canonicalThreshold
plain-language theorem explainer
Defines the canonical collapse threshold as φ − 3/2, which equals the J-cost at the golden ratio. Collapse-rate and GRW-style analyses in this module cite it as the structural scale. The body is a one-line real definition from Constants.phi.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ is the golden ratio (self-similar fixed point of Recognition Science).
background
Recognition Science forces a unique nonnegative cost $J(x)=(x+x^{-1})/2-1$ (T5) and the golden ratio $\varphi$ as the self-similar fixed point (T6). Because $\varphi$ obeys $\varphi=1+\varphi^{-1}$, one has $J(\varphi)=\varphi-3/2$ exactly.
This module studies an objective (GRW-style) wavefunction collapse rate built from that J-cost: $\lambda=J(\varphi)/(m_{\mathrm{nucleon}}\varphi^{20})$. The numerical value $J(\varphi)\approx 0.118$ is the structural numerator; the definition packages it as a named real constant for the rest of the file.
Local status is structural: zero sorry, zero axioms. The module notes that matching the experimental $\lambda\sim 10^{-16},\mathrm{s}^{-1}$ is still off by many orders; the threshold itself is exact algebra.
proof idea
Pure definition: bind the real phi - 3/2 from IndisputableMonolith.Constants. No proof obligations. Downstream positivity (canonicalThreshold_pos) and certificate packing (WFCollapse3Cert) consume the name directly.
why it matters
Gives a single named scale for the collapse-from-J-cost story in Plan v7. It is exactly $J(\varphi)$, so every rate formula that begins with the T5 cost at the T6 fixed point can cite one symbol instead of re-deriving $\varphi-3/2$.
Siblings use it for nonnegativity and for the inhabited collapse certificate. Framework landmarks: T5 J-uniqueness and T6 $\varphi$-forcing; the eight-tick and $D=3$ steps are not needed here. The open quantitative gap (orders-of-magnitude mismatch with GRW $\lambda$) is acknowledged in the module doc and is not closed by this definition.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.