eight_beat_period
plain-language theorem explainer
The eight-beat period is defined as the natural number 8 and supplies the base interval for relaxation dynamics in the glass transition model. Researchers deriving fragility indices or Kauzmann ratios in Recognition Science cite this constant when scaling exponential decay with powers of 1/phi. The definition is a direct assignment with no lemmas or reduction steps.
Claim. Define the eight-beat period as the natural number $T_8 := 8$.
background
The module treats glass transition as the point where a supercooled liquid vitrifies, with fragility measuring the rate of viscosity increase near Tg. Strong glasses exhibit low fragility while fragile glasses show rapid departure from Arrhenius behavior. The 8-tick period is introduced as the fundamental relaxation interval, with phi-scaling controlling the departure from simple exponential relaxation. Fragility at index k is then given by (1/phi) raised to the product of the eight-beat period and k+1.
proof idea
This is a direct definition that assigns the constant value 8. No lemmas are invoked and no tactics are applied.
why it matters
The definition realizes the eight-tick octave (period 2^3) from the forcing chain and supplies the scaling factor used by fragility, fragility_one_lt_zero, and glass_univ. Fragility_one_lt_zero relies on it to establish decay between successive multiples, while glass_univ uses it to prove strict positivity for every k. It anchors the RS prediction of universal Tg/Tm ratio approximately 2/3 and the correlation of fragility with molecular complexity.
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