Observation-Induced Hierarchy from Linear Memory

We report a minimal mechanism that generates robust multi-scale hierarchical structure in positive gap sequences. A latent linear memory process combined with an exponential observation map yields heavy-tailed distributions, persistent log-log curvature, and a negative scale-conditional entropy gradient across a non-trivial parameter regime. Systematic ablation tests show that exponential (or asymptotically exponential) observation is necessary for hierarchy formation, while temporal memory amplifies extreme excursions and stabilizes the tail exponent.