canonicalThreshold
plain-language theorem explainer
Defines the real constant φ − 3/2 as the canonical threshold used in the RS Shannon-entropy-maximum development. Information theorists working the phi-rung alphabet efficiency claims cite it as the numerical cut separating the domain-cost regime from the entropy-max regime. The body is a one-line abbreviation of the golden-ratio constant minus three halves.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ is the golden ratio fixed by the Recognition self-similarity equation.
background
The module treats maximum Shannon entropy for an $n$-symbol alphabet: $H_{\max}=\log_2 n$ bits. In Recognition Science one specializes to alphabets whose cardinality sits on a power of the golden ratio, $n=\varphi^k$. Then $H_{\max}=k\log_2\varphi\approx k\cdot 0.694$ bits, and recognition systems that use a $\varphi$-rung alphabet are claimed to maximize information efficiency.
The constant $\varphi$ itself is forced earlier in the foundation chain (T6) as the unique self-similar fixed point of the cost functional. The present definition simply subtracts the rational $3/2$ from that constant, producing a small positive real that later lemmas treat as a numerical threshold for domain-cost comparisons.
proof idea
Pure definitional abbreviation: the right-hand side is the imported golden-ratio constant minus the rational literal $3/2$. No lemmas or tactics are invoked.
why it matters
Supplies the concrete numerical cut that the surrounding Shannon-entropy-max certificate and domain-cost lemmas compare against. Inside the broader RS program it sits downstream of the forcing of $\varphi$ (T6) and upstream of any claim that a recognition system operating at a $\varphi$-rung alphabet is information-theoretically optimal. The module is marked structural (zero sorry, zero axiom), so this constant is part of the closed, non-scaffolded layer of the information theory development.
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