canonicalThreshold
plain-language theorem explainer
Defines the canonical numerical threshold as the golden ratio minus three-halves, a fixed real used in the RS Holevo module. Anyone citing the RS-adjusted Holevo capacity or domain-cost comparisons will pull this constant. The body is a one-line abbreviation, not a derived equality.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ denotes the golden ratio (self-similar fixed point of the Recognition forcing chain).
background
The module develops an RS form of the Holevo bound: classical Holevo $\chi$ is at most the ensemble Shannon entropy $H$, while the RS version inserts a recognition overhead so that effective quantum information transmission is $\varphi^{-1}$ of Shannon capacity (about $0.618,H$).
Here $\varphi$ is the unique positive self-similar fixed point forced at T6 of the Unified Forcing Chain, imported from Constants. The same module defines a nonnegative domain cost built from the RS cost functional $J$, and compares that cost against a fixed real cutoff. This declaration simply names that cutoff.
No upstream lemma is required: the value is pure arithmetic in $\varphi$.
proof idea
Bare definition: the identifier is bound to the real expression $\varphi - 3/2$. There is no tactic block, no lemma application, and no proof obligation.
why it matters
Gives a single named real that sibling lemmas (positivity of the threshold, the RS Holevo bound certificate) can cite without repeating the arithmetic. In the broader framework it sits inside the information-theoretic layer that rescales Shannon capacity by the recognition factor $\varphi^{-1}$, consistent with the forced constants $c=1$, $\hbar=\varphi^{-5}$ and the eight-tick octave structure. It does not itself close a forcing-chain step; it is local scaffolding for the structural Holevo theorem claimed by the module (zero sorry, zero axiom).
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