canonicalThreshold
plain-language theorem explainer
Defines the canonical materials threshold as the golden ratio minus three halves: φ − 3/2. Materials and continuum-mechanics arguments in the RS stack cite this constant when comparing domain costs to a fixed positive cutoff. The declaration is a bare real definition, not a derived equality.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ is the golden ratio (self-similar fixed point of the Recognition forcing chain).
background
Recognition Science forces $\varphi$ as the unique self-similar scale factor (T6 in the unified forcing chain). Constants live in RS-native units with $c=1$ and related powers of $\varphi$; material predictions are read off the $\varphi$-ladder.
This module (Materials RS Module 1) records a structural match for steel Young's modulus: $\varphi^{25}$ MPa $\approx 196$ GPa, near the experimental $\sim 200$ GPa band. Sibling definitions introduce a nonnegative domain cost on the reals; the present constant is the fixed cutoff those costs are compared against.
No upstream lemmas are required: the value is written directly in terms of the imported $\varphi$ from Constants.
proof idea
Bare definition: the name is bound to the real expression $\varphi - 3/2$. There is no proof body, tactic script, or lemma application.
why it matters
Supplies the numerical cutoff used by the materials certificate layer in this module (siblings such as positivity of the threshold and the inhabited certificate). It sits under the structural theorem claim of Module 1: zero sorry, zero axiom, and a concrete $\varphi$-power match for steel stiffness.
In the broader framework it is a local materials constant, not a forcing-chain step (T0–T8) or an instance of the Recognition Composition Law. Downstream use is internal to the materials certificate; no external parent theorem is wired in the graph yet.
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