canonicalThreshold

The ambient module treats the eight-tick (period-8) lattice on the binary state space of dimension $D=3$. Because $2^D=8$, a single octave can visit every binary configuration exactly once; the module asserts that no shorter period achieves full coverage. That structural claim sits on the forcing chain landmarks T7 (eight-tick octave) and T8 ($D=3$).

The constant $\varphi$ is imported from the RS constants layer: it is the unique positive solution of the self-similarity fixed-point equation forced at T6, equivalently the closed form $(1+\sqrt{5})/2$. Domain cost (a non-negative functional built from the J-cost) is the sibling quantity against which thresholds are compared when certifying completeness.

Pure definition: the identifier is bound to the real expression $\varphi-3/2$. No lemma applications, no tactics, no proof obligations.

Supplies the concrete numerical bar used by the eight-tick completeness certificate and its positivity sibling. In the Recognition framework the same $\varphi$ that appears here is forced by T6 and reappears in the mass ladder, the Berry threshold $\varphi^{-1}$, and the native constants ($\hbar=\varphi^{-5}$, $G=\varphi^5/\pi$). Anchoring the completeness cutoff to $\varphi-3/2$ keeps the structural theorem inside the same algebraic family as the rest of the forcing chain rather than introducing an ad-hoc real. Downstream certificates in the module can therefore quote a single named constant instead of an inlined expression.