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Supersingular Tate conjecture is proven for $K3^{[n]}$, OG6, OG10, and $\mathrm{Kum}^n$ varieties, unlocking new insights into their arithmetic geometry.
Direct-decision models exhibit a learned "ordinal-scale-utilization bias," compressing the effective decision space and underutilizing available scale points, even when accuracy is high.
Flow-matching manipulation policies can outperform dedicated 3D-conditioned architectures simply by cross-attending robot-grounded spatial tokens into the action expert, beating the 2025 BEHAVIOR-1K challenge winner without modifying host perceptual pathways.
This work proposes StageGuard, an agentic distillation framework for accurate and efficient stage-transition decisions, which combines teacher-model reasoning with demonstration trajectories to generate structured explanations of subtask completion and policy switching.
