arXiv:2603.30031v3 Announce Type: replace Abstract: Autonomous tool-using agents in networked environments must decide which information source to query and when to stop querying and act. Without principled bounds on information-acquisition costs, unconstrained agents exhibit systematic failure modes: excessive tool use under congestion, prolonged deliberation under time decay, and brittle behavior under ambiguous evidence. We propose the Triadic Cognitive Architecture (TCA), a decision-theoretic framework that formalizes these failure modes via cognitive friction. By combining nonlinear filtering, congestion-dependent cost dynamics, and HJB optimal stopping, TCA models deliberation as stochastic control over a joint belief-congestion state, explicitly pricing information by tool signal quality and live network load. TCA yields an HJB-inspired stopping boundary and a computable rollout-based approximation of belief-dependent value-of-information with a net-utility halting condition. We validate TCA in two controlled environments (EMDG and NSTG) designed to isolate stopping quality, action selection under congestion, and temporal urgency. TCA improves resource outcomes while reducing time-to-action without degrading accuracy, gaining 36 viability points in EMDG and 33 integrity points in NSTG over greedy baselines. Ablations show that selection and stopping must be optimized jointly, as stopping rules alone recover at most 4 viability points. Sensitivity sweeps over alpha, beta, and lambda_S yield stable accuracy and interpretable trade-offs, and a continuation-value sweep over eta values 0, 0.1, 0.3, and 0.5 finds eta equal to zero is optimal under high temporal urgency. Finally, we demonstrate an illustrative instantiation around a black-box LLM on a memorisation-free corpus, where the same stopping principle executes using empirically computable uncertainty and value-of-information proxies.

arXiv:2603.30031v1 Announce Type: new Abstract: Current autonomous AI agents, driven primarily by Large Language Models (LLMs), operate in a state of cognitive weightlessness: they process information without an intrinsic sense of network topology, temporal pacing, or epistemic limits. Consequently, heuristic agentic loops (e.g., ReAct) can exhibit failure modes in interactive environments, including excessive tool use under congestion, prolonged deliberation under time decay, and brittle behavior under ambiguous evidence. In this paper, we propose the Triadic Cognitive Architecture (TCA), a unified mathematical framework that grounds machine reasoning in continuous-time physics. By synthesizing nonlinear filtering theory, Riemannian routing geometry, and optimal control, we formally define the concept of Cognitive Friction. We map the agent's deliberation process to a coupled stochastic control problem where information acquisition is path-dependent and physically constrained. Rather than relying on arbitrary heuristic stop-tokens, the TCA uses an HJB-motivated stopping boundary and instantiates a rollout-based approximation of belief-dependent value-of-information with a net-utility halting condition. Through empirical validation in a simulated Emergency Medical Diagnostic Grid (EMDG), we demonstrate that while greedy baselines over-deliberate under latency and congestion costs, the triadic policy reduces time-to-action while improving patient viability without degrading diagnostic accuracy in this environment.

arXiv:2603.22384v1 Announce Type: cross Abstract: Autonomous agents operating in continuous environments must decide not only what to do, but when to act. We introduce a lightweight adaptive temporal control system that learns the optimal interval between cognitive ticks from experience, replacing ad hoc biologically inspired timers with a principled learned policy. The policy state is augmented with a predictive hyperbolic spread signal (a "curvature signal" shorthand) derived from hyperbolic geometry: the mean pairwise Poincare distance among n sampled futures embedded in the Poincare ball. High spread indicates a branching, uncertain future and drives the agent to act sooner; low spread signals predictability and permits longer rest intervals. We further propose an interval-aware reward that explicitly penalises inefficiency relative to the chosen wait time, correcting a systematic credit-assignment failure of naive outcome-based rewards in timing problems. We additionally introduce a joint spatio-temporal embedding (ATCPG-ST) that concatenates independently normalised state and position projections in the Poincare ball; spatial trajectory divergence provides an independent timing signal unavailable to the state-only variant (ATCPG-SO). This extension raises mean hyperbolic spread (kappa) from 1.88 to 3.37 and yields a further 5.8 percent efficiency gain over the state-only baseline. Ablation experiments across five random seeds demonstrate that (i) learning is the dominant efficiency factor (54.8 percent over no-learning), (ii) hyperbolic spread provides significant complementary gain (26.2 percent over geometry-free control), (iii) the combined system achieves 22.8 percent efficiency over the fixed-interval baseline, and (iv) adding spatial position information to the spread embedding yields an additional 5.8 percent.

arXiv:2603.17112v2 Announce Type: replace Abstract: Advanced AI reasoning systems route tasks through dynamic execution graphs of specialized agents. We identify a structural blind spot in this architecture: schedulers optimize load and fitness but lack a model of how failure propagates differently in tree-like versus cyclic graphs. In tree-like regimes, a single failure cascades exponentially; in dense cyclic regimes, it self-limits. A geometry-blind scheduler cannot distinguish these cases. We formalize this observability gap as an online geometry-control problem. We prove a cascade-sensitivity condition: failure spread is supercritical when per-edge propagation probability exceeds the inverse of the graph's branching factor (p > e^{-\gamma}, where \gamma is the BFS shell-growth exponent). We close this gap with a spatio-temporal sidecar that predicts which routing geometry fits the current topology. The sidecar comprises (i) a Euclidean propagation scorer for dense, cyclic subgraphs, (ii) a hyperbolic scorer capturing exponential risk in tree-like subgraphs, and (iii) a compact learned gate (133 parameters) that blends the two scores using topology and geometry-aware features. On 250 benchmark scenarios spanning five topology regimes, the sidecar lifts the native scheduler's win rate from 50.4% to 87.2% (+36.8 pp). In tree-like regimes, gains reach +48 to +68 pp. The learned gate achieves held-out AUC = 0.9247, confirming geometry preference is recoverable from live signals. Cross-architecture validation on Barabasi-Albert, Watts-Strogatz, and Erdos-Renyi graphs confirms propagation modeling generalizes across graph families.