[WARNING: Technical Failure] Scaling Fixed Points in Hierarchical Recursive Estimation Systems

**Technical Failure:** The recursive construction employed in this work enforces equality in all constraints and selects the minimum allowed sample size at each step. While mathematically rigorous, this construction can only capture **finite (constant) fixed points**, as it inherently restricts the system to trajectories with non‑growing sample size. Consequently, the framework fails to describe *scaling fixed points*, where sample size grows while precision adapts. The subsequent introduction of asymptotic assumptions to discuss such fixed points contradicts the construction rules; furthermore, extracting limits via a diagonal argument can obscure this discrepancy—finite‑layer sequences obey the constant‑sample‑size rule, whereas the limit sequence may spuriously suggest growth. This illustrates how an overly rigid construction can lead to a failure in generality, and how sophisticated limiting techniques may conceal logical inconsistency. A more general framework, analyzing the evolution's intrinsic features directly, is required to fully classify and construct all asymptotic behaviors.