canonicalThreshold_pos
plain-language theorem explainer
The canonical threshold for the structural physics certificate at recognition rung 36 is strictly positive. Anyone using that certificate's cutoffs or domain-cost comparisons needs this fact. The proof is a one-line wrapper: unfold the threshold definition, then close by linear arithmetic from φ > 1.5.
Claim. The canonical threshold $T$ of the structural physics certificate is strictly positive: $0 < T$. Here $T$ is the real constant defined in this module by an explicit expression in the golden ratio $\varphi$.
background
This module is the Recognition Science structural certificate for the Physics domain at recognition rung 36 (Plan v7, 120th pass). Status is structural theorem: zero sorry, zero axiom. It packages RS-native cutoffs and domain costs used by the physics-side certificate.
The golden ratio $\varphi = (1+\sqrt{5})/2$ is the self-similar fixed point forced at T6 in the unified forcing chain. The upstream lemma supplies a tight numerical lower bound: $\varphi > 1.5$, proved from $\sqrt{5} > 2$. The canonical threshold is a real built from $\varphi$ (unfolded in the proof); positivity of that expression is the local claim.
Sibling material in the same file defines domain cost, its nonnegativity, the threshold itself, and the inhabited structural certificate StructPhysicsM36Cert.
proof idea
One-line wrapper. Unfold the definition of the canonical threshold to an explicit real expression in $\varphi$, then apply linarith with the single upstream fact $\varphi > 1.5$ (phi_gt_onePointFive). No case split and no further lemmas.
why it matters
Positivity of the canonical threshold keeps the Physics rung-36 structural certificate's cutoffs on the correct side of zero, so domain-cost comparisons and certificate inhabitation stay meaningful. The module frames this as a structural RS prediction for Physics at recognition rung 36.
No downstream dependents are recorded yet (used_by empty); the immediate consumers are the sibling certificate constructors in the same file. In the broader framework this sits under the φ-forced constants layer (T6) rather than the mass ladder or the α band, and it does not itself invoke RCL, the eight-tick octave, or D = 3.
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