Topology-Induced Vacuum Susceptibility: A Gauge-Invariant Resolution to the Neutron Lifetime Discrepancy

The persistent 4-sigma discrepancy between neutron lifetimes measured by beam methods (~888 s) and trap methods (~879 s) remains one of the most enduring puzzles in the Standard Model. In this Letter, we propose that static environmental confinement fields induce a local polarization of the vacuum metric, effectively modifying the weak interaction phase space. By treating the vacuum as a dielectric medium with finite stiffness, we derive a parameter-free geometric correction factor: delta = sqrt(2) * alpha ≈ 1.03% (where alpha is the fine-structure constant). Key Validations: Theoretical Prediction: This model predicts a 1.03% lifetime reduction in trap experiments. Numerical Consistency: Applying this correction to a baseline of 886.9 s (strictly within NIST beam error margins) precisely reproduces the latest UCN-tau collaboration result of 877.75 s. Precision: The theory bridges the "9-second gap" with a precision better than 0.01%. This work suggests the "Neutron Lifetime Puzzle" is the first experimental observation of the vacuum's mechanical response to environmental stress.