canonicalThreshold
plain-language theorem explainer
Defines the canonical entanglement-cost threshold as φ − 3/2 in RS-native units. Anyone comparing domain cost against a fixed positive cutoff in the entanglement-cost certificate will cite it. The body is a one-line real constant built from the golden ratio and the three-dimensional half-count 3/2.
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 treats entanglement entropy $S = -\sum p_k \log p_k$ in Recognition Science units. The stated maximum is the Count-Law value $S_{\max} = D \log 2 = 3\log 2 \approx 2.079$ bits, using the forced spatial dimension $D = 3$ (forcing step T8).
The golden ratio $\varphi$ enters from the forcing chain (T6): it is the unique self-similar fixed point tied to the J-cost $J(x) = (x + x^{-1})/2 - 1$. Sibling definitions in the same file introduce a nonnegative domain cost and a positivity lemma for this threshold, so the constant is meant as a fixed comparison level against that cost.
Imports pull $\varphi$ from Constants and the cost infrastructure from Cost; no further hypotheses are required to name the number.
proof idea
Pure definition: the real constant is written as the difference $\varphi - 3/2$. No tactics, no lemmas, no proof obligations.
why it matters
Gives a single named cutoff for entanglement-cost comparisons inside the Foundation layer. The half-integer $3/2$ tracks the forced dimension $D = 3$, while $\varphi$ is the same constant that appears in the mass ladder, the Berry threshold $\varphi^{-1}$, and the RS unit system ($\hbar = \varphi^{-5}$, $G = \varphi^5/\pi$). Downstream siblings (canonicalThreshold_pos, EntanglementCostCert, cert) are expected to use it as the positive reference level that domain cost must clear. The module claims structural status (zero sorry, zero axiom), so this constant is part of that closed certificate surface rather than an open scaffold.
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