canonicalThreshold

This module records structural facts about the Recognition Science J-cost: $J(x)=(x+x^{-1})/2-1$, which is ratio-symmetric, $J(x)=J(1/x)$. The local setting is pure structure (no sorry, no axioms): nonnegativity and evaluation identities for a domain cost built from $J$, plus a named positive threshold used to separate regimes.

The constant $\varphi$ is the unique positive self-similar fixed point forced in the T6 step of the unified forcing chain. Numerically $\varphi\approx 1.618$, so $\varphi-3/2$ is a small positive scale of order $0.118$. It is imported from the RS constants layer and appears here only as a named real, not as a derived dynamical quantity.

Sibling declarations in the same file prove the threshold is positive and package the J-symmetry facts into a certificate structure; this definition supplies the numeric cut those lemmas refer to.

Pure definition: the real is introduced as the difference $\varphi-3/2$. No proof obligations, no lemmas applied. Downstream positivity is handled by a separate one-line inequality on the same constant.

Gives a single named scale for the RS gravity structural module on J-cost ratio symmetry. Parent certificate constructors in the same file (the RSGRV structural-007 cert and its inhabited instance) thread this value when they assert a positive cut below which domain-cost comparisons remain controlled. In the broader framework it sits under the T5–T6 landmarks: J-uniqueness and the forced golden ratio, not under the eight-tick or $D=3$ steps. It does not itself encode dynamics or a mass ladder rung; it is bookkeeping so later gravity inequalities can cite one symbol instead of an inline $\varphi-3/2$.