Prepared-State Hydrogenic Spectroscopy as a Null Test of Information-Gauge Entanglement Couplings

This preprint develops a residual-based null-test framework for probing information-gauge entanglement couplings with hydrogenic precision spectroscopy. The work formulates a local Stueckelberg (U(1)\Lambda) effective description in which entanglement-sensitive subsystem data define a conserved information current (J^\mu{\rm info}). The framework is applied to hyperfine, Ramsey/maser phase, and prepared-state spin-entanglement observables in hydrogen, deuterium, muonium, and positronium. The manuscript does not claim a detection of an information-gauge field. Instead, it identifies experimentally testable signal patterns: neutrality-preserving phase drifts, prepared-state triplet responses, (n^{-3}) contact scaling for (nS) states, and correlated H--D--Mu--Ps residuals. In the minimal spin-contact realization, the overall strength is encoded in a Wilson coefficient (\eta_0), while the relative prepared-state pattern is fixed, with (\Delta\mathcal I_{\rm tri}=1) and (\Delta\mathcal I_{S-\overline T}=2/3). Using the current hydrogen 21-cm benchmark sensitivity, the corresponding illustrative energy-shift scale is (|\Delta E_{\rm IG}|\lesssim8.3\times10^{-18},\mathrm{eV}). Charge-screening realizations are separately constrained by laboratory tests of atomic, molecular, and bulk-matter neutrality. The accompanying Supplemental Material provides matrix-element details, benchmark sensitivity conversions, systematic-error considerations, residual-based fitting structure, and comparison with wormhole-flux-leakage interpretations. This version is prepared as a preprint manuscript intended for journal submission. Keywordshydrogenic spectroscopy; hyperfine structure; information-gauge field; entanglement; Ramsey spectroscopy; muonium; positronium; null test; effective field theory; precision spectroscopy