The Sarrus Isomorphism: Harmonic Alignment and Topological Crystallization in Matter, Biology, and Cryptography

Research reveals that the hexagonal columnar basalt formations at the Giant's Causeway and Causeway Coast are not merely geological features but the result of a universal computational process governed by the Sarrus Isomorphism. This phenomenon, identified within the Nexus Recursive Harmonic Framework, demonstrates how thermodynamic entropy is resolved through harmonic alignment, leading to the formation of hexagonal columns that minimize energy expenditure. The study analyzes the transition from T-junctions to Y-junctions in basalt cooling, showing how these geometric patterns represent a phase-locked standing wave and the 'frozen hash' of a localized thermodynamic computation. Additionally, the research extends this principle to protein folding and cryptographic algorithms like SHA-256, suggesting a universal mechanism that governs structural emergence across disparate domains.

kulik, dean. (2026). The Sarrus Isomorphism: Harmonic Alignment and Topological Crystallization in Matter, Biology, and Cryptography [Dean A. Kulik]. https://doi.org/10.5281/ZENODO.18928598