canonicalThreshold
plain-language theorem explainer
Defines the canonical recognition threshold as the real number φ − 3/2. Cosmology and cost-functional arguments in the RS module cite it as the fixed comparison level against domain cost. The body is a one-line constant abbreviation in terms of the golden ratio.
Claim. The canonical threshold is the real constant $\varphi - 3/2$, where $\varphi$ is the golden ratio fixed by self-similarity in Recognition Science.
background
This module is the first RS cosmology structural block. Its headline claim is the dark-energy density match $\Omega_\Lambda = 11/16 - \alpha/\pi \approx 0.685$ (Planck-compatible at $0.665\sigma$), recorded as a zero-sorry structural theorem.
The golden ratio $\varphi$ enters from the forcing chain (T6): it is the unique self-similar fixed point of the cost geometry. The cost layer (imported from Cost and Constants) supplies the J-cost $J(x)=(x+x^{-1})/2-1$ and nonnegativity facts used by sibling lemmas such as domain cost and positivity of this threshold.
Locally, domain cost is compared to a fixed real level; that level is this definition.
proof idea
Pure definition: the real constant is introduced by the closed-form expression $\varphi - 3/2$. No proof obligations, tactics, or lemmas.
why it matters
Gives the module a single named comparison value for recognition/cost thresholds in the cosmology certificate stack (siblings include positivity of the threshold and the RSCosmo001 certificate). In the broader framework it sits downstream of T6 ($\varphi$ forced) and upstream of structural cosmology identities such as the $\Omega_\Lambda$ match highlighted in the module doc. It does not itself prove the Planck match; it only pins the numeric level those arguments may reference.
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