Hierarchical Sorting Methodology Framework for Reducing Possibilities in High-Density Digital Systems

This work presents a two-layer hierarchical sorting framework designed to reduce the combinatorial explosion in high‑density digital systems. The method separates canonical entropy‑based partitioning from objective‑driven hierarchical merging, providing containment guarantees, a positional non‑overlap condition, and an information‑theoretic budget that links merge loss to mutual information. The framework clarifies the limits of deterministic aggregation, establishes when non‑overlap is possible, and formulates topology selection as an optimization problem. It also provides diagnostic tools for table refinement and correlation analysis between node outputs.