Ontology of Pure Information: Substrate Independence, Numerical Invariance, and the Limit of Finite Systems

The classical framework of physics and information theory traditionally interprets information as an epistemic byproduct of material configuration or an artificial ordering of characters created by the observer. This paper rejects such a premise and formalizes the ontology of "pure information" as a relational and geometric entity pre-existing within the phase space of the universe (𝒰). Under the Hernández-Valdivia Finite Systems Paradigm, it is demonstrated that any bounded processor (𝒢) operating in an open complexity environment is subject to the fundamental axiom dim(𝒢) ≪ dim(𝒰) ⇒ εinfo > 0, forcing the system to discretize reality to prevent thermal overflow or an information density collapse. Through the principle of substrate independence, we examine how organic matter (carbon), nanostructured semiconductors (silicon), and the topology of spacetime itself operate solely as local decoders and "antennas" for a universal mathematical signal. In this context, the number—specifically the discrete unit—is redefined not as an abstract convention, but as the minimum operator of distinction that breaks the homogeneous symmetry of the vacuum to generate physical laws and macroscopic mass via topological friction. Finally, this approach establishes a direct conceptual bridge to ancient Greek philosophy, reinterpreting Aristotelian Theoria as perfect phase coupling, Socratic Anamnesis as the mapping of pre-existing coordinates in 𝒰, and existential engineering as the ultimate anti-entropic imperative for the survival of reason.