TASK-ORIENTED COGNITIVE ORGANISATIONS. How an Organisation Turns Experience into Knowledge: Crowding Out of Integration, Knowledge Debt, and Twin Divergence.

Abstract Cognitive organisations are evaluated mainly by their results on current tasks, yet such evaluation does not show whether they turn the experience they acquire into knowledge that increases future productivity. We distinguish first-order productivity, the results on the current sequence of tasks, from second-order productivity, the change in the quality, cost, and reliability of solving subsequent tasks, and we link them by a causal chain: experience → knowledge integration → stock of usable knowledge → future productivity. Knowledge integration is treated as a distinct mechanism comprising verification, recording of provenance, justification, description of conditions of applicability, linking with prior knowledge, and revision of outdated conclusions. A simple budget model yields two mechanisms of knowledge underproduction: crowding out of integration, whereby, under evaluation by current results alone, a zero share of resources for retrospective integration and revision is optimal on every task; and knowledge debt, the unverified results on which the organisation already relies, which in the model grows without bound when the flow of results put into use persistently exceeds the capacity to integrate and revise them. The payoff of integration is conditional and depends on the reuse horizon: the frequency of related tasks, the transfer distance, and the rate at which knowledge becomes obsolete. For testing, we propose a twin divergence experiment: identical organisations with equal budgets go through the same sequence of tasks but differ in how they handle experience; the archive group is matched with the integrating group in storage and retrieval; and comparisons are made on near, far, and negative transfer. The declaration by Fields Medalists on the misalignment of AI and mathematics (September 2026) serves as a motivating example. The work formulates a testable research programme for artificial and hybrid cognitive organisations.