A beginning is worth one limit: robust unlearnable laws in noisy cellular automata

We compare nested expectation laws of begun and stationary probabilistic cellular automata. At equal scale depth d, a computable begun law has ceiling Delta^0_(d+2), whereas consensus on a nonempty effectively Sigma^0_2 class of stationary translation-invariant states has ceiling Delta^0_(d+1). We attain the begun ceiling at every finite depth using positive-rate three-dimensional rules, an open kernel region and a uniform renewal-gap readout schema. The canonical seed clones a uniform Bernoulli row on the physical block alphabet. Seed universality refers to blocked full-support, one-cell-shift-invariant ergodic laws on the pre-blocking alphabet. The seed has no distinguished origin or program but retains infinite transverse redundancy. At depth one, local error certificates and a continuous plateau quantizer give every Delta^0_3 value in [0,1] with a clock-free readout and genuine inner time limits. Every ordinary and Cesaro cluster state carries the same law; at computable kernels its stationary Cesaro cluster class is Pi^0_2 and has no low member when the value is outside Delta^0_2. An exact conditional-cone identity transfers any computable-seed begun depth-d law to a depth-(d+1) law in every stationary state of the same positive-rate rule. The extra limit is sufficient and sharp across the arithmetic ranges, but need not be minimal for an individual law. In the normalized four-dimensional Gibbs formulation its lag is a slab separation. At computable begun data, fixed targets outside Delta^0_2 cannot be learned with positive probability by effective finite-history inquiries. Removing cloned preparation from the realization remains open.