canonicalThreshold
plain-language theorem explainer
Canonical threshold for the physics-domain structural certificate at recognition rung 56 is the real constant φ − 3/2. Structural-physics and certificate authors cite it as the fixed comparison level against the domain cost. The declaration is a bare numeric definition in RS units, not a derived identity.
Claim. Define the canonical threshold as the real number $\varphi - 3/2$, where $\varphi$ is the golden-ratio self-similar fixed point of Recognition Science.
background
Module Structural_Physics_mod56 packages a structural Recognition Science certificate for the Physics domain at recognition rung 56 (Plan v7, 120th pass). Status is a structural theorem block with zero sorry and zero axioms.
The golden ratio $\varphi$ is imported from Constants; in the forcing chain it is the unique self-similar fixed point (T6). Cost infrastructure from the Cost import supplies the non-negative domain cost against which thresholds are compared. Sibling material in the same file defines that domain cost, proves it non-negative, and records positivity of this threshold.
In RS-native units the same $\varphi$ scales masses on the phi-ladder and appears in the native values of $\hbar$ and $G$. Here it only enters as the offset that sets the numeric bar $\varphi - 3/2$.
proof idea
No proof. The declaration is a one-line real definition: assign the closed form $\varphi - 3/2$. Downstream positivity and certificate packing are separate siblings.
why it matters
Gives the fixed numeric bar used by the mod-56 physics structural certificate when comparing domain cost to a canonical level. Without a named threshold the certificate cannot state a sharp pass/fail inequality in RS units.
It sits next to domain-cost lemmas and the inhabited certificate record in the same module, so the structural claim for Physics at rung 56 is fully grounded in named constants rather than ad hoc reals. Framework-wise it is local scaffolding for that certificate, not a step in the T0–T8 forcing chain; $\varphi$ itself is already forced upstream (T6).
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