Asymptotic Access: Structural Limits on Truth in Finite Systems

This manuscript articulates a boundary condition on human knowledge grounded in the structural limits of finite systems. It formalizes that while truth exists independently of observers, access to truth is necessarily bounded, converging toward workable approximations rather than exhaustive capture. Cognition operates through compression, producing partial yet non-arbitrary representations that can remain inferentially aligned with underlying structure. Epistemic success is therefore defined not by total correspondence but by sufficient proximity to reality to sustain reliable reasoning and action. The framework rejects both absolutism, which mistakes coherence for completeness, and relativism, which mistakes incompleteness for falsity. It explains how multiple, locally effective models may coexist without implying plural truths, reflecting constraint-induced approximation rather than ontological divergence. Asymptotic Access reframes epistemic progress as incremental tightening and refinement rather than terminal resolution, clarifying why demands for final certainty generate predictable failure modes. An illustrative analogy to transformer-based language models demonstrates how bounded systems can produce coherent outputs without global access to truth. The manuscript positions Asymptotic Access not as a theory of knowledge content, but as a necessary constraint on the interpretation and evaluation of all knowledge claims.