Presence, Perspective, and Stored Energy: A Slice-Wise Evaluation Framework for Black Hole Interior Dynamics

This work presents a finite-evaluation framework for analyzing black hole interior dynamics by correcting how physical observables are evaluated rather than modifying spacetime dynamics. Classical singularities in general relativity are typically identified through pointwise or global limits that exceed physically realizable observation. This paper demonstrates that such evaluation methods introduce mathematical incompleteness and lead to apparent divergences that need not correspond to physically experienced quantities. The framework applies the Presence–Residue–Alignment–Weighting (PRAW) formalism—previously developed as a general finite-window mathematical theory—to relativistic physics by treating curvature, expansion, and energy density as functions parameterized by proper time. In this setting, Stabilized Proper Time (SPT) provides the physically realized finite window over which observables are accumulated, ensuring bounded evaluation under relativistic stress without altering the spacetime metric or Einstein field equations. Under finite proper-time evaluation, quantities traditionally associated with black hole singularities remain bounded when considered over realized slices of experience. Energy is interpreted as conserved and stored in structured form rather than destroyed, and apparent divergences are reclassified as artifacts of invalid evaluation limits. The framework restores operational completeness while remaining fully consistent with classical general relativity and observed astrophysical structure. This work does not claim elimination of mathematical singularities, global spacetime extensions, or new physical laws. Instead, it demonstrates that finite proper-time evaluation provides a mathematically complete and physically meaningful way to interpret extreme spacetime regimes.