canonicalThreshold
plain-language theorem explainer
The canonical threshold is the real constant φ − 3/2. It is the comparison level used inside the RS forcing-chain module that forces spatial dimension D = 3 from the eight-tick period. Anyone citing domain-cost bounds or the structural D = 3 package in this module would name it. The declaration is a one-line arithmetic definition in the forced fixed point φ.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ is the self-similar fixed point of Recognition Science.
background
Foundation RS Module 6 packages the structural claim that spatial dimension $D = 3$ is forced by the eight-tick octave (period $2^3$), with zero free parameters and zero sorry. In the unified forcing chain this is the T7–T8 step: the discrete period $2^3$ selects three spatial dimensions once the self-similar scale $\varphi$ is already fixed at T6.
The constant $\varphi$ is imported from Constants and is the unique positive solution of the self-similarity fixed-point equation forced by J-uniqueness. Domain-cost quantities (siblings domainCost, domainCost_nonneg) live in the Cost layer and compare against numerical cutoffs built from $\varphi$. The present definition simply shifts $\varphi$ by $3/2$ to obtain one such cutoff.
proof idea
Definitional only: the real is set equal to $\varphi - 3/2$ by a single arithmetic expression. No lemmas, tactics, or proof obligations.
why it matters
Supplies the named numerical level against which domain costs are measured in the D = 3 forcing module. The module status line records a structural theorem (0 sorry, 0 axiom) that T7’s eight-tick period forces T8’s three spatial dimensions; this constant is the local scale used in that package. Sibling positivity (canonicalThreshold_pos) and the module certificate (RSForcingChain006Cert) sit immediately downstream in the same file. In the broader RS landscape it is a φ-native cutoff, distinct from the Berry creation threshold $\varphi^{-1}$ but in the same family of forced scales.
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