Sensorimotor identifiability determines the geometry of predictive representations

Learned world models are often evaluated against physical state even when their observation and action history does not identify that state. Sensorimotor identifiability formalizes this: the finest state recoverable fromhistory is the quotient X/G_eff under the subgroup of unresolved environmental symmetries. Under symmetry-paired, episode-held-out evaluation, entropy-matched one-bit signals reach 0.500 and 0.982 orbit-phase accuracy in a C2 arena, while the corrected asymmetric control differs by only 0.00133. In a C4 arena, partial and full invariance reach 0.480 and 0.243 near the exact 0.500 and 0.250 ceilings, and folded codes preserve local quotient geometry.The right evaluation target for a learned representation is the state its sensorimotor history can actually support.