Phase Transitions and Metastable Regimes in Real-Time Cognitive Connectomes

Big systems do not fail only by “breaking.” They also fail by getting stuck. A cognitive runtime can look active while it quietly collapses into one style of structure. The simplest way to detect that collapse is to watch the connectome itself with two plain measurements: how many edges are active and how unevenly those edges are distributed across nodes. If those numbers spend long periods in distinct bands, and if the trajectory jumps between them, then the runtime is switching modes. We test that operational idea on three independent, non-trained runtime datasets (all N=1000) with saved directed connectome checkpoints. We define a two-dimensional orderparameter plane using the number of active edges (nnz) and the Gini coefficient of out-degree (G). We estimate an empirical proxy free-energy landscape F(nnz, G) = − log p(nnz, G) from the snapshot cloud and label metastable regimes as dominant basins of this surface. In the primary full-run dataset (485 snapshots, ticks 60–29160), the landscape is strongly bimodal with basin centers near (1.49×104 , 0.54) and (2.10×104 , 0.44), separated by ≈ 3.33 standard deviations in the standardized plane and by a barrier height ∆F ≈ 8.9. The trajectory exhibits alternating dwell segments (median durations 3660 and 960 ticks) separated by discrete transition events. Transition direction aligns with external input context: switches into the sparse/high-inequality basin occur during input episodes, while switches into the dense/lower-inequality basin occur in no-input periods. A lag-0 transfer-entropy summary over scalar telemetry further shows connectome entropy as a strong directional source for UTD output channels. Shorter replication runs occupy consistent regions of the same order-parameter plane. The result is an instrumented, reproducible operationalization of “phase transitions” in a real-time cognitive connectome: discrete regime switching in a low-dimensional structural manifold, with measurable dwell statistics, barrier height, and input-linked directionality.