canonicalThreshold
plain-language theorem explainer
Defines the canonical recognition threshold as φ − 3/2 in RS-native units. Cosmology and cost-symmetry arguments cite it as the fixed cutoff against which domain J-cost is compared. The body is a one-line constant definition from the golden-ratio fixed point.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ is the self-similar fixed point of Recognition Science.
background
The module treats structural consequences of J-cost ratio symmetry: $J(x)=J(1/x)$, with $J(x)=(x+x^{-1})/2-1$. Recognition cost is therefore blind to inversion of the scale ratio.
$\varphi$ is imported from Constants as the unique positive fixed point forced by the self-similarity step of the forcing chain (T6). The same module defines a domain cost functional and proves it nonnegative; the present constant supplies the numerical bar those comparisons use.
No further hypotheses are attached: the value is pure RS arithmetic once $\varphi$ is fixed.
proof idea
Not a proof. Single definitional equation: the real constant equals $\varphi$ minus three halves. Downstream positivity is left to the sibling lemma that shows $\varphi>3/2$.
why it matters
Gives the cosmology stack a named, reusable cutoff built only from $\varphi$, so structural certificates (the module's RSCOSStructural007Cert and related inhabitation lemmas) can state inequalities without inlining magic numbers. Ties the local J-symmetry story to the global forcing landmarks: $\varphi$ from T6 and the cost $J$ from T5/RCL. Does not itself close an open physics claim; it is infrastructure for the structural theorem package of this module.
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