canonicalThreshold
plain-language theorem explainer
Defines the real number φ − 3/2 as the module’s canonical threshold. Astrophysicists working the RS magnetar-field ladder (Module 11) cite it as the fixed comparison scale against domain cost. The body is a one-line abbreviation of the golden-ratio constant minus 3/2.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ is the golden ratio.
background
Recognition Science forces $\varphi$ as the unique self-similar fixed point of the cost geometry (forcing step T6). In RS-native units many dimensionless cutoffs are simple polynomials in $\varphi$.
This module treats magnetar surface fields as a structural $\varphi$-ladder statement: $\varphi^{72}$ Gauss is of order $10^{14}$ Gauss. The local cost functional (imported from Cost and Constants) is compared against a single fixed real threshold rather than an ad-hoc numerical cut.
Sibling material in the same file introduces a non-negative domain cost and proves the threshold is positive; the present declaration only names the number.
proof idea
Pure definition: unfold to the arithmetic expression $\varphi - 3/2$. No lemmas, no tactics.
why it matters
Supplies the named real that Module 11’s magnetar structural certificate compares against domain cost. Keeps the $\varphi$-ladder arithmetic explicit and reusable for the claimed $\varphi^{72},\mathrm{G}\sim 10^{14},\mathrm{G}$ scaling. Downstream positivity and certificate inhabitants (siblings) depend on having this constant in scope. It is scaffolding-free definitional infrastructure, not a dynamical derivation of magnetar physics.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.