Non-Local Retrocausal Information Extraction via Center-Shifted Toroidal Geodesics and Interaction-Free Berry Phase Shifts

This paper introduces a self-consistent, non-paradoxical mathematical framework for non-local information extraction from future spacetime boundaries using Center-Shifted Toroidal Spacetime Cavities and Interaction-Free Measurement (IFM) protocols. By establishing the rotational axis (bearing center) of the temporal geodesic loop at a future coordinate $t_{\text{center}} = r$, the lower boundary of the loop tangentially intersects the present at $t = 0$, strictly confining the temporal coordinate to non-negative values ($t \ge 0$) and eliminating any reliance on historical metric generators or closed timelike curve (CTC) grandfather paradoxes. Furthermore, photons interacting with future boundary conditions at $t = 2r$ via an IFM exclusion protocol encode the spatial configuration of the future state directly into a topologically protected Berry Phase Shift ($\Delta \Phi_{\text{Berry}} \approx 0.142 \text{ rad}$) without quantum state collapse. Utilizing an effective optical metric (analog gravity via nonlinear Kerr media), this model offers a novel, verifiable pathway for retrocausal quantum optics experiments.