We compare two observer-count scales for distinguishing sampled configurations from local observations: an adaptive-greedy threshold and an information-theoretic birthday-bound threshold. Defining the efficiency ratio \ (= K^* ₁₃₀ₘ / K^* ₆ₑ₄₄₃ₘ \), we observe a three-regime pattern across 2D Ising and Potts models: redundant observations (\ (1 \) ) at high temperature. A conditional conjecture under polynomial alpha-mixing suggests \ (1 \) at \ (Tc \) for FK (\ (q \) ) with \ (q \2, 3, 4\ \).
Xinlei Wang (Wed,) studied this question.