Access Collapse: A Typed Structural Boundary for Operational Access

Abstract

Our main technical contribution is Observation Algebra Relativity (Theorem 2): a metatheorem formalising that security and robustness predicates are indexed to observation algebras and do not transfer across algebra boundaries. As an application framework, we present the Access Collapse Theorem: a typed structural result showing that direct operational access to the complete state of any system — physical, formal, or social — necessarily collapses at least one of two invariants: operational separateness (d) or scale separation (s). When either invariant reaches zero the access operation does not become inaccurate — it becomes a type error: the predicate is no longer typed to the system being operated. The framework is applied to six instantiations: Planck-scale measurement, zero-knowledge proofs, side-channel attacks, multi-party computation, adversarial explainability, and machine learning model extraction. A Non-Universality Proposition explicitly bounds the framework's scope. A Collapse Diagnostic provides a practical checklist for identifying collapse boundaries in concrete systems. A practical application framework building on this theoretical work is presented in:Isopahkala (2026) – Epistemic Hygiene in Practice.