Exponential positive-evidence requirements for two-tier strictly local languages

We construct strictly 2-local languages L_{r,d} over dr + 2 symbols whose smallest positive characteristic sample has d² words when hypotheses use one tier and exactly d^r words when hypotheses may intersect constraints on two nested tiers (r ≥ 2, d ≥ 2). Each competing hypothesis adds one tier-bigram constraint, so the separation already holds for intersections of a strictly 2-local and a tier-based strictly 2-local language. Every two-tier characteristic sample has total length at least (r + 2)d^r, yet the targets have minimal automata with r + 4 states, J-trivial syntactic monoids with (r + 2)(r + 3)/2 + 2 elements satisfying x² = x³, and canonical multitier grammars of polynomial size. Hence no polynomial in alphabet size, grammar size, automaton size, and monoid size bounds positive characteristic data for two nested tiers. A second construction expresses characteristic length as an exact weighted count of minimal hypergraph transversals. With r forbidden tier bigrams and at most t blockers per constraint the worst case is (r + 2)t^r, and for t = 2 the canonical grammar has size 6r. Both constructions contradict the polynomial representative-sample bound stated by Swanson (2025) for multi-tier strictly 2-local string learning, and we locate the step of its proof that fails. Qualitative identification in the limit is unaffected. For the layered target and its single-word deletions, a family of VC and Littlestone dimension one, exact identification from independent uniform positive data needs Θ(d^r(r log d + log(1/δ))) draws.