Constraints That Compute: A Unified Framework for Efficient Intelligence from Prime Harmonics to Latent Reasoning

This paper introduces a domain-agnostic framework that replaces brute-force computation with structural efficiency by translating systems into their intrinsic, dimensionless geometries. Validated across pure mathematics (prime harmonics), dynamical systems (a zero-knowledge emergent chess engine), high-energy physics (scale-invariant jet tagging), and artificial intelligence (Relational-CoT for latent reasoning), the research demonstrates a unified principle: intelligent, adaptive, and highly efficient behavior emerges from rigorous internal constraints rather than massive computational scale.