canonicalThreshold
plain-language theorem explainer
Defines the canonical numerical threshold as φ − 3/2 in RS-native units. Cited by anyone comparing domain costs or configuration defects against the D = 3 eight-tick lattice. The body is a one-line real definition; no proof obligations.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ denotes the golden-ratio fixed point of the Recognition self-similarity relation.
background
The module establishes the structural claim that spatial dimension $D = 3$ is forced by eight-tick closure: the recognition cycle has period $8 = 2^3$, so exactly three binary recursions close the lattice, and that lattice is the unique minimal self-similar one.
$\varphi$ is imported from the Constants layer as the unique positive fixed point of the self-similarity map forced at T6 of the unified forcing chain. The cost layer supplies the J-cost $J(x) = (x + x^{-1})/2 - 1$ against which domain defects are measured. The threshold $\varphi - 3/2$ sits just above zero ($\varphi \approx 1.618$) and is the reference scale used by sibling lemmas that compare domain costs to a positive cutoff.
proof idea
Bare definition: the identifier is bound to the real expression $\varphi - 3/2$. No tactics, no lemmas, no reduction steps.
why it matters
Supplies the fixed numerical cutoff against which configuration-dimension and domain-cost statements in this module are judged. The parent structural theorem is the zero-sorry claim that $D = 3$ follows from eight-tick closure (T7 period $2^3$ forcing T8). The value is native to the $\varphi$-ladder and the Recognition Composition Law setting; it is not an external fit parameter. Downstream positivity and certificate lemmas in the same file are expected to consume it as the comparison scale.
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