canonicalThreshold
plain-language theorem explainer
Defines the real scalar threshold φ − 3/2 used as the comparison level for domain costs in the RS Higgs–top coupling module. Anyone checking the structural claim that the top Yukawa sits at unity on the φ^6 rung cites this constant. The body is a one-line arithmetic definition from the golden-ratio constant.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ denotes the golden-ratio fixed point of the Recognition self-similarity relation.
background
The module treats the top Yukawa in Recognition Science units. Empirically $y_t = \sqrt{2}, m_t/v \approx 0.994$, which RS identifies with exact unity at the $\varphi^6$ rung, and with $y_t = 1$ already at the Planck/unification scale.
$\varphi$ is the unique self-similar fixed point forced by the T6 step of the unified forcing chain (the positive solution of $x = 1 + 1/x$). The Cost import supplies the J-cost and related nonnegativity infrastructure used by sibling domain-cost lemmas; this declaration simply names the numerical cut $\varphi - 3/2$ against which those costs are compared.
proof idea
Pure definition: the real constant is introduced by the arithmetic expression $\varphi - 3/2$. No tactics, no lemmas, no proof obligations.
why it matters
Gives the fixed comparison level for the Higgs-coupling certificate in this module (siblings domainCost, canonicalThreshold_pos, HiggsCouplingCert, cert). It anchors the structural claim that the top Yukawa equals 1 on the $\varphi^6$ rung and remains 1 at unification, consistent with the RS mass ladder and the T6 forcing of $\varphi$. No open scaffold: the module is marked zero-sorry structural.
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