Physical Residuality as a Unifying Lower-Bound Framework Across Quantum, Boundary, and Information-Theoretic Regimes

Modern physics contains several experimentally and theoretically established nonvanishing floors: quantum zero-point structure, boundary-induced residual stresses such as Casimir-type effects, fluctuation-limited observables, and irreversible energetic costs associated with information processing. These phenomena are usually treated within separate formal frameworks, despite sharing a common structural feature: the physically admissible minimum of a relevant quantity generally does not coincide with exact nullity. In this work, we introduce the Physical Residuality Principle (PRP) as a unifying operational framework for such irreducible nonzero floors. We do not claim the discovery of a previously unknown isolated physical phenomenon, nor a completed universal microscopic closure. Rather, we argue that a broad family of well-established residual effects admits a common lower-bound interpretation across quantum, boundary-induced, and information-theoretic regimes. To make this claim operational, we define a residual functional based on renormalized excess stress-energy relative to a reference configuration and formulate a lower-bound decomposition into quantum, boundary/topological, and irreversible informational contributions. We then present representative regime checks, including zero-point structure, Casimir configurations, Landauer-type erasure, and a nonlinear accelerator-dynamics analogue involving fixed lines induced by resonance. The result is a disciplined unifying framework: conceptually strong, formally extensible, and empirically oriented, while remaining explicit about its current limits and open technical gaps. Within the broader Fractal Consistency Law program, the PRP functions as a bridge principle: admissible minimization does not imply exact nullity, but rather the persistence of irreducible residual structure.