arXiv:2609.09228v1 Announce Type: new Abstract: The quantum model of the two-sentence liar paradox proposed by Aerts, Broekaert, and Smets is an early example of the use of quantum formalism to describe cognitive dynamics. Our reconstruction is primarily pedagogical in intent, but it also leads to a number of clarifications, and to some new observations, concerning the structure of the model. Rewriting the model in Dirac notation, we make explicit the distinction between truth values originating from a decision and from semantic inference, and show that the associated enlargement of the one-sentence state space corresponds to a factorization with respect to which the non-paradoxical configurations are separable while the genuine liar state is entangled. We also derive the Hamiltonian generating the four-state cyclic evolution, express it in compact operator form, and give the resulting transition probabilities in closed form. We emphasize that the liar cycle admits a unitarily equivalent representation in the four-dimensional truth-only space, where the unmeasured liar state is separable, so the dimensional enlargement is not required by the unitary part of the dynamics; it is required, however, by the measurement structure. The enlargement is also required by the dynamics as soon as revision processes are admitted, in which states with identical truth content but different origins have different successors, the origin degree of freedom then acting as a minimal form of cognitive memory. We conclude by discussing the possible relationship between the model and more general deliberative processes.

arXiv:2605.23943v1 Announce Type: new Abstract: Quantum cognition often explains order effects, contextuality, and violations of the law of total probability by replacing classical probability with quantum probability on a fixed event structure. This paper proposes a different interpretation: quantum probability is the fixed-spacetime projection of contextual spacetime formation under finite-state requirements. The framework begins not with time, space, objects, or probabilities, but with requirements such as finite representational capacity, single-state semantic stability, context-sensitive intervention, avoidance of explicit context labels, coherent world-formation, and intersubjective transformability. When these requirements cannot be realized within a single global Boolean event structure, the mismatch appears, under fixed-spacetime projection, as noncommutativity, interference, and quantum-like probability. Building on prior single-state approaches to contextuality, we reinterpret classical contextual bookkeeping cost as the fixed-spacetime shadow of contextual spacetime formation. Auxiliary memory or context labels in a classical representation correspond, in this account, to holonomy-like mismatch among locally Boolean logic-worlds. The interference term is the cross term generated when locally classical realization contributions are nontrivially glued and projected back into a fixed classical spacetime form. The result is a transcendental-operational realist account: objecthood, eventhood, probability, and spacetime are treated as forms of realization under requirements, while objectivity is defined by invariants preserved across observer- and history-dependent spacetime formations.