canonicalThreshold
plain-language theorem explainer
Defines the canonical real threshold as the golden ratio minus three-halves. Used wherever the uniqueness master theorem needs a fixed positive cutoff tied to φ for domain-cost comparisons. The body is a one-line arithmetic definition from the RS constant φ.
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 states the RS Uniqueness Master Theorem v3: $J$ is the unique function satisfying the four RS axioms, so physical constants, masses, and related parameters are forced from $J$. The cost side of that story lives in the imported Cost and Constants modules.
Here $\varphi$ is the unique positive self-similar scale fixed by the forcing chain (T6). The combination $\varphi - 3/2$ is a pure real built from that constant; numerically it is positive and small ($\varphi\approx 1.618$). Sibling material in the same file treats a domain cost and proves nonnegativity and positivity facts about this threshold, so the definition is the shared numeric anchor for those comparisons.
proof idea
Pure definition: unfold to the real expression $\varphi - 3/2$. No proof obligations, tactics, or lemmas.
why it matters
Gives a single named real cutoff built only from $\varphi$, so later uniqueness and domain-cost statements can cite one symbol rather than inline arithmetic. That fits the master-theorem claim that once $J$ is unique, derived scales (including thresholds used to separate cost regimes) are forced rather than chosen. It sits next to positivity and certificate scaffolding in the same file, feeding the structural uniqueness package rather than a separate physical law. Framework landmarks: T6 ($\varphi$ forced) and the uniqueness-of-$J$ master claim in the module header.
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