pith. sign in
theorem

kauzmann_lt_one

proved
show as:
module
IndisputableMonolith.Chemistry.GlassTransition
domain
Chemistry
line
82 · github
papers citing
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plain-language theorem explainer

The theorem establishes that the Kauzmann ratio equals 2/3 and is therefore strictly less than 1. Condensed-matter researchers modeling vitrification cite this to anchor the predicted Tg/Tm scaling in supercooled liquids. The term proof reduces the claim by unfolding the constant definition and applying numerical normalization.

Claim. The Kauzmann ratio $T_g/T_m$ satisfies $2/3 < 1$.

background

The module treats glass transition as the point where supercooled liquids vitrify under 8-tick relaxation dynamics. Fragility classifies glasses by how sharply viscosity rises near Tg: strong glasses (SiO2-like) show low values while fragile glasses (polymers) show high values. The key prediction is a universal Tg/Tm ratio of approximately 2/3, called the Kauzmann ratio.

proof idea

The proof is a term-mode reduction that unfolds the definition of kauzmannRatio to the constant 2/3 and applies norm_num to confirm the inequality.

why it matters

This result secures the universal Tg/Tm ratio prediction inside the glass-transition module, which traces to the eight-tick octave (T7) of the unified forcing chain. It supports downstream classification of strong versus fragile glasses via the fragility proxy that decays as (1/φ)^(8(k+1)). The claim is fully proved with no open scaffolding.

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