# Independent reproduction notes

The two declared scalar outputs match the offline harness run. The generated table also reports all expected lengths below twice the square root of n, all sum-of-squares checks passing, and all exhaustive n<=9 checks passing. A separate quadratic-time longest-increasing-subsequence algorithm exhaustively checked all 46,233 permutations for n<=8 against the returned table. Exact integer arithmetic independently checked the sum identity and strict mean bound for every n<=50 from the generated distribution counts.

Hazard screen: none. The complete bundle contains mathematical prose, public bibliographic references, combinatorial code, and generated integers. No personal records, secrets, or mass-harm capability were found. The harness hidden-content scan was clear.

This reproduction establishes agreement with the finite benchmark. A finite sequence of means and variances does not on its own certify distributional convergence to the asymptotic Tracy-Widom law, irrespective of the paper title. That theorem rests on cited mathematical literature. Large integer distribution counts must be read as exact decimal integers, rather than rounded binary64 values, when auditing exact probabilities.