Critical Bubble Radius Against the Ceiling Energy Density: When Thin-Wall Bookkeeping Breaks Down

At the electroweak scale the critical radius is 0.039 fm and exceeds the wall thickness by a factor of 20, so thin-wall bookkeeping is comfortable. Because both the radius and the thickness scale as inverse powers of the transition scale under the benchmark ties, their ratio is the same at every scale examined, while the absolute radius shrinks to 3.95e-09 fm at the highest scale. The energy fraction tells the scale-dependent part of the story: at 10^9 GeV the vacuum energy difference is still only 2.39e-04 of the ceiling. Thin-wall validity, in this benchmark, is therefore a statement about the dimensionless ties among the potential parameters and not about proximity to the ceiling; the ceiling audit and the thin-wall audit are independent checks, and a calculation must pass both. This study is simulated and computed from stated assumptions; it is not a measurement.