canonicalThreshold
plain-language theorem explainer
The canonical materials threshold is the real number φ − 3/2, with φ the golden-ratio fixed point of Recognition self-similarity. Materials authors cite it as the structural cutoff for domain-cost comparisons in the Hall-resistance module. It is a one-line arithmetic definition, not a derived inequality.
Claim. Define the canonical threshold by $\varphi - 3/2$, where $\varphi$ is the unique positive self-similar fixed point forced by the Recognition cost.
background
Materials RS Module 8 is a structural layer for Hall resistance $R_H = h/e^2$ obtained from the RS fine-structure derivation. Status is structural theorem: zero sorry, zero axiom. The module imports Constants (for $\varphi$) and Cost (for the J-cost and related defect measures).
In the forcing chain, T6 fixes $\varphi$ as the self-similar fixed point of the cost. The present constant is the plain real $\varphi - 3/2 \approx 0.118$, a materials-scale gate distinct from the Berry creation threshold $\varphi^{-1}$ and from $Z_{\mathrm{cf}} = \varphi^5$. Sibling lemmas compare domain cost against this gate and package the comparison into a certificate.
proof idea
Definitional only. The body is the arithmetic expression $\varphi - 3/2$ with $\varphi$ drawn from Constants; there is no tactic proof and no lemma application.
why it matters
Gives the φ-native numerical gate used by the module’s positivity and certificate siblings (threshold positivity, RSMatl008Cert). Keeps materials cutoffs inside the same constant hierarchy as the forcing chain (T6) rather than introducing an external scale. Supports the structural claim that Hall-resistance bookkeeping can be stated entirely in RS units, consistent with the module’s zero-sorry status. Does not itself derive $R_H$ or $\alpha$; it only supplies the comparison constant those structural statements need.
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