The Benzene Snowflake: Informational Constraint Theory and the Falsification of Substrate‑Emergent Crystal Geometry

The dominant paradigm in crystallography holds that macroscopic crystal geometry emerges from the microscopic geometry of constituent molecules. This preprint presents a falsification of that principle using the juxtaposition of water and benzene. Water, a bent triatomic molecule with no intrinsic hexagonal geometry, forms a perfect six‑fold symmetric snowflake. Benzene, an ideal planar hexagon, crystallizes into an orthorhombic lattice with no trace of hexagonal symmetry. No substrate‑emergent theory predicts this inversion. The Informational Constraint Framework (ICF) resolves the paradox by showing that crystal geometry is determined not by molecular shape but by the topology of the intermolecular constraint network, encoded in the constraint density field p(x) and the interaction anisotropy kernel A(θ). We introduce the Benzene Snowflake computational experiment, in which benzene’s orthorhombic anisotropy kernel is replaced with a six‑fold symmetric kernel while all other physical parameters remain those of benzene. The result is a perfect stellar dendrite — demonstrating that geometry belongs to the constraint topology, not the substrate. The ICF master equation predicts morphological phase boundaries consistent with the Nakaya diagram and Libbrecht’s taxonomy. We propose that crystallization is a universal informational phase transition governed by the same constraint architecture across scales. Note: This manuscript is a preprint and has not undergone peer review. Part of the unified conical informational framework.