canonicalThreshold
plain-language theorem explainer
Defines the canonical numerical threshold as φ − 3/2 in the recognition-Heisenberg module. Anyone citing the deep J-cost form of Δ_J Δ_σ ≥ ħ_R/2 will use this constant as the comparison level against domain cost. The body is a one-line real abbreviation; no proof content.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ is the golden ratio (self-similar fixed point of the Recognition forcing chain).
background
The module derives a recognition form of the Heisenberg uncertainty principle from the J-cost: $\Delta_J \cdot \Delta_\sigma \ge \hbar_R/2$ with $\hbar_R = J(\varphi),\hbar$, as a structural theorem (zero sorry, zero axiom). Here $J$ is the unique cost $J(x)=(x+x^{-1})/2-1$ forced by the Recognition Composition Law, and $\varphi$ is the self-similar scale fixed at T6 of the forcing chain.
Domain cost measures how far a configuration sits from the recognition minimum. The canonical threshold supplies a fixed real level, built only from $\varphi$, against which that cost is compared when certifying the deep uncertainty bound. Constants live in RS-native units ($c=1$, $\hbar=\varphi^{-5}$).
proof idea
Pure definition: the real constant is introduced by the arithmetic expression $\varphi - 3/2$. No tactics, no lemmas, no reduction.
why it matters
Gives the module a single named scale for the deep HUP certificate path (siblings such as positivity of the threshold and the HUP3DeepCert package). It sits inside the Foundation layer that turns J-uniqueness (T5) and $\varphi$ (T6) into a recognition-Heisenberg inequality consistent with the classical $\Delta x,\Delta p\ge\hbar/2$ shape. No open scaffold: the surrounding module is already marked structural with zero sorry.
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