Uniform Physical Exponential Tilts

This preprint studies geometric failures in period-doubling Hénon-like maps under exponential weighting by canonical source generation. For two specified scaled stable families, it establishes uniform asymptotics for the weighted physical failure mass and a joint limit law in which normalized failure size, observation offset, and standardized source generation converge to independent Pareto, uniform, and Gaussian factors.The proof combines a compact-real-parameter renewal theorem for the exact finite-word defect with a source-preserving geometric transfer. Consequences include convergence of generation moments, mixed moments below the critical size exponent, moderate deviations, and local large-deviation exponents on the exposed mean interval. The uniform physical results apply when the negative logarithm of the average Jacobian grows sublinearly with the observation level, with vanishing thresholds above an admissible exponential floor. A separate three-variable limit theorem is also established for each fixed map in the broader native class.This work builds on the geometric framework and primitive estimates developed in Hae Gyu Kim, Exact Geometric-Failure Tails for Period-Doubling Hénon-like Maps: https://doi.org/10.6084/m9.figshare.34895790. --- Author's Note: Artificial intelligence (AI) tools were utilized in the course of this research, including language translation, drafting assistance, and code verification. (이 연구는 번역, 원고 검토 및 코드 검증 등에 AI를 활용하여 수행되었습니다.)