canonicalThreshold
plain-language theorem explainer
Defines the canonical cost threshold as φ − 3/2 in RS-native units. Cosmology certificates for reionization redshift compare a domain cost against this constant. Pure abbreviation of the golden-ratio offset; no proof content.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ denotes the golden ratio (self-similar fixed point of the Recognition cost).
background
The module treats reionization redshift in Recognition Science. Observationally $z_{\mathrm{reion}}$ lies roughly in 7–10. RS brackets that window by successive powers of $\varphi$: $\varphi^4 \approx 6.85$ and $\varphi^5 \approx 11.09$, so the interval $[\varphi^4,\varphi^5]$ is the structural prediction.
The golden ratio $\varphi$ is forced earlier in the foundation chain (T6) as the unique self-similar fixed point of the J-cost. Constants and Cost supply $\varphi$ and the non-negative cost functional used to score cosmological domains. The threshold $\varphi - 3/2$ is the numerical cut that the reionization certificate later compares against a domain cost.
proof idea
Definitional abbreviation only: the right-hand side is the real expression $\varphi - 3/2$. No tactics, lemmas, or rewriting.
why it matters
Supplies the fixed numeric cut used by the reionization certificate in this module (siblings canonicalThreshold_pos, ReionizationCert, cert). It sits inside the structural claim that $\varphi^4$–$\varphi^5$ brackets observed $z_{\mathrm{reion}}$, consistent with the eight-tick / $\varphi$-ladder architecture (T6–T7). No open scaffold: the module is marked structural with zero sorry.
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