1
Quantized estimation rate
Supported · scaled audit
MSE falls with sample size at slope −0.938 (R² = 0.997) before reaching the quantization floor.
Control: Unquantized sample means remove the floor.
2
Stable versus unstable rollout
Supported · premise stress test
Stable dynamics show polynomial-like horizon growth; ρ = 1.3 produces exponential growth with semilog slope 0.267.
Control: The unstable run deliberately violates the stability premise.
3
One-step error can mislead
Supported · counterexample mechanism
One-step error falls from 0.72 to 0.045 as εq shrinks, while deployed regret remains fixed at 0.63 per horizon.
Control: A smooth quantizer makes deployed error shrink.
4
Rollout augmentation
Misstated · registered citation or scope
Auxiliary rollout correction restores linear εq scaling (slope 1.000) and reaches a 21.91× improvement at the finest grid.
Control: Without augmentation the deployed curve stays constant.
5
Deterministic and stochastic rates
Supported · formula audit
The registered lower-bound forms cleanly separate 1/n deterministic behavior from 1/√n stochastic behavior at fixed quantization error.
Control: Setting εq = 0 isolates the statistical terms.
6
Hard-policy discontinuity
Misstated · registered citation or scope
Adjacent-grid TV change is 5.93e−5 for a soft binned policy but remains exactly 1 for the learned hard rule.
Control: Grid refinement shrinks the soft jump, not the hard jump.