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

The dominant paradigm in crystallography holds that macroscopic crystal geometry is emergent from the microscopic shape of constituent molecules. We present a computational falsification of this substrate‑emergent paradigm via the Benzene Snowflake experiment: by surgically replacing benzene’s native orthorhombic anisotropy kernel with a six‑fold projection A (θ) = 1 + ε₆ cos (6θ) while holding all thermodynamic parameters fixed, the canonical FreezeMachine run (seed 42) produces a sharply faceted six‑armed stellar dendrite with sixfold fraction f₆ ≈ 0. 947. The Informational Constraint Framework (ICF) developed in the paper formalizes crystallization as a capacity‑limited topological collapse governed by two informational fields — the constraint density p (x) and the interaction anisotropy kernel A (θ) — and shows that macroscopic habit is determined by the topology of the constraint network rather than by molecular shape. The ICF is presented as a closed five‑equation system whose master constraint equation integrates out microscopic degrees of freedom subject to (i) a capacity threshold Ccrit and (ii) the anisotropy‑weighted informational map FC, A (θ). The framework reproduces the qualitative structure of the Nakaya morphology diagram and Libbrecht’s taxonomy as emergent contours in Deff (x, T), and yields testable, quantitative predictions for morphological phase boundaries. The Benzene Snowflake therefore provides a reproducible, deterministic demonstration that directional informational routing encoded in A (θ) can override substrate molecular symmetry to set macroscopic crystal geometry. Quoted from the manuscript (Edwards, May 2026): “The dominant paradigm in crystallography holds that macroscopic crystal geometry is emergent from the microscopic shape of its constituent molecules - a principle we term substrate‑emergent geometry. ” “We introduce the construct of the Benzene Snowflake - a computational experiment in which benzene's orthorhombic anisotropy kernel is surgically replaced by a six‑fold symmetric kernel, while all other physical parameters (specific heat, freezing temperature, molecular mass) remain those of benzene. ” Full deposit summary This deposit contains the complete reproducibility bundle for the Benzene Crystalline Plate experiment implementing the Informational Constraint Framework (ICF). The canonical computational experiment replaces benzene’s native orthorhombic anisotropy kernel with a sixfold projection A (θ) = 1 + ε₆ cos (6θ), producing a sharply faceted hexagonal plate despite benzene’s molecular symmetry favoring orthorhombic packing. This provides a direct computational falsification of substrate‑emergent crystal geometry under controlled informational constraints. The bundle includes the canonical regeneration script (regen. py) and a checksum‑verified plain‑text copy (regen. py. txt), canonical. npz outputs (including Cfield, TopologyMask, sixfoldfraction, and dtₛummary), zoom arrays for Figure 2, diagnostic logs, plotting cells used to generate Figures 1 and 2, and a manifest with SHA‑256 fingerprints for byte‑level verification. An optional notebook wrapper (FreezeMachinecanonicalᵥ1ₛeed42. ipynb) is included for inspection only; the canonical execution path is the script regen. py. Representative contents: • TheBenzeneSnowflakePreprint. pdf — full manuscript (May 2026) • README. md • regen. py — canonical regeneration script (one‑command pipeline) • regen. py. txt — checksum‑verified plain‑text copy • freezeᵣunₛeed42. npz — canonical scientific arrays (Cfield, TopologyMask, sixfoldfraction, dtₛummary) • freezeᵦoomₛeed42. npz — zoom arrays for Figure 2 • freezeᵣunₑ6₀. 21g150ₙ0. 02. npz — parameter‑sweep output (non‑canonical) • Figure1freezeₛeed42. png • Figure2freezeₛeed42. png • Figure2freezeₛeed42ᵢmprovedC. png • Figure2ABᵦoomₛkeleton. png • freezeₒutputsbundle. zip — complete regenerated artifact bundle • manifestfreezeᵣuns. csv — manifest (see Manifest and Verification section) • regenₗog. txt — run log • FreezeMachinecanonicalᵥ1ₛeed42. ipynb — optional notebook wrapper Live development repository: https: //github. com/ICF26-me/SNOWFREEZEᵥ1 For inquiries, please open an issue on the GitHub repository Version history: • Version 2. 0. 0 — Supersedes the earlier Benzene Snowflake deposit and provides a fully revised manuscript, corrected filenames, and a complete reproducibility bundle. Includes the canonical regeneration script (regen. py) and checksum‑verified plaintext (regen. py. txt), canonical. npz arrays and zoom files, updated figures, diagnostic logs, plotting cells for Figures 1–2, and a manifest with SHA‑256 fingerprints. All outputs were regenerated deterministically with seed 42; this release is the authoritative reproducibility package. • Version 2. 0. 1 — Added the GitHub URL as an Alternative Identifier. • Version 2. 0. 2 — Updated README. md with formal citation block, canonical parameters, and clarified reproducibility instructions. AI disclosure and license guidance AI disclosure: Microsoft Copilot assisted with code organization and editorial refinement; all scientific decisions and analyses were made by the author. License: include the LICENSE files in the deposit (e. g. , MIT for code; CC‑BY 4. 0 for manuscript and data) or state the chosen license explicitly in the Zenodo metadata. Note: This manuscript is a preprint and has not undergone peer review. Part of the unified conical informational framework.