Revisiting the Neutron Lifetime Puzzle: A Unified Systematics-Geometry Framework with a Falsifiable Residual Operator

The persistent discrepancy between neutron lifetime determinations from beam and bottle experiments (at the level of ~8-10 s) remains a key anomaly in precision weak-interaction physics. We develop a conservative, unified framework in which the reported lifetime is treated as an effective estimator shaped by (i) correlated loss channels in ultra-cold neutron (UCN) storage, (ii) detector-response and background modeling in beam measurements, and (iii) geometry-dependent confinement dynamics that can bias the mapping from measured survival curves to the intrinsic beta-decay rate. The central point is that systematic contributions need not combine additively when the corresponding nuisance parameters are correlated and enter the likelihood nonlinearly. As an optional extension, we introduce a small residual time-modulation operator A(t) = 1 + \epsilon(t) as a purely phenomenological parameterization of any remaining mismatch, constrained by stability and independent observables. The framework yields explicit, falsifiable predictions for geometry randomization tests, energy-tagged UCN survival analyses, and correlated re-analyses of beam efficiency systematics.