Emergent Resonant Brane Framework - A Formal Field-Theoretic and Statistical Draft

We present a formalized draft of the Emergent Resonant Brane (ERB) framework as aspeculative field-theoretic model in which a two-brane vacuum substrate generates effectiveparticle spectra, mixing observables, and stability conditions through resonant mode locking.The model is organized around a single ratio parameter ξ = 3/2, interpreted as the relativevacuum scale of two coupled branes, and a weak interaction scale g = 0.12.We define an effective mismatch functional over rational approximants, derive a candidatestability minimum at ξ = 3/2, and formulate a cavity-based Hamiltonian whose low-lyingmodes provide an effective spectral basis. Mixing observables are defined as overlapintegrals of these modes and the model is assessed via likelihood and Bayesian evidenceagainst a null hypothesis.The centerpiece of this work is the Global Rigidity Matrix (ERB v60), which demonstratesthat the simultaneous derivation of subatomic masses, neutrino mixing angles, andcosmological expansion is mathematically locked — rendering independent parameter fittingstructurally impossible. The gravitational sector is derived from a refractive index gradient inthe vacuum medium (ERB v53), with Black Holes reinterpreted as total-reflection phasemirrors.Core falsifiable prediction: δCP ≈ 352° (to be tested at DUNE ~2030). The manuscript iswritten as a formal research draft and is not presented as an established physical theory.