catalyticFactor
plain-language theorem explainer
The catalyticFactor definition supplies the ratio of uncatalyzed to catalyzed activation energies as the quantitative measure of enzymatic stabilization in the J-cost model of reaction barriers. Researchers working on Arrhenius kinetics or enzyme rate enhancement within Recognition Science would cite it when comparing barrier heights. The definition is a direct ratio with no lemmas or computation steps required.
Claim. The catalytic factor is defined by $E_ {uncat}/E_ {cat}$, where $E_ {uncat}$ and $E_ {cat}$ are the activation energies of the uncatalyzed and catalyzed reactions.
background
Activation energy barriers emerge from the J-cost landscape, with the transition state identified as the maximum J-cost along the reaction coordinate. The module states that the Arrhenius form arises from Boltzmann statistics over this landscape and that characteristic barrier heights scale with powers of φ relative to the coherence energy E_coh. Enzyme catalysis is described as reshaping the J-cost landscape to reduce the transition-state value while leaving overall reaction energetics unchanged.
proof idea
This declaration is a direct definition whose body is the division of the two real arguments. No lemmas are applied and no tactics are used.
why it matters
The definition is invoked by the downstream theorem catalysis_lowers_barrier, whose doc-comment states 'Catalysis means lower activation energy.' It supplies the enzymatic transition-state stabilization factor required by the CH-017 module and connects the predicted J-cost reduction to observable rate increases. The construction supports the claim that enzymes lower the transition-state J-value without disturbing the underlying φ-scaling of barriers.
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