We study the minimum number of local observers needed to uniquely identify a global configuration in elementary cellular automata (ECA). We prove that the mean two-observer objectivity is non-decreasing (data processing inequality), then classify all 256 ECA rules by a local degeneracy mechanism into four regimes: T∗=1 T^* = 1 T∗=1 (single observer suffices), T∗=2 T^* = 2 T∗=2 or 3 3 3 (Nyquist-like threshold K∗=⌈N/ (w+1) ⌉ K^* = N / (w+1) K∗=⌈N/ (w+1) ⌉, verified for all 26 rules), and T∗=∞ T^* = T∗=∞ (maximum observer cost). For Rule 110, a spectral bound on the de Bruijn transfer matrix proves O2N (1) /N<1 O₂₍^ (1) / N < 1 O2N (1) /N<1 for all N≥8 N 8 N≥8, establishing a persistent epistemic boundary. Observable discipline separates two-observer mutual information from single-observer quantities throughout.
Xinlei Wang (Wed,) studied this question.