canonicalThreshold
plain-language theorem explainer
Defines the canonical real threshold as the golden ratio minus three-halves. Astrophysicists working the RS solar-radius ladder (Module 8) cite it as the fixed cutoff against which domain costs are compared. The body is a one-line real assignment, not a derived equality.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ is the golden-ratio fixed point of the Recognition self-similarity relation.
background
Module 8 of the RS astrophysics stack targets the solar radius: the claim is that $\varphi^{43}$ meters equals $7.0\times 10^8,\mathrm{m}$, within $0.6%$ of the observed $R_\odot\approx 6.96\times 10^8,\mathrm{m}$. The module is marked structural (zero sorry, zero axiom).
The constant $\varphi$ is imported from Constants and is the unique self-similar fixed point forced at T6 of the unified forcing chain. The Cost import supplies the J-cost and related nonnegativity infrastructure used by sibling lemmas that evaluate domain costs at this threshold.
In RS units the same $\varphi$ also sets the mass ladder yardstick and the eight-tick octave; here it is reused only as a pure real scale for an astrophysical cutoff.
proof idea
Pure definition: the real is bound to the closed-form expression $\varphi - 3/2$. No tactics, no lemmas, no reduction. Downstream positivity and certificate lemmas simply unfold this binder.
why it matters
Gives Module 8 a single named cutoff so that domain-cost comparisons and the RSAstro008Cert certificate stay uniform. The module-level MATCH claim (solar radius on the $\varphi$-ladder) sits downstream of this constant together with the nonnegativity and certificate siblings. It does not itself invoke T5 J-uniqueness or the RCL; it only reuses the forced $\varphi$ from T6 as a numerical scale. No open scaffold is attached: the declaration is a finished definition.
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