canonicalThreshold
plain-language theorem explainer
Defines the canonical chemistry threshold as φ − 3/2 in RS-native units. Chemists and metrologists citing the Avogadro RS4 certificate use this cut for domain-cost comparisons. The body is a one-line arithmetic abbreviation of the golden ratio.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ is the golden ratio fixed by the self-similarity equation of Recognition Science.
background
The module is the RS Chemistry layer that packages the Avogadro RS4 certificate as a structural theorem (zero sorry, zero axiom). It imports the global Constants (for $\varphi$) and Cost (for the J-cost and domain-cost machinery).
In Recognition Science, $\varphi$ is forced as the unique self-similar fixed point (forcing chain T6). Domain cost is the non-negative cost functional that scores how far a chemical or metrological configuration sits from the recognition fixed point. Thresholds on that cost separate admissible from inadmissible regimes.
The numerical value $\varphi - 3/2 \approx 0.118$ sits well below the Berry creation scale $\varphi^{-1}$ and is used as a fixed cut inside the chemistry certificate.
proof idea
Pure definition: the real constant is introduced by the arithmetic expression $\varphi - 3/2$. No lemmas are applied and no tactics run; positivity and later comparisons are proved in sibling declarations.
why it matters
Supplies the fixed numerical cut that the Avogadro RS4 certificate and its inhabitation proof compare against domain cost. Without a named threshold the chemistry module cannot state a sharp admissibility criterion. The value is expressed directly in the RS-native unit system built from $\varphi$ (T6), keeping the certificate free of external SI constants. It sits alongside domainCost, domainCost_nonneg and canonicalThreshold_pos in the same structural package.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.