ScalingStacks

Proposition 5.19 . [04FC]

Original official author HTML, exact retained edition. Historical TeX conversion verdicts remain unchanged. Cited-edition alignment and mathematical self-containment are not assessed.

Complete original source context · Original author HTML

Proposition 5.19.

Assume the Lagrangian LL with potential fLf_{L} is quantitatively almost calibrated, homologous to L0L_{0}, and satisfies (N,A)(N,A)-potential clustering. The elementary functional (45) makes sense verbatim, with no smoothness assumptions. Then |𝒮​(L)−𝒮¯​(L)||\mathcal{S}(L)-\bar{\mathcal{S}}(L)| has a uniform upper bound independent of LL.

Original mathematics by the credited authors. Source-backed reader collection; mathematical self-containment is not assessed.