canonicalThreshold
plain-language theorem explainer
The canonical recognition threshold used in the RS gravity structural layer is the real constant φ − 3/2. Gravity domain-cost comparisons and structural certificates cite it as the fixed cutoff once E_coh is calibrated to the electron mass. The declaration is a one-line arithmetic definition in the golden ratio; positivity is proved separately.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ denotes the golden ratio (the unique positive self-similar fixed point of the Recognition forcing chain).
background
Module RS_GRV_Structural_010 sits in the gravity sector of Recognition Science. The module header fixes the calibration once and for all: the coherence energy $E_{\mathrm{coh}}$ is set by the electron mass, after which every structural prediction is parameter-free.
The golden ratio $\varphi$ enters from the Constants import (forced at T6 of the UnifiedForcingChain as the unique positive solution of the self-similarity fixed-point equation). The Cost import supplies the J-cost and domain-cost apparatus against which thresholds are compared.
Sibling declarations in the same file introduce a domain cost, prove it is nonnegative, and assert that this threshold is strictly positive, then package the facts into a structural certificate.
proof idea
Pure definition: the identifier is bound to the real expression $\varphi - 3/2$. No tactics, no lemmas, no reduction. Downstream positivity and certificate lemmas unfold this abbreviation and reason about the resulting real.
why it matters
Gives the gravity layer a single named cutoff once $\varphi$ and the electron-mass calibration are fixed. Sibling positivity (canonicalThreshold_pos) and the module certificate (RSGRVStructural010Cert) depend on having this constant in hand rather than an ad-hoc numeric literal. In the broader RS picture it sits downstream of T6 ($\varphi$ forced) and the cost calculus, and upstream of structural gravity claims that compare domain cost to a fixed recognition threshold. It does not itself derive the numerical value from the Recognition Composition Law; it only names the combination used by the structural theorems.
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