Beyond IQ: A Biophysical Framework for Cognitive Flexibility

Standard intelligence tests (IQ) capture the depth and richness of cognitive attractor landscapes but leave unmeasured the dynamic flexibility with which those attractors are explored. We propose a General Quotient GQ = IQ × CQ, where the Cognitive Quotient (CQ) formalizes inter-attractor mobility as the entropy rate of the θ-band attractor transition sequence. Building on Fractal Mechanics of Consciousness (FMC) [Leroy R. & Claude 2026], we extend the deterministic attractor dynamics of Hopfield networks to a Langevin stochastic process parameterized by a cognitive temperature T, yielding a continuous-time phase transition in CQ(T) at a critical threshold T_c. CQ is estimated empirically by the Lempel-Ziv complexity of the θ-band microstate sequence — a measurement accessible to standard EEG. We validate the framework in two steps: (i) Hopfield network simulation confirming the predicted phase transition at T_c ≈ 0.25, and (ii) application to a real epileptic EEG from the CHB-MIT dataset, revealing a highly significant pre-ictal CQ decrease (Mann-Whitney U, p = 1.6 × 10⁻⁸ Bonferroni-corrected; Cohen's d = 1.31) beginning 106 seconds before clinical seizure onset, with an absolute minimum of CQ = 0.195 at seizure onset (-40% vs. baseline). These results are consistent with the FMC prediction that seizure onset constitutes an extreme crystallization event. We formulate four experimentally testable predictions and discuss clinical implications for depression, OCD, creativity assessment, and early-warning biomarkers.