SHRF v0.1: Scalar-Halo Resonance Framework — Field Equations, Transfer Functions, and Preliminary Phenomenology

SHRF v0.1 is an exploratory preprint introducing the Scalar-Halo Resonance Framework, a toy phenomenology for resonantly coupled scalar dark matter halos. The work derives the field equations, static halo sector, weak-lensing observable, FRW background behavior, and reduced matter-era transfer function. Numerical integration yields a viable transfer-function branch with a derived Lyman-α-inspired bound, while galaxy rotation-curve tests show SHRF remains individually competitive with NFW fits on published data. However, the initially suggested universal halo-scale window does not survive replication, and no cross-galaxy shared halo scale is currently supported. The framework remains conditionally viable with one numerically closed branch, one analytically derived observational branch, and one empirically competitive but non-universal phenomenology branch. Keywords scalar field dark matter, halo resonance, galaxy rotation curves, cored dark matter halos, weak lensing, transfer function, Lyman-alpha forest, scalar halo phenomenology, dark matter halo profiles, NFW comparison, FRW perturbations, matter power spectrum, SPARC galaxies, halo core radius, exploratory cosmology