canonicalThreshold
plain-language theorem explainer
Defines the canonical numerical threshold as φ − 3/2 in RS units. Anyone comparing domain costs or BIT-kernel certificates against a fixed cutoff cites this constant. The body is a one-line real definition, not a derived equality.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ is the golden-ratio fixed point of the Recognition self-similarity relation.
background
The module develops a deep BIT-kernel certificate from the J-cost. In Recognition Science, bosonic vacuum fluctuations contribute $J(\varphi)/45$ per recognition tick; cumulative Z-aging is that cost times the tick count. The golden ratio $\varphi$ is the unique self-similar fixed point forced by the T6 step of the unified forcing chain, and $J(x)=(x+x^{-1})/2-1$ is the unique cost functional from T5.
Sibling definitions introduce a domain cost on the reals and prove it is nonnegative. The present constant supplies the fixed comparison level against which those costs are measured when building the BITKernel4 deep certificate.
proof idea
Bare definition: the identifier is bound to the real expression $\varphi - 3/2$. No lemmas, tactics, or rewriting are involved. Positivity and any comparison lemmas live in sibling declarations.
why it matters
Gives the module a single named cutoff for domain-cost comparisons inside the BIT Kernel Family Deep v4 development (Plan v7 final deep session). That development aims at a structural theorem with zero sorry and zero axioms, tying bosonic vacuum fluctuations $J(\varphi)/45$ per tick to cumulative cosmic aging. The threshold sits next to the domain-cost API and the inhabited certificate, so later positivity and certification results can quote one symbol rather than an inline expression. It is local scaffolding for the certificate, not a forcing-chain landmark itself.
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