canonicalThreshold
plain-language theorem explainer
The canonical GW memory fraction is the real constant φ − 3/2 (≈ 0.118). It is the RS-native permanent-strain offset relative to peak strain, equal to the J-cost of the golden ratio. Gravity and waveform analysts cite it when matching the predicted memory amplitude to the empirical 5–15% band. The declaration is a one-line arithmetic definition.
Claim. The canonical gravitational-wave memory threshold is the real number $\varphi - 3/2$, where $\varphi$ denotes the golden ratio.
background
The module treats gravitational-wave memory as a Recognition-Science cost effect: the permanent metric offset after a burst is a fixed fraction of the peak strain. That fraction is identified with the J-cost of φ.
J is the unique cost functional forced by the Recognition Composition Law, $J(x)=(x+x^{-1})/2-1$. For the golden ratio one has $J(\varphi)=\varphi-3/2$, since $\varphi^{-1}=\varphi-1$. Numerically this is about 11.8%, inside the observed memory range of roughly 5–15% of peak strain.
The surrounding file builds a zero-sorry structural certificate that the memory amplitude equals this canonical fraction times peak strain, using only the Cost and Constants imports.
proof idea
Pure definition: the constant is introduced by the arithmetic expression $\varphi-3/2$. No tactics or lemmas are invoked. Algebraically the same expression is $J(\varphi)$, which is why later positivity and certificate lemmas can treat the threshold as a nonnegative J-value without further computation.
why it matters
This constant is the numerical anchor of the GW-memory-from-J-cost story in the module. Downstream siblings (positivity of the threshold, the GWMemory3Cert bundle, and the inhabited certificate) all read the memory fraction from this definition. It realises the module claim that RS predicts $\delta h=J(\varphi),h_{\mathrm{peak}}$, tying the permanent strain offset to the same J forced at T5 of the unified forcing chain and to the self-similar fixed point φ of T6. Empirically it lands inside the accepted 5–15% memory band, giving a sharp, parameter-free target for waveform extraction.
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