Data-Constrained Gauge-Invariant Information-Gauge Signatures in Neutrino Oscillations

This preprint presents a gauge-invariant information-gauge effective field theory (IG-EFT) framework for testing possible new propagation effects in neutrino oscillations. The framework supplements the standard three-flavor neutrino oscillation model by coupling active neutrinos nonuniversally to the gauge-invariant Stueckelberg combination Bμ=Λμ−mΛ−1∂μΘ.B_μ = Λ_μ - m_Λ⁻¹∂_μΘ . It identifies three complementary experimental signatures:(i) a coherent phase contribution that violates pure L/EL/E scaling,(ii) sidereal modulation generated by a spatially anisotropic information-gauge background, and(iii) stochastic pure dephasing generated by fluctuations of the information-gauge field. Published IceCube Lorentz-symmetry limits are conditionally mapped onto mass-basis IG coefficients using NuFIT-6.0 mixing parameters. The resulting one-coefficient-at-a-time projection scales are ∣A21T∣<8.6×10−24 GeV,∣A31T∣<5.9×10−24 GeV,|A₂₁T|<8.6×10⁻²⁴\ { GeV}, |A₃₁T|<5.9×10⁻²⁴\ { GeV}, based on the published IceCube 99% C.L. SME limits. Existing IceCube sidereal results provide corresponding transverse scales of order 10−23 GeV10⁻²³\,GeV. For stochastic fluctuations, the IG pure-dephasing model is matched to the IceCube energy-independent phase-perturbation result, Γ0PP<1.18×10−24 GeV(90% C.L.),Γ_0PP < 1.18×10⁻²⁴\ { GeV} (90%~{ C.L.}), yielding the conditional constraint (Δgij)2σb2ℓc≲1.18×10−24 GeV.(Δ gᵢⱼ)^2σ_b^2_c 1.18×10⁻²⁴\ { GeV}. The first JUNO reactor-antineutrino oscillation measurement is additionally used to provide an independent MeV-scale proxy sensitivity to the same class of energy-independent propagation effects. The JUNO result is treated as a phenomenological single-scale estimate rather than a full experimental likelihood constraint. An auxiliary analysis of the IceCube public data release reproduces the 305,735 selected events in the published 13×2013×20 analysis grid and finds the simplified likelihood minimum at the physical boundary Γ0=0Γ_0=0. This validation is used only as a reproducibility and order-of-magnitude diagnostic and does not replace the official IceCube likelihood. The associated Python analysis and public-data validation materials are archived separately on Zenodo at DOI 10.5281/zenodo.22177495. This manuscript is intended as a falsifiable phenomenological framework for testing whether coherent phase shifts, directional anisotropy, and stochastic decoherence can arise from a common gauge-invariant information-sector background.