Forward stability in the Boolean class: refined constant term

Establish that for independent permutations u,v drawn uniformly from the Boolean class 𝔅_n, the expected forward stability satisfies E[FS(u,v)] = n + 3 + o(1) as n→∞.

Background

The paper proves E[FS(u,v)] = n + O(1) for u,v sampled uniformly from the Boolean permutations 𝔅_n by developing a record-driven analysis and strong-mixing bounds. Monte Carlo evidence suggests a sharper constant term. Formalizing this, the authors conjecture that the precise asymptotic constant equals 3.

Confirming this would refine the asymptotic understanding of stabilization for Schubert products restricted to Boolean permutations, a class with special commutativity properties and canonical block-tag encodings developed in the paper.