Epistemic Horizon Theory: Informational Accessibility, Formal Saturation, and Observer-Bounded Knowledge

This preprint introduces Epistemic Horizon Theory (EHT) as a foundational structural framework for studying limits of informational accessibility across formal mathematics, computation, physics, quantum theory, cognition, and biological perception. EHT analyzes cases in which a property, structure, truth, or information state may be well-defined, real, determinate, or physically present, while remaining inaccessible to a bounded observer or access system under a given representation, partition, and resource regime. Its central schema is that an epistemic horizon emerges when the cost of resolving a property exceeds the accessible capacity of the observer or access system. The paper develops EHT through several domains: formal systems and proof certification, the Axiomatic Saturation Threshold, computational irreducibility and algorithmic horizons, the Riemann Hypothesis as a boundary object, black-hole informational accessibility, the Schwarzschild surface as a physical analogue of an epistemic boundary, quantum measurement and entanglement, and cognitive or conscious-access limits. The framework is comparative and diagnostic rather than reductive. It does not claim that Gödelian incompleteness, computational undecidability, black-hole horizons, quantum measurement, and conscious access share the same mechanism. Instead, it compares them at the level of accessibility structure: observer, system, property, representation, partition, cost, and capacity. This version is deposited as preprint v1.0 for scholarly discussion, citation, criticism, and future formal development.