canonicalThreshold
plain-language theorem explainer
The canonical threshold is the real number φ − 3/2, with φ the golden ratio. It is the fixed cutoff used inside the eight-tick structural mathematics module. Anyone comparing domain costs on the binary recognition lattice would cite it. The body is a one-line arithmetic definition in the RS constant φ.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ is the golden ratio.
background
Recognition Science forces the golden ratio $\varphi$ as the unique self-similar fixed point of the cost functional (forcing-chain step T6). The ambient module treats the eight-tick octave: one complete traversal of the binary recognition lattice, with period $2^D = 8$ when spatial dimension $D = 3$ (T7–T8).
Domain costs in this file are built from the standard J-cost $J(x) = (x + x^{-1})/2 - 1$. The threshold $\varphi - 3/2$ is the fixed real against which those costs are compared. Numerically $\varphi \approx 1.618$, so the threshold is a small positive constant near $0.118$.
proof idea
Definitional abbreviation only. The real is set equal to $\varphi$ minus three halves; there is no proof body and no lemma application.
why it matters
Supplies the named cutoff for the eight-tick structural package (module status: 0 sorry, 0 axiom). Sibling lemmas establish positivity of the same constant and non-negativity of domain costs, so the threshold is the comparison point those facts rely on. It sits downstream of T6 (φ forced) and inside the T7 eight-tick lattice story; it does not itself close a forcing-chain step.
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