THE KINETIC CONSTITUENT MASS . Relativistic Rotation of the ER String, Spin-1/2 from Bilateral Brane Anchoring, and the Symmetric Self-Energy Ledger (XVIII v6)

Abstract

In the FCD-RBv6 pregeometric framework, hadronic constituent mass, fermionic spin, and the isospin mass gap are derived from the elastodynamics of trans-brane Einstein–Rosen (ER) bridges embedded in the AdS5 bulk and regularized at the centrifugal Compton floor R0 ≈ 0.6308 fm. We establish five unified foundations: (1) The Two Mass Regimes: the primordial formation regime fixes bare catalytic quark masses (mu ≈ 2.16 MeV, md ≈ 4.67 MeV, representing ~1% of rest mass) via Mouth C injection, while the operating regime establishes the nucleon core through hyper-relativistic spin-space rotation; (2) Kinetic Constituent Mass: endpoints rotate at v ≈ 0.999976c (γ_u ≈ 145) at the Compton attempt frequency ν0 ≈ 7.6 × 10²² Hz, generating the constituent mass scale m_const = M_p/3 ≈ 312.8 MeV (~938 MeV total) to balance the baseline string tension σ0 ≈ 0.99 GeV/fm against bulk collapse; (3) The Trinity of Mass Manifestations: strict separation between bare catalytic mass (S = 0 boundary anchors), gyroscopic inertial mass (throat-stabilizing kinetic energy), and emergent gravitational mass (bulk phase-space depletion, dS = 0); (4) Hadronic Spin-1/2 via Bilateral Brane Anchoring: the unit orbital angular momentum (L = ℏ) generated by relativistic rotation is halved to exactly s = L/2 = 1/2 ℏ by equal projection across the two bounding branes (Brane A and Brane B); and (5) The Symmetric Self-Energy Ledger: accounting for the residual Mode-B phase oscillation (ε_B ≈ 0.10) assigns equal electromagnetic self-energies to proton and neutron (E_p ≈ E_n ≈ 0.61 MeV), yielding an emergent mass gap Δ_np = (m_d - m_u) - E_p - E_n = 1.290 MeV (0.2% agreement with CODATA). All interactions preserve strict adiabatic invariance (dS = 0).