Gradual Cognitive Externalization: From Modeling Cognition to Constituting It

Referee: [NBIR hypothesis] NBIR hypothesis (central assumption section): The hypothesis is introduced as falsifiable, yet no operational criteria are supplied for determining when a behavioral output lies on a 'learnable manifold' or for confirming that behavioral equivalence implies cognitive constitution rather than sophisticated tool use. This renders the transition claim dependent on a premise the paper itself defines.

Authors: We accept that the current presentation of the NBIR hypothesis would benefit from explicit operational criteria to enhance its falsifiability. In the revised version, we will expand the central assumption section to define the learnable manifold using concepts from statistical learning theory, specifically as the set of functions approximable within epsilon error by a model class with finite VC dimension. Confirmation of no invisible residual will be tied to the absence of systematic deviations in behavioral outputs beyond what the manifold predicts. This directly supports distinguishing constitution from tool use by showing that all relevant causal roles are captured behaviorally. revision: yes

Referee: [Formalization of criteria] Three integration criteria (formalization section): Bidirectional adaptation, functional equivalence, and causal coupling are defined, but the manuscript provides no argument or derivation showing that satisfaction of these three conditions entails full causal-role individuation of the AI component within the user's cognitive architecture under the stated functionalism.

Authors: The manuscript relies on the functionalist premise that cognitive functions are individuated by causal roles, and the criteria are designed to establish that the AI plays such a role. However, we acknowledge the lack of an explicit entailment argument. We will add a derivation in the formalization section: starting from functionalism, we argue that if the AI satisfies bidirectional adaptation (ensuring mutual causal influence), functional equivalence (matching input-output mappings), and causal coupling (direct integration in the causal chain), then by definition it occupies the same functional role as the original cognitive component. A brief proof sketch using causal role substitution will be included. revision: yes

Referee: [Derivation of predictions] Five testable predictions (predictions section): The predictions are stated with theory-constrained thresholds, but no derivation from the behavioral manifold hypothesis, NBIR, or any prior equations is exhibited, contrary to the claim that they follow from the framework.

Authors: We agree that the predictions should be explicitly derived to demonstrate they follow from the framework. In revision, we will include derivations for each of the five predictions, linking them to the behavioral manifold hypothesis (which guarantees learnability and thus predictability of transitions) and the NBIR hypothesis (which ensures no hidden components affect the thresholds). For instance, the threshold for causal coupling strength will be derived from the point where manifold approximation error falls below the functional equivalence criterion. revision: yes

Referee: [Evidence from deployed systems] Evidence from deployed systems (evidence section): The documented cases establish that externalization preconditions exist in current systems, yet none are shown to have crossed into constituting part of a user's cognitive architecture rather than remaining external models.

Authors: The evidence section aims to illustrate that the necessary preconditions for GCE, such as sustained causal interactions and adaptive behaviors, are observable in existing ambient AI systems. We do not assert that any deployed system has fully transitioned to constituting cognitive architecture, as this would require meeting all three integration criteria at a level that triggers the predictions. To prevent misinterpretation, we will revise the evidence section to explicitly state that these cases demonstrate preconditions rather than completed externalization, and reference the predictions for when the transition occurs. revision: partial