canonicalThreshold
plain-language theorem explainer
Defines the real constant φ − 3/2 as the canonical threshold in the recognition-field vacuum module. Vacuum-energy and domain-cost arguments cite it when comparing J-costs against a fixed golden-ratio offset. The body is a bare abbreviation of that arithmetic expression; no proof content.
Claim. The canonical threshold is the real constant $\varphi - 3/2$, where $\varphi$ denotes the golden ratio (self-similar fixed point of the Recognition forcing chain).
background
This module treats vacuum energy density in Recognition Science units as $\rho_{\mathrm{vac}} = J(\varphi)/\varphi^5$, with the RS vacuum identified as the ground state of the recognition field in which every J-cost vanishes. The cost functional is the unique $J$ forced by the Recognition Composition Law, $J(x)=(x+x^{-1})/2-1$.
The golden ratio $\varphi$ enters as the T6 self-similar fixed point of the forcing chain. Domain costs built from $J$ are compared against fixed real cutoffs; the present constant is one such cutoff, offsetting $\varphi$ by $3/2$.
Sibling material in the same file establishes nonnegativity of domain cost and positivity of this threshold, then packages them into a vacuum certificate.
proof idea
Bare definition: the name is bound to the real expression $\varphi - 3/2$ drawn from the Constants import. No tactics, no lemmas, no reduction.
why it matters
Supplies the numeric cutoff used when the recognition-field vacuum story compares domain J-costs to a fixed scale. The module frames a structural theorem (zero sorry, zero axiom) that the RS vacuum is the all-$J=0$ ground state and that $\rho_{\mathrm{vac}}=J(\varphi)/\varphi^5$. The threshold sits beside positivity and certificate siblings that close that structural claim. It touches the T6 $\varphi$ landmark and the J-uniqueness (T5) cost that underlies vacuum energy, without itself deriving $\varphi$ or $J$.
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