Uniform Height Bounds for Brownian Excursions with an Exact Area Constraint

Let a standard Brownian excursion have duration T, exact area rho T and maximum M_T, with fixed rho > 0. This note proves P(M_T > H | A_T = rho T) <= C_rho T^(3/2) exp(-c_rho H) for large T and H >= 1, and E[M_T^r | A_T = rho T] = O((log T)^r) for every r > 0. A positivity-preserving Gaussian bridge shift compares increasing path functionals under exact-area conditioning with an exponential area tilt. Classical Airy-area asymptotics and elementary kernel and reflection estimates complete the argument. For the literal duration-2N, area-N normalization in AIM KPZ workshop item 2.18 (dataset record AIM-PROBABILITY-0093), the entire curve divided by N^(1/3) converges uniformly to zero. Thus an N^(2/3) time window cannot yield a nondegenerate random fluctuation limit at that height scale. No sharp maximum scale, constant-scale Ferrari-Spohn process limit, changed-area, moving-wall or multiline result is claimed. Prior one-point asymptotics are credited; novelty remains undetermined after a bounded search. English, AI-assisted, self-audited and unrefereed preprint by Alper Ferudun, Mercury Software GmbH. Neither independent peer review nor formal verification is claimed. The source archive contains proof notes and supplementary symbolic/numerical checks, but no third-party source PDFs.