canonicalThreshold
plain-language theorem explainer
Defines the real threshold value φ − 3/2 used when reading string compactification radii off the φ-ladder. Anyone checking Planck-scale or electroweak-scale compactification certificates in this module cites it as the fixed comparison level. It is a one-line constant abbreviation, not a proved inequality.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ is the golden ratio fixed by the Recognition self-similarity equation.
background
The module treats extra-dimension compactification radii as $R_{\mathrm{comp}} = \ell_{\mathrm{Pl}} \times \varphi^{-k}$ on the φ-ladder. Near the Planck scale one takes $k = 0$; the electroweak scale sits near $k \approx \log(M_{\mathrm{Pl}}/M_{\mathrm{EW}})/\log\varphi \approx 106$ rungs.
In Recognition Science, $\varphi$ is forced as the unique self-similar fixed point (forcing step T6). Cost and domain-cost functionals imported from the Cost and Constants modules supply the non-negative comparison quantities against which radii or rung defects are judged. The constant $\varphi - 3/2$ is the fixed numerical level used for those comparisons inside this file.
proof idea
Pure definitional abbreviation: the real constant is set equal to $\varphi - 3/2$ with no proof obligations. Downstream positivity or certificate lemmas simply unfold this name.
why it matters
Gives a single named level for string-length and compactification certificates built later in the same module (positivity of the threshold, inhabited certificates). It sits inside the φ-ladder mass and length bookkeeping of Recognition Science, where lengths scale as powers of $\varphi$ relative to the Planck yardstick. No forcing-chain step (T0–T8) is discharged here; the definition only supplies the numerical cut used by those structural certificates.
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