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We present a unified, rigorously formulated p-series deformation framework for gravitational interaction inspired by classical Ramanujan-type series constructions. The theory is developed from first principles as a mathematically well-defined operator acting on radial gravitational potentials. We provide explicit proofs of convergence, boundedness, regularity, and asymptotic behavior, followed by physics-based consistency derivations establishing recovery of Newtonian gravity and controlled long-range suppression. A chemistry-consistent interpretation is introduced via interaction-kernel analogies familiar from statistical mechanics and molecular physics. The framework is complemented by explicit numerical implementations in Python and Java. This work establishes a mathematically rigorous, physically consistent, and computationally realizable foundation for scale-dependent gravitational modeling.