canonicalThreshold
plain-language theorem explainer
Defines the canonical recognition threshold on the D=3 configuration space as φ − 3/2. Anyone working the J-cost Riemannian metric on the positive orthant or the ConfigSpaceD3 certificate cites this constant. The body is a one-line real definition in terms of 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
The module treats the D=3 configuration space $C_3 = \mathbb{R}^3$ equipped with the recognition metric. That metric is the J-cost Riemannian structure $ds^2 = J(dx/x)$ on the positive orthant; J is the unique cost $J(x) = (x + x^{-1})/2 - 1$ forced by the Recognition Composition Law, and the metric is positive definite for all $x > 0$.
Constants live in RS-native units with $\varphi$ the self-similar fixed point (forcing step T6). The present definition simply names the real $\varphi - 3/2$ that later positivity and certificate lemmas treat as the working threshold on this space.
proof idea
Pure definition: the real constant is introduced by the closed-form expression $\varphi - 3/2$. No proof obligations, tactics, or upstream lemmas are involved.
why it matters
Supplies the numeric threshold used by the D=3 configuration-space certificate stack (siblings such as canonicalThreshold_pos and ConfigSpaceD3Cert). In the broader forcing chain it sits under T8 (D = 3 spatial dimensions) and T6 (φ forced), giving a concrete cut-off once the J-metric is in place on the positive orthant. Without a named threshold the structural certificate for the recognition metric cannot state its comparison bounds.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.