Operationalising Extended Cognition: Formal Metrics for Corporate Knowledge and Legal Accountability

Corporate responsibility turns on notions of corporate \textit{mens rea}, traditionally imputed from human agents. Yet these assumptions are under challenge as generative AI increasingly mediates enterprise decision-making. Building on the theory of extended cognition, we argue that in response corporate knowledge may be redefined as a dynamic capability, measurable by the efficiency of its information-access procedures and the validated reliability of their outputs. We develop a formal model that captures epistemic states of corporations deploying sophisticated AI or information systems, introducing a continuous organisational knowledge metric $S_S(\varphi)$ which integrates a pipeline's computational cost and its statistically validated error rate. We derive a thresholded knowledge predicate $\mathsf{K}_S$ to impute knowledge and a firm-wide epistemic capacity index $\mathcal{K}_{S,t}$ to measure overall capability. We then operationally map these quantitative metrics onto the legal standards of actual knowledge, constructive knowledge, wilful blindness, and recklessness. Our work provides a pathway towards creating measurable and justiciable audit artefacts, that render the corporate mind tractable and accountable in the algorithmic age.