The definition of cognition remains fragmented across disciplines, often con-flated with behavioral heuristics or raw processing power. This paper presents theCognition Substrate Theorem (CST), a formal framework defining the necessary andsufficient conditions for a system to sustain a valid cognitive worldline. We definethe cognitive substrate as a 6-tuple C = ⟨T, S, F, J, ⊕, Φ⟩, treating cognitive validitynot as a scalar output, but as a structural invariant: a Justified Epistemic Trajec-tory. We establish three primary metatheoretic results: (1) the necessity of eachoperator to prevent structural collapse (e.g., into stochasticity or infinite regress),(2) the sufficiency of the 6-tuple for sustaining a non-Markovian trajectory, and (3)the minimality of these requirements, establishing the 6-tuple as the IrreducibleIntersection of structural necessity. The theorem posits that validity is a propertyof Structural Orchestration (Φ), functionally independent of the computational ca-pacity of the inference engine (F ). Crucially, these theoretical claims are supportedby a machine-checked formalization in Lean 4, providing constructive proofs ofexistence and establishing axiomatic independence via a hybrid strategy of struc-tural ablation (for components) and logical non-formation (for the protocol). TheCST thus provides a mathematically verified, implementation-agnostic foundationfor defining, comparing, and constructing biological, artificial, and institutionalcognitive substrates.
Divyansh Pandya (Fri,) studied this question.