canonicalThreshold
plain-language theorem explainer
Defines the canonical numerical threshold as φ − 3/2 in RS-native units. Cited by anyone comparing domain J-cost against a fixed cutoff in Standard Model structural certificates. The body is a one-line real constant built from the forced golden ratio.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ is the golden ratio fixed by self-similarity.
background
Recognition Science forces a unique nonnegative cost $J$ on positive reals satisfying the Recognition Composition Law; the closed form is $J(x)=(x+x^{-1})/2-1$, equivalently $\cosh(\log x)-1$. A basic symmetry is $J(x)=J(1/x)$: cost depends only on the ratio, not its orientation.
The constant $\varphi$ is the unique self-similar fixed point of the forcing chain (T6). This module packages structural facts about that ratio-symmetric cost for Standard Model bookkeeping. The threshold $\varphi-3/2$ is the fixed real cutoff against which domain costs are later compared.
proof idea
Pure definition: the real constant is written as $\varphi-3/2$ with no proof obligations. Downstream lemmas (e.g. positivity) discharge analytic properties of this expression.
why it matters
Supplies the named cutoff used by the module’s structural certificate for J-cost symmetry in the Standard Model layer. Ties the local comparison scale to the forced golden ratio rather than an ad-hoc number, keeping the certificate inside the T5–T6 forcing chain. Sibling positivity and certificate inhabitants consume this constant; it does not itself close any open physics claim.
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