canonicalThreshold
plain-language theorem explainer
The canonical threshold in the RS chemistry stack is the real constant φ − 3/2. Workers calibrating hydrogen-bond domain costs against the module-5 H-bond scale cite it as the fixed comparison level. It is introduced by bare definition from the golden-ratio constant, with no proof obligations.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ denotes the golden ratio (self-similar fixed point of the Recognition forcing chain).
background
Chemistry RS Module 5 treats hydrogen-bond energetics as a structural consistency check: the combination $J(\varphi)^{-1},kT,N_A$ is asserted to land near 20.8 kJ/mol, inside the empirical H-bond window. The module is marked structural (zero sorry, zero axiom) and imports the global constants and cost layers.
The golden ratio $\varphi$ enters from the Constants import; in the broader Recognition framework it is the unique self-similar fixed point forced at step T6 of the unified forcing chain. The cost functional $J$ (imported from Cost) is the unique generator satisfying the Recognition Composition Law, with $J(x)=(x+x^{-1})/2-1$.
Sibling declarations in the same file introduce a domain cost, prove it nonnegative, and assert positivity of this threshold, so the constant is the numerical hinge for those comparisons.
proof idea
Bare definition: the symbol is bound to the real expression $\varphi-3/2$. No tactics, no lemmas, no reduction.
why it matters
Module 5 needs a fixed dimensionless cut against which domain costs are judged when matching the H-bond energy scale $J(\varphi)^{-1} kT N_A\approx 20.8$ kJ/mol. Placing that cut at $\varphi-3/2$ keeps the threshold inside the same $\varphi$-native arithmetic used for the mass ladder, the eight-tick octave, and the fine-structure band.
No downstream consumers are recorded yet; the immediate siblings (positivity of the threshold, the domain-cost nonnegativity lemma, and the module certificate) are the natural parents. The definition therefore closes a small structural gap rather than a paper proposition, but it keeps the chemistry layer aligned with T5–T6 uniqueness of $J$ and $\varphi$.
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