A Covariant Distributed-Field Ansatz for Late-Time Brane-Dark-Sector Energy Exchange (The Q-Rubin Framework, Version 3.2)

We propose a covariant phenomenological ansatz for late-time energy exchange between a pressureless matter-like sector and an emergent dark sector on a four-dimensional brane. The interaction is represented by a transfer current JμJ^\mu coupled to a dimensionless emergent scalar field ϕQ\phi_Q. To make the perturbation theory explicit, JμJ^\mu is decomposed into an energy-transfer scalar QQ and an orthogonal momentum-transfer vector FμF^\mu, allowing the background and first-order perturbation equations to be written in standard interacting-fluid form. Early-universe shielding is implemented through a bounded activation window and a hyperbolic relaxation-diffusion law, rather than through a background source term alone. A candidate higher-dimensional motivation is provided by a Randall–Sundrum-type five-dimensional bulk scalar whose projected normal flux can induce apparent brane-sector non-conservation through the Codazzi relation. The result is a mathematically organized and falsifiable framework whose next required step is numerical implementation in a Boltzmann solver, preferably CLASS, followed by Bayesian inference with MontePython or Cobaya and comparison against CMB, BAO, Type Ia supernova, weak-lensing, and structure-growth data. Spectral-distortion constraints are relevant only if an explicit visible-sector heating channel is introduced.