kauzmannRatio
plain-language theorem explainer
The declaration sets the Kauzmann ratio to exactly 2/3, encoding the predicted universal ratio of glass transition temperature to melting temperature in Recognition Science. Materials physicists studying supercooled liquids and fragility would reference this constant when classifying strong versus fragile glasses under the 8-tick relaxation model. The definition requires no proof steps beyond the assignment itself.
Claim. The Kauzmann ratio is the constant $K := 2/3$ where $K = T_g/T_m$ for the glass transition temperature $T_g$ and melting temperature $T_m$.
background
The Chemistry.GlassTransition module models glass transition via 8-tick relaxation dynamics. Glasses are classified as strong (low fragility, e.g., SiO2) or fragile (high fragility, e.g., polymers) according to how rapidly viscosity rises near Tg, with the fragility index tied to phi-scaling departures from Arrhenius behavior. The module documentation states that the 8-tick period sets the fundamental relaxation time and predicts a universal Tg/Tm ratio of approximately 2/3.
proof idea
The definition is a direct constant assignment with no lemmas applied or tactics used.
why it matters
This definition supplies the universal Kauzmann ratio that feeds directly into the positivity and upper-bound theorems kauzmann_pos and kauzmann_lt_one. It realizes the key prediction stated in the module documentation for glass transition properties under 8-tick relaxation. The value aligns with the eight-tick octave (T7) from the forcing chain and supplies an empirical anchor for chemistry applications within the Recognition Science framework.
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