canonicalThreshold
plain-language theorem explainer
The canonical threshold is the dimensionless real φ − 3/2 built from the RS golden-ratio fixed point. Workers on the structural astrophysics module (Jupiter-period ladder match) cite it as the fixed barrier against which domain costs are compared. The declaration is a one-line definition with no proof content.
Claim. Define the canonical threshold by $T := \varphi - 3/2$, where $\varphi$ is the self-similar fixed point of the Recognition forcing chain.
background
Recognition Science fixes $\varphi$ as the unique self-similar scale (forcing step T6). Constants and the J-cost live in the imported Constants and Cost modules; here only the bare real $\varphi$ is needed.
This file is Astrophysics RS Module 4. Its module brief states a structural claim: the Jupiter sidereal period sits near $\varphi^5$ yr ($11.09$ vs $11.86$, about $6.5%$ relative error), with status STRUCTURAL and zero sorry/axiom.
Sibling declarations introduce a domain cost functional and prove it nonnegative. The threshold supplies the fixed dimensionless level those costs are measured against.
proof idea
Pure definitional abbreviation: the name is bound to the real expression $\varphi - 3/2$. No tactics, no lemmas, no proof obligations.
why it matters
Gives the module a single named RS-native cutoff rather than an ad-hoc numerical barrier. It sits next to the domain-cost lemmas and the module certificate (RSAstro004Cert), so positivity and comparison facts can quote one symbol.
Framework link: $\varphi$ is the T6 fixed point; the same ladder supplies $Z_{\mathrm{cf}} = \varphi^5 \in (11,12)$, the structural anchor for the Jupiter-period match stated in the module doc. The threshold itself is not that period claim; it is scaffolding for cost comparisons inside the structural astrophysics layer.
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