canonicalThreshold
plain-language theorem explainer
The canonical threshold is the real scalar φ − 3/2, with φ the golden ratio fixed by the Recognition forcing chain. Structural gravity arguments in this module use it as the reference cutoff for domain-cost comparisons. Anyone citing RS gravity structural certificates will hit this constant. It is a one-line definition, not a proved inequality.
Claim. Let $\varphi$ be the golden ratio. The canonical threshold is the real number $\varphi - 3/2$.
background
This module sits in the gravity structural layer of Recognition Science. The local setting is the forcing chain from J-uniqueness through dimension: T5 fixes the cost $J(x)=(x+x^{-1})/2-1$, T6 forces $\varphi$ as the self-similar fixed point, T7 the eight-tick octave, and T8 spatial dimension $D=3$. Status is structural (no sorry, no axioms).
The constant $\varphi$ is imported from the RS constants layer. Sibling definitions in the same file introduce a nonnegative domain cost and compare it to this threshold; positivity of the threshold itself is a separate lemma. No deeper cost identity is needed to name the scalar.
proof idea
Pure definition: the name is bound to the real expression $\varphi - 3/2$. No tactics, no lemmas, no reduction.
why it matters
Gives the gravity structural module a single named cutoff built from the forced golden ratio rather than an ad hoc real. Downstream siblings (threshold positivity, the structural certificate, and its inhabited instance) treat this value as the comparison point for domain cost. It ties the gravity layer to T6 ($\varphi$ forced) without reopening the J-uniqueness or eight-tick steps. No paper proposition number is attached in the source; the role is infrastructural inside RS_GRV_Structural_009.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.