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

We present a formalized draft of the Emergent Resonant Brane (ERB) framework as a
speculative field-theoretic model in which a two-brane vacuum substrate generates effective
particle 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 relative
vacuum scale of two coupled branes, and a weak interaction scale g = 0.12.
We define an effective mismatch functional over rational approximants, derive a candidate
stability minimum at ξ = 3/2, and formulate a cavity-based Hamiltonian whose low-lying
modes provide an effective spectral basis. Mixing observables are defined as overlap
integrals of these modes and the model is assessed via likelihood and Bayesian evidence
against a null hypothesis.
The centerpiece of this work is the Global Rigidity Matrix (ERB v60), which demonstrates
that the simultaneous derivation of subatomic masses, neutrino mixing angles, and
cosmological expansion is mathematically locked — rendering independent parameter fitting
structurally impossible. The gravitational sector is derived from a refractive index gradient in
the vacuum medium (ERB v53), with Black Holes reinterpreted as total-reflection phase
mirrors.
Core falsifiable prediction: δCP ≈ 352° (to be tested at DUNE ~2030). The manuscript is
written as a formal research draft and is not presented as an established physical theory.