Toward a Metrological System for Cognition: Substrate Independence, Thermodynamic Bounds, and the Definition of the Measurand

Can cognition be represented by an invariant metrological quan-tity whose definition is strictly decoupled from the physical substrateof the cognitive system? Contemporary measures of cognitive perfor-mance are fundamentally operational, quantifying task-specific behav-iors under constrained conditions without anchoring them to a fun-damental quantity of cognition itself. This paper establishes a formal metrological framework that defines cognition as an implementation-independent measurand. By structurally distinguishing the cogni-tive phenomenon from its observable manifestations and measurementprocedures, we introduce a mathematical equivalence relation overdisparate physical realizations (e.g., biological neural networks, sili-con, and neuromorphic architectures). Furthermore, we constrain this framework within foundational physical realities, exploring how an emergent unit of cognition scales against thermodynamic principles,specifically the Landauer and Bremermann limits. The objective isto define the necessary and sufficient conditions under which a uni-versal, energy-bounded cognitive quantity can coherently exist and beempirically measured