kauzmann_pos
plain-language theorem explainer
Chemists modeling vitrification in supercooled liquids cite this result to bound the Kauzmann ratio away from non-physical values. The declaration confirms that the ratio of glass transition temperature to melting temperature is strictly positive. The proof reduces the inequality directly to the constant definition via unfolding and numerical evaluation.
Claim. The Kauzmann ratio satisfies $T_g/T_m > 0$, where the ratio is the constant $2/3$.
background
The module treats glass transition as the point where a supercooled liquid forms an amorphous solid under 8-tick relaxation dynamics. Fragility measures the rate of viscosity increase near the transition temperature, distinguishing strong glasses such as SiO2 from fragile glasses such as polymers. The upstream definition supplies the explicit constant kauzmannRatio := 2/3, which the module presents as the universal Tg/Tm prediction.
proof idea
The term-mode proof first unfolds the definition of kauzmannRatio to the constant 2/3 and then applies numerical normalization to verify the inequality 2/3 > 0.
why it matters
The result secures the positivity of the universal Tg/Tm ratio that the module lists among its key predictions for glass transition. It anchors subsequent statements on fragility indices and relaxation times that rely on the 8-tick period. The declaration closes a basic consistency check within the Recognition Science treatment of vitrification.
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