Sourcewise Transfer under Moving Observation Kernels

This paper develops a general framework for sourcewise finite-measure transfer under moving integer observation kernels, accounting for observation multiplicity, boundary resonance, source-dependent weights, and moving marks. It establishes distribution-free boundary laws and renewal inspection limits, including results under positive count tilts. The framework is applied to two specified scaled families of period-doubling Hénon-like maps, yielding common-clock laws, compact-tilt transforms, and resonance moments. The analysis distinguishes general probabilistic principles from the geometric assumptions required for the dynamical applications.--- 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.)