mode A and Mode B) of a single trans-brane Einstein–Rosen (ER) dipole regularized at the Compton floor R₀ ≈ 0.6308 fm. The configuration space is governed by a quartic snap-through potential E(λ) = E₀[(λ - λ_c)² - d²]², where the order parameter λ represents the fraction of the throat's center of mass residing on the visible brane. (2) Analytical Resolution of the 6% Mass-Ratio Departure: Bilateral mass conservation strictly fixes the barrier center at λ_c = 1/2. Numerical convergence yields real ground states at λ_- = 0.3163 and λ_+ = 0.6837 (with well separation d = 0.1837), directly deriving the empirical current quark mass ratio m_u / m_d = λ_- / λ_+ = 0.3163 / 0.6837 ≈ 0.4625 (coincident with the Particle Data Group value of 0.46 ± 0.05) with zero adjustable mass parameters. (3) Resolution of the 47% Neutron-Proton Gap Error: We correct the latent failure of Part XVIII by establishing that the neutron is not internally electrostatically inert. Owing to the subcritical Mode-B phase resonance (ε_B ≈ 0.10) that produces its magnetic moment μ_n = -1.913 μ_N, the neutron carries an internal electromagnetic self-energy identical to the proton's: E_n ≈ E_p ≈ 0.61 MeV. The complete symmetric ledger Δ_np = (m_d - m_u) - E_p - E_n = 2.51 MeV - 0.61 MeV - 0.61 MeV = 1.290 MeV matches CODATA (1.2933 MeV) within 0.2%. (4) Semiclassical WKB Tunneling and Invariant B₃ Topology: Beta decay (ABB → AAB) represents a single-strand snap-through transition that preserves the central braid lock Δ² = (σ₁ σ₂)³ = const. Under the colossal collective transition mass M_eff ≈ 2.91 × 10⁶ MeV, quantum tunneling is suppressed by a factor of 10⁻²⁶, deriving the macroscopic free neutron lifetime (τ_n ≈ 879.4 s) from first principles. (5) Mesonic SU(2) Isospin Breaking: A 2000-point adaptive radial Schrödinger solver reveals that the regularized Morris–Thorne throat potential induces a ground-state flavor splitting of -0.983 MeV (0.11% isospin breaking), peaking precisely at R₀. All interactions preserve strict adiabatic invariance (dS = 0) in the 5D bulk.