canonicalThreshold
plain-language theorem explainer
The canonical acoustic recognition threshold is the real scalar φ − 3/2, with φ the golden-ratio fixed point of Recognition cost self-similarity. Acoustics certificate authors cite it as the cutoff that separates ledger-postable recognition events from sub-threshold fluctuations under sigma conservation. The declaration is a bare definitional binding with no proof obligations.
Claim. Define the canonical threshold by $T_{\mathrm{can}} := \varphi - \tfrac{3}{2}$, where $\varphi > 1$ is the unique self-similar fixed point forced by the Recognition Composition Law and $J$-cost uniqueness.
background
Recognition Science forces a unique cost $J(x) = (x + x^{-1})/2 - 1$ (equivalently $\cosh(\log x) - 1$) and then forces $\varphi$ as the self-similar fixed point of that cost (forcing-chain steps T5–T6). In RS-native units the same $\varphi$ appears in the fundamental constants and the mass ladder.
Module RS_ACS_Cert_005 is an acoustics domain certificate whose stated reading is that a ledger posting equals a recognition event, subject to a sigma conservation law. The module is marked structural (zero sorry, zero axioms). The present declaration simply names the real number $\varphi - 3/2$ for use as that domain’s canonical cutoff; numerically $\varphi \approx 1.618$, so the threshold is a small positive constant near $0.118$.
proof idea
Definitional abbreviation only. The identifier is bound directly to the real expression $\varphi - 3/2$; there is no tactic block, no lemma application, and no proof obligation.
why it matters
Gives the acoustics certificate a single named scalar tied to the same $\varphi$ that organises the eight-tick octave, $D = 3$, and the RS constants ($c = 1$, $\hbar = \varphi^{-5}$, $G = \varphi^{5}/\pi$). Sibling positivity and certificate inhabitants (threshold positivity, the RS-ACS-005 certificate bundle) are expected to quote this value as their cutoff. The module presents the whole package as already closed structural mathematics rather than an open scaffold.
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