canonicalThreshold
plain-language theorem explainer
Canonical threshold for the carbon-oxygen stellar module equals φ − 3/2. Recognition Science astrophysics cites it as the structural real cutoff paired with the C/O abundance claim. Bare constant definition: no proof, only the arithmetic expression in terms of the golden ratio.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ denotes the golden-ratio fixed point of Recognition Science.
background
Module RS_Astro_Module_012 treats carbon-oxygen stellar structure as a structural theorem: the predicted C/O abundance is $\varphi^{-1.5}\approx 0.504$, compared with the empirical $\sim 0.55$ (about 10% off). Status is zero sorry and zero axiom.
The golden ratio $\varphi$ is the self-similar fixed point forced at T6 of the unified forcing chain. Constants and the J-cost live in the imported Constants and Cost modules; this definition simply names the real $\varphi-3/2$ for use as a threshold against domain cost in the same file.
proof idea
Pure definition: the real constant is introduced by the arithmetic expression $\varphi-3/2$. No lemmas, tactics, or proof body.
why it matters
Supplies the named real cutoff that the sibling positivity lemma and the module certificate RSAstro012Cert can reference when comparing domain cost to a structural threshold. Sits inside the carbon-oxygen stellar claim of Module 12, which anchors C/O to the $\varphi$-ladder exponent $-1.5$. Links the astrophysics layer to the T6 forcing of $\varphi$ without reopening the forcing chain.
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