canonicalThreshold
plain-language theorem explainer
Defines the canonical recognition threshold as φ − 3/2 in RS-native units. Standard-model structural arguments that compare domain costs to a fixed cutoff cite this constant. The body is a one-line real definition from the golden ratio.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ is the golden-ratio fixed point of the Recognition self-similarity relation.
background
Module RS_STD_Structural_003 packages the RS Count Law: with spatial dimension $D=3$ forced upstream, there are $2^D-1=7$ independent channels. Status is structural (no sorry, no axioms).
The constant $\varphi$ is imported from IndisputableMonolith.Constants; in the forcing chain it is the unique self-similar fixed point (T6). The Cost import supplies the J-cost and related domain-cost machinery that later compare values against a fixed real cutoff.
Sibling definitions in the same file introduce a domain cost, prove it is nonnegative, and assert that this threshold is positive, then wrap the package in a certificate type.
proof idea
Pure definition: the real is set equal to $\varphi - 3/2$. No proof obligations, tactics, or lemmas.
why it matters
Gives a single named cutoff for structural Standard Model comparisons in this module. Downstream siblings (positivity of the threshold, domain-cost inequalities, and the RSSTDStructural003 certificate) hang off this value so channel-counting and cost bounds share one RS-native scale.
In the broader framework the scale sits next to other φ-ladder landmarks (Berry threshold $\varphi^{-1}$, $Z_{\mathrm{cf}}=\varphi^5$, dream fraction $\varphi^{-3}$). Here the offset by $3/2$ is the local structural choice tied to the $D=3$ count law, not a re-derivation of T5–T8.
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