uncatalyzedRate
plain-language theorem explainer
The uncatalyzed rate factor is defined as the Boltzmann factor of the bare reaction barrier evaluated at the transition state coordinate. Researchers modeling enzyme kinetics in Recognition Science cite this when establishing the baseline rate prior to catalytic enhancement. The definition is a direct one-line composition of the exponential rate factor with the activation barrier function.
Claim. The uncatalyzed rate factor for transition-state coordinate $x^*$ is given by $e^{-B(x^*)}$, where $B(x^*)$ is the J-cost activation barrier of the bare reaction.
background
Recognition Science treats chemical reactions via J-cost landscapes in which the transition state appears as a saddle with positive cost. The module frames enzymes as J-cost lenses whose topology supplies the additive inverse that flattens this saddle to zero. The uncatalyzed barrier is obtained by applying the activation barrier function to the transition coordinate. The Boltzmann factor then converts the barrier into a dimensionless rate via the exponential, with $kT$ scaled to unity in native units. This rests on the Boltzmann factor definitions imported from the activation energy and thermodynamics modules, which recover the Arrhenius form $k = A e^{-E_a/RT}$.
proof idea
The definition is a one-line wrapper that applies the Boltzmann factor directly to the uncatalyzed barrier evaluated at the supplied coordinate.
why it matters
This definition supplies the baseline rate used in the rate enhancement theorem, which recovers the full activation energy as the multiplicative factor between catalyzed and uncatalyzed rates. It realizes the module's core claim that zero saddle cost yields unit Boltzmann factor for the catalyzed path. In the framework it recovers the Arrhenius law from the J-cost formalism and connects to phi-ladder scaling of barriers on the eight-tick octave.
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