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^{-γ}, where γis 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.

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