canonicalThreshold
plain-language theorem explainer
Defines the canonical recognition threshold as φ − 3/2 in RS-native units. Cosmology and structural certificates cite it as the fixed cutoff against which domain costs are compared. The body is a one-line definitional equality using the golden-ratio constant from Constants.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ is the golden ratio (the unique self-similar fixed point forced by the Recognition Science chain).
background
The module sits in the cosmology structural layer of Recognition Science. Its header records the forcing chain T5 (J-uniqueness) through T6 (φ forced as the self-similar fixed point), T7 (eight-tick octave), and T8 (D = 3). Status is structural: zero sorry, zero axioms.
φ enters from IndisputableMonolith.Constants as the unique positive solution of the self-similarity relation forced at T6. The cost layer (IndisputableMonolith.Cost) supplies the J-cost and related nonnegativity facts used by sibling lemmas that compare a domain cost to this threshold.
Sibling definitions in the same file introduce a domain cost functional and prove it is nonnegative; positivity of the threshold itself is recorded separately so certificates can discharge strict inequalities without unfolding φ.
proof idea
Pure definition: the real constant is introduced by the equality φ - 3/2. No tactics, no lemmas. Downstream positivity or comparison proofs unfold or rewrite with this abbreviation and then use arithmetic facts about φ.
why it matters
Gives a single named cutoff for structural cosmology certificates in this module (e.g. the inhabited certificate bundle and positivity lemmas that sit beside it). In the RS chain it inherits meaning from T6: once φ is forced, every derived numerical gate is a fixed combination of φ, here the simple shift by 3/2. It does not itself prove a physical bound; it standardizes the comparison value so later cost-versus-threshold statements stay uniform across the cosmology structural series.
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