The General Epistemic Dispersion Theory

Abstract

Title: The General Epistemic Dispersion Theory: The Information Cost of Global Integrity in Fragmented Data Author: Massimo Comitato Description: This work studies the informational cost required to determine the global integrity of fragmented data processed in a distributed architecture. We distinguish between two classes of architectures: systems in which nodes must receive sufficient semantic and relational metadata to interpret and reconstruct the global state from partial states, and systems in which global relations are inherited and encoded in a reusable structural core, while peripheral nodes manage the partial data exclusively in a local environment. We demonstrate, based on the stated informational assumptions, that any architecture lacking a sufficient structural core must transmit, pre-install, or reconstruct the information needed to resolve residual uncertainty about the global configuration. Conversely, when structural invariants, role associations, internal relations, and topology make the global configuration structurally determinable, the additional metadata transcription required to reconstruct that configuration may be null or limited to the information needed to resolve residual structural uncertainty. Information is not eliminated, but rather shifted from explicit and repeated communication to an implicit and reusable structure. An overall cost advantage occurs when the amortized cost of building, distributing, accessing, and maintaining the structure is lower than the dynamic costs of metadata, coordination, semantic replication, and communication that it avoids. Release Notes / Update Description: An updated version of the manuscript "The General Epistemic Dispersion Theory" (October 2026) has been published. This revision strengthens the mathematical scaffolding of the framework by introducing an algebraic and constructive definition for the reusable structural core. Key updates to the text include: Binary space formalization: The configuration space is now explicitly modeled on a binary basis, defining the admissible configuration set P as a function of operational constraints. Canonical definition of the core (S_0): Leveraging lattice theory, the structural core is now formally derived as the greatest lower bound of the structural descriptions of the admissible family. Logical derivation: Through the operation S_0, the core is unambiguously defined as the structural analogue of a greatest common divisor. Invariance and separation: This formulation, supported by the principles of Formal Concept Analysis, mathematically isolates the relations and roles that persist across the entire admissible space, consolidating the strict theoretical separation between global structural invariance and instance-specific configurational identification. The updated PDF file ("The_General_Epistemic_Dispersione_Theory_ENGv.pdf") fully replaces the previous version.