canonicalThreshold
plain-language theorem explainer
The canonical threshold is the real number φ − 3/2, with φ the golden ratio fixed by self-similarity. Arrow-of-time and ledger-irreversibility arguments in the RS foundation cite it as the comparison scale against domain J-cost. The declaration is a one-line definition, not a proved inequality.
Claim. The canonical threshold is the real constant $\varphi - 3/2$, where $\varphi$ denotes the golden-ratio fixed point of the Recognition self-similarity relation.
background
The module treats the thermodynamic arrow of time in Recognition Science: J-cost is not time-reversal symmetric at the statistical level of ledger postings, the eight-tick cycle supplies a preferred phase direction, and entropy is identified with J-cost integrated over recognition channels.
Here $\varphi$ is the unique self-similar scale forced in the foundation chain (T6). The cost functional $J$ is the unique nonnegative solution of the Recognition Composition Law with $J(1)=0$ and the usual normalization; domain cost is the restriction of that functional to the channels under study. The threshold $\varphi-3/2$ is the fixed numerical cut used to decide when a domain cost is large enough to mark irreversible posting.
proof idea
Pure definition: the identifier is bound to the real expression $\varphi - 3/2$. No lemmas, tactics, or proof obligations.
why it matters
Supplies the numerical scale against which domain J-cost is compared when the module argues that ledger postings are irreversible and that the eight-tick octave orients time. Sibling positivity and certificate declarations (canonical threshold positivity, the RS arrow-of-time certificate) are expected to consume this constant. It sits in the structural, sorry-free layer of the foundation rather than in the forcing chain T0–T8 itself, but it inherits $\varphi$ from that chain and feeds the entropy-as-integrated-J reading of the arrow of time.
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