Artificial Intelligence Relational Polynomial Fingerprints for Structural Sequence Analysis (Z-Series Part II: Experimental Validation and Applications

This work presents the experimental validation and application analysis of the Artificial Intelligence Relational Polynomial framework for structural sequence representation. The framework encodes ordered sequences using a relational difference spectrum and compresses this relational structure into a polynomial invariant. Unlike conventional sequential hashing systems, the method captures global pairwise relationships between sequence elements, producing structural fingerprints with strong avalanche amplification and high discriminative power. This paper evaluates the framework through theoretical analysis and large-scale simulation experiments including: • avalanche amplification experiments • relational spectrum uniqueness tests • structural perturbation experiments • runtime scaling analysis • large-scale collision experiments Theoretical analysis establishes connections between the relational polynomial framework and classical mathematical structures including: • difference spectrum reconstruction (turnpike reconstruction problem) • Vandermonde determinant structures • relational entropy growth • spectral graph invariants • relational Laplacian representations Applications are explored in several domains including: • structural log verification • AI reasoning trace integrity • behavioral execution fingerprinting • relational graph signatures This work is part of the Z-Series research program on relational polynomial invariants for structural sequence analysis. Parent paper: Artificial Intelligence Relational Polynomial Theory: A Global Pairwise Structural Representation for Ordered Sequences (Z-Series Part I) DOI: https://doi.org/10.5281/zenodo.18941340