Materials Science Extensions (H2m) PRELIMINARY

Summary: Phase transitions in 18 materials (H₂O, steel, NiTi shape-memory alloy, Li-ion batteries, BaTiO₃ ferroelectric) exhibit hysteresis asymmetry ratios clustering at geometric attractors.

Statistical Results (N=201 materials):

e → ductile transitions: p=8×10⁻⁸
3:2 → ductile: p=0.011
2:1 → brittle: p=0.008
√2 → brittle: p=0.03

Dual mechanism identified: Boltzmann (e) + Pythagorean (3:2).

Note: φ-specific testing not yet completed; reported ratios are related but not identical to climate hierarchy.

Status

These results demonstrate statistical clustering at known constants but require:

Preregistered holdout testing
Direct φ-specific hypothesis testing
Independent validation in external materials databases
Theoretical bridge to KAM theory and resonance zones

Citation: Mendoza (2026), in preparation

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