THE QUARK ER DIPOLE: A MINIMAL SUB-HADRONIC ONTOLOGY (XIII v6)

We formalize the minimal sub-hadronic ontology within the FCD-RBv6 framework, extending trans-brane Einstein–Rosen (ER) dipoles regularized at the Compton floor R₀ ≈ 0.6308 fm. Three unified foundational principles are established: (1) The Single-Quark Hypothesis, demonstrating that up and down quarks are not separate fundamental entities, but the two stable elastic eigenmodes (Mode A and Mode B) of a single trans-brane ER dipole; (2) The Distinction between Construction Budget and Observable Mass: the 6m energy budget represents the non-radiative injection ledger supplied via Mouth C from the AdS₅ bulk to nucleate the pair, whereas observable gravitational and inertial mass arises strictly from compactification confinement at the Compton floor where zero-entropy boundary conditions (S = 0) induce isotropic phase-space depletion (dS = 0); (3) The Trans-Brane Mass-Asymmetry Rule (TBMAR) coupled to the global orientation parameter Ω = ±1, deriving electric charge as an emergent metric imbalance (Q_visible = Ω · (m_mirror / M)e) that unifies CPT without physical mass transfer; and (4) The Electron as a Surface Rayleigh Wave acting as an elastic boundary plug sealing Mouth A of the Y-gate against bulk negative pressure. Anomaly cancellation (q_e + 2q_u + q_d = 0) is derived as a geometric boundary condition of the tri-coordinated junction, while the snap-through quartic potential analytically yields m_u / m_d ≈ 0.4625, matching empirical PDG evaluations without fine-tuning.