barrierLadder
plain-language theorem explainer
barrierLadder assigns the n-th rung barrier height as E_coh multiplied by phi to the power n on the activation energy ladder. Chemists modeling reaction rates inside the Recognition Science framework cite this when scaling barriers from hydrogen-bond to covalent strengths. The definition is a direct one-line assignment that composes the pre-defined coherence energy with the phi exponential from the upstream scale function.
Claim. The barrier height for the n-th rung is $E_ {coh} phi^n$, where $E_{coh} := phi^{-5}$.
background
The ActivationEnergy module derives chemical barriers from the J-cost landscape, with the transition state at a J-maximum and Arrhenius rates following from Boltzmann statistics over that landscape. E_coh is the base scale defined as phi to the power -5, approximately 0.09 eV, and serves as the reference for hydrogen-bond barriers. The phi-ladder scaling is inherited from the upstream scale definition in LargeScaleStructureFromRS, which sets scale(k) = phi^k for integer k.
proof idea
One-line definition that directly multiplies the E_coh constant by the phi power term, using the upstream scale construction for the exponential.
why it matters
barrierLadder supplies the explicit scaling law required by the downstream theorems hbond_barrier_scale (which recovers E_coh at n=0) and covalent_barrier_higher (which shows n=1 exceeds the base). It realizes the module's stated prediction that characteristic barriers scale with phi powers of E_coh, linking activation energies to the RS phi-ladder and the eight-tick octave. No open scaffolding questions are closed by this definition.
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