canonicalThreshold
plain-language theorem explainer
Defines the canonical economic threshold as the real constant φ − 3/2. This equals the J-cost of the golden ratio and is the recognition-optimal firm growth factor (~11.8% when scaled by revenue growth). Cited by anyone working the RS economics layer or Gibrat scaling. The declaration is a one-line real abbreviation.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ denotes the golden ratio.
background
Recognition Science forces the cost functional $J(x)=(x+x^{-1})/2-1$ (T5) and the golden ratio $\varphi$ as the unique self-similar fixed point (T6). A direct evaluation yields $J(\varphi)=\varphi-3/2$.
The Economics module (session 3) treats structural theorems for firm growth under Gibrat's law: growth rate independent of size, with the recognition-optimal trajectory carrying rate $J(\varphi)$ times revenue growth, quoted near 11.8% per year. The module imports Constants (for $\varphi$) and Cost (for $J$).
proof idea
Definition only: the constant is introduced by the real expression $\varphi-3/2$. No lemmas, tactics, or proof obligations.
why it matters
Supplies the numerical anchor for the module's growth-rate claim and for sibling positivity and certificate results (canonicalThreshold_pos, FirmGrowth4Cert). Links the economics layer directly to the T5/T6 forcing chain via the identity with $J(\varphi)$, so downstream firm-growth statements inherit the same unique cost that governs the rest of the RS ladder.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.