Relational Order in Sampling Blackwell Deficiency: Rényi Collision Complexity and Exact Parity Gaps

Blackwell deficiency is a decision-theoretic distance between experiments on a common state space. We show that, under posterior-array sampling that hides state names, estimating this distance faces a distinct relational sample-complexity barrier: arbitrarily many independent predictive row draws cannot compensate for shared-state relations that were never sampled. For a finite local pair we introduce posterior relational order, the smallest arity at which restricted row laws differ, and a distinguishing clutter of minimal distinguishing coordinate sets. Before any sampled block contains such a set, the complete arrays are identical regardless of row count; under small low-order perturbations this becomes a quantitative soft firewall. We derive the exact finite safe-set generating function and a Chen–Stein Poisson limit whose critical scale is governed by a Rényi effective block count. A paired-sign family realizes every order r ≥ 2 with a non-saturated clutter and exact symmetric deficiency a/r under arbitrary block masses. A second witness based on even and odd permutations has order k − 1 and exact harmonic gap ∆(v) =(∑︁j(vj −vj+1)−1)−1; we also determine its sharp fixed-k maximum. Explicit resolvers give finite minimax bands and exact critical two-point curves, and the collision firewall survives a natural opaque adaptive oracle.