Critical Reassessment of Gallium and Reactor Neutrino Anomalies in 3+2 Sterile Neutrino Models: Incorporating Recent Exclusions, Bayesian Analyses, and Alternative Hypotheses

This study proposes and critically evaluates a 3+2 sterile neutrino framework to address the gallium anomaly (20--24% deficit at >4σ from BEST and prior experiments [barinov2022results,semenov2023revised]) and the reactor antineutrino anomaly (reduced to <1.5σ with refined flux models [giunti2022reactor,berryman2022reactor]). The model includes an eV-scale sterile neutrino for anomalies and a keV-scale for dark matter, but recent exclusions from MicroBooNE, KATRIN, and SBN at ≥95% CL [microboone2021,abrams2022katrin,acero2022nova] render it untenable. We perform Bayesian fits to raw BEST data, yielding posterior odds of 1:15 against sterile vs. cross-section alternatives. Oscillation parameters (Δm²₄₁ = 1.3 ± 0.5 eV², sin² 2θ₁₄ = 0.26 ± 0.09) are tested against Lyman-α bounds (m_th > 4.1 keV [irsic2017lyman]) and NuSTAR limits [roach2020nustar]. Numerical simulations confirm 20.5% monoenergetic gallium deficit and 16.3% spectrum-averaged, with χ²/d.o.f. = 1.12. Matter effects are negligible (A ∼ 10⁻¹⁵ eV²), proven via exact MSW derivations. For keV sterile, corrected QKE yield Ω_s h² ≈ 0.12, but ΔN_eff > 0.3 tensions persist. Monte Carlo sensitivity (10,000 draws) quantifies degeneracies. We derive self-interaction potentials and TOV modifications rigorously. Supernova and neutron star implications are detailed, but limited by exclusions. Falsifiable predictions for DUNE and XRISM are provided, favoring non-sterile resolutions like wave function corrections [semenov2023revised]. This work quantifies systematics, advocating peer-reviewed alternatives with full derivations and verifiable codes.