canonicalThreshold
plain-language theorem explainer
The canonical bandwidth threshold is the real constant φ − 3/2, with φ the golden ratio. Recognition Science information theorists cite it as the structural cutoff for the φ-resonant Shannon band. It is introduced by direct definition from the RS constant φ, with no proof obligations.
Claim. Define the canonical threshold by $T_{\mathrm{can}} := \varphi - \tfrac{3}{2}$, where $\varphi$ is the golden ratio fixed by the Recognition Science cost functional.
background
The module treats Shannon channel capacity $C = B\log_2(1+\mathrm{SNR})$ under Recognition Science structure. At φ-resonance the SNR is identified with $\varphi^D = \varphi^3 \approx 4.24$ (about 6.27 dB), so $C_{\mathrm{RS}} = B\log_2(\varphi^3+1) \approx 2.39,B$ bits/Hz as a structural identity.
The golden ratio $\varphi$ is forced earlier (T6) as the unique self-similar fixed point of the J-cost. The module imports Constants and Cost, placing $\varphi$ and the cost infrastructure in scope. Sibling definitions package a domain cost, its nonnegativity, and positivity of this threshold.
proof idea
Definitional only: the real is set equal to $\varphi - 3/2$. No tactics, lemmas, or proof body.
why it matters
Anchors the numeric cutoff used by the module's bandwidth certificates (positivity of the threshold, the inhabited BandwidthPhiCert). The parent setting is the structural RS Shannon identity $C_{\mathrm{RS}} = B\log_2(\varphi^3+1)$, tied to D = 3 spatial dimensions (T8) which fixes resonant SNR as $\varphi^3$, and to φ from the forcing chain (T6). The offset below 3/2 places the operating point relative to that resonant band without introducing free parameters.
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