canonicalThreshold_pos
plain-language theorem explainer
The canonical threshold entering RS wave-function collapse is strictly positive. Collapse and measurement-as-ledger-posting arguments cite this to keep the cost barrier above zero. The proof unfolds the threshold and finishes by linear arithmetic from the bound φ > 1.5.
Claim. The canonical collapse threshold is strictly positive: $0 < \tau$, where $\tau$ is the threshold built from the golden ratio $\varphi$ in this module.
background
This module treats wave-function collapse as a recognition event: measurement equals a ledger posting. Collapse is J-cost minimization onto the nearest rung of the φ-ladder; the eight-tick cycle sets the minimal recognition time. No hidden variables are introduced.
The canonical threshold is the positive cost barrier used in that collapse picture (tied to the Berry-scale φ-ladder geometry). The only external fact needed here is the Constants lemma that φ > 1.5, which follows from √5 > 2 and the closed form φ = (1+√5)/2.
proof idea
One-line wrapper. Unfold the definition of the canonical threshold, then apply linarith to the hypothesis φ > 1.5 from phi_gt_onePointFive. No further case splits or cost identities are required.
why it matters
Positivity of the collapse threshold is a structural prerequisite for the RS measurement story in this file: ledger posting only makes sense if the barrier that separates rungs is strictly above zero. The module is marked structural (0 sorry, 0 axiom). Downstream certificate objects in the same file (RSWFCollapseCert, cert, cert_inhabited) sit on this positivity, even though no external used-by edge is recorded yet. In the broader framework it aligns with the Berry creation scale φ^{-1} and with J-cost minimization on the φ-ladder (T5–T7 landmarks: unique J, φ fixed point, eight-tick octave).
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