canonicalThreshold
plain-language theorem explainer
The canonical threshold is the fixed real scale φ − 3/2 in RS-native units. Cosmology certificates in this structural module compare domain costs against that cutoff. Anyone citing the parameter-free RS cosmology calibration uses it as the reference level. The declaration is a one-line arithmetic definition in the golden ratio.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ denotes the golden ratio (the self-similar fixed point of the Recognition forcing chain).
background
Module RS_COS_Structural_010 is a structural cosmology certificate: $E_{\mathrm{coh}}$ is fixed once from the electron mass, after which predictions carry no free parameters. The module imports the RS constants (including $\varphi$) and the cost layer.
In Recognition Science, $\varphi$ is forced as the unique self-similar fixed point (forcing step T6). Costs are measured by the J-functional $J(x)=(x+x^{-1})/2-1$ and related domain costs. A fixed numerical threshold built from $\varphi$ supplies a parameter-free comparison level for those costs.
Sibling facts in the same file establish nonnegativity of the domain cost and positivity of this threshold; the present declaration only names the scale itself.
proof idea
Pure definition: the real constant is introduced as the arithmetic expression $\varphi - 3/2$. No proof obligations, lemmas, or tactics.
why it matters
Structural cosmology in RS needs a single, dimensionless cutoff once $E_{\mathrm{coh}}$ is pinned by the electron mass. Defining that cutoff as $\varphi-3/2$ keeps every later comparison inside the phi-ladder and the forcing chain (T6), with no external fit parameters.
Sibling positivity (canonicalThreshold_pos) and the module certificate (RSCOSStructural010Cert) sit on top of this value. The threshold is the numerical hinge between the cost layer and the cosmology claims of the module; without it the structural theorem would have nothing fixed to compare against.
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