canonicalThreshold
plain-language theorem explainer
The canonical threshold is the real constant φ − 3/2 built from the golden ratio. It lives in the structural module on RS rung spacing, where adjacent rungs differ by the factor φ. Anyone fixing a positive cutoff against domain costs or ladder gaps would cite it. The declaration is a bare definitional binding, not an inequality or uniqueness claim.
Claim. Define the canonical threshold by $\mathrm{canonicalThreshold} := \varphi - \tfrac{3}{2}$, where $\varphi$ is the golden ratio (self-similar fixed point of the Recognition ladder).
background
Module RS_FDN_Structural_008 packages structural facts about Recognition Science rung spacing: adjacent rungs on the φ-ladder are separated by the multiplicative factor φ ≈ 1.618. The module imports the global Constants (where φ is fixed) and the Cost layer (J-cost and related nonnegativity).
In the forcing chain, T6 forces φ as the unique self-similar fixed point compatible with the Recognition Composition Law and J-uniqueness (T5). Thresholds built from φ therefore inherit that uniqueness rather than being free parameters. The numerical value φ − 3/2 is positive and of order 0.118, sitting well below the unit rung step.
Sibling declarations in the same file treat domain cost evaluations and prove that this threshold is strictly positive; the present binding only names the constant.
proof idea
Definitional one-liner: the real is bound to the closed term φ − 3/2. No tactics, no lemmas, no rewriting. Downstream positivity or comparison proofs unfold this abbreviation and reason about φ from Constants.
why it matters
Gives a single named cutoff for structural comparisons in the rung-spacing module, so later certificates (for example the module's RSFDNStructural008Cert) can refer to one φ-native scale instead of an ad-hoc real. Ties directly to T6 (φ forced) and to the φ-ladder used in the mass formula (yardstick · φ^(rung−8+gap(Z))). It is not itself a forcing step; it is scaffolding notation that keeps structural theorems φ-native and dimension-free in RS units.
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