canonicalThreshold
plain-language theorem explainer
The canonical recognition threshold is the fixed real level φ − 3/2 on the golden-ratio scale. It is the comparison constant used with domain costs in the eight-tick structural module. Anyone bounding nonnegativity or certificate checks against that scale would cite it. The declaration is a one-line arithmetic definition, not a derived identity.
Claim. Define the canonical threshold as the real constant $\varphi - 3/2$, where $\varphi$ denotes the golden ratio (self-similar fixed point of the Recognition forcing chain).
background
Module RS_FDN_Structural_005 packages structural facts for the Recognition eight-tick: one full traversal of the binary recognition lattice has period $2^D = 8$ when $D = 3$. Status is structural (no sorry, no axioms).
The golden ratio $\varphi$ enters from the Constants import as the T6 fixed point of self-similarity. Domain cost (sibling domainCost in the Cost import lineage) is the nonnegatively valued cost functional evaluated on recognition configurations; the threshold supplies a fixed real cut against which those costs are compared.
No upstream lemmas are required: the value is pure arithmetic in $\varphi$.
proof idea
Pure definition. The name is bound to the real expression $\varphi - 3/2$ with no proof obligations, rewrites, or lemma applications.
why it matters
Gives the module a single named cut-level for eight-tick structural certificates (siblings include positivity of the threshold and the inhabited certificate bundle). In the broader framework it sits next to the T7 eight-tick octave and T6 $\varphi$-forcing: a concrete real built from $\varphi$ against which domain costs can be scored. It does not itself close a forcing step; it is infrastructure for the structural certificate in this file.
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