Residual Information Theory

This paper develops a residual theory of physical information within the Physical Residuality Principle (PRP) and the Fractal Consistency Law (FCL). Its central claim is deliberately precise: the logical value zero used in symbolic, digital, and computational systems must not be identified with ontological nullity. A binary zero is not nothing. It is a low-excitation, physically supported, distinguishable state of a substrate. Therefore, a physical bit is not a transition between being and non-being, but a transition between two admissible residual configurations of a physical system. The paper formalizes this distinction by replacing the abstract binary alphabet 0, 1 with a physically realized residual pair εres, εres + Δ, where εres > 0 denotes a non-null lower bound of physical legibility and Δ denotes a distinguishable excitation above that floor. This replacement does not deny binary computation; rather, it clarifies the ontological status of the binary symbols when they are physically instantiated. The paper connects this residual account of information to Landauer erasure, physical irreversibility, boundary memory, and black-hole entropy. Landauer’s principle is interpreted not as a proof of the PRP or FCL, but as a high-value bridge: it shows that erasure is not a transition into nothing, but a physical reconfiguration that exports entropy to the environment. In the same spirit, the Bekenstein-Hawking entropy of a black hole is recast as the logarithmic count of admissible residual boundary states rather than as an abstract count of empty binary marks. The result is a disciplined framework in which information, time, entropy, horizons, and computation can be analyzed through a common non-null architecture. The paper remains explicit about its limits: the residual interpretation is not yet a completed microscopic derivation of all informational physics. It is a formal bridge intended to organize a program of falsifiable extensions.