RSAstro011Cert
plain-language theorem explainer
Certificate bundle for astrophysics module 11 (magnetar field scale): diagonal vanishing of the domain cost, nonnegativity for positive arguments, and positivity of the canonical threshold. Downstream code builds a concrete inhabitant and proves the type is nonempty. Pure structure definition with no proof body.
Claim. A certificate for RS astrophysics module 11 is a triple of properties: (i) the domain cost vanishes on the diagonal, $\mathrm{cost}(r,r)=0$ whenever $r\neq 0$; (ii) $\mathrm{cost}(m,e)\ge 0$ for all $m>0$ and $e>0$; (iii) the canonical threshold $T$ satisfies $T>0$.
background
Module 11 is the structural magnetar-field entry in the RS astrophysics stack: the claimed field scale is $\phi^{72}$ Gauss, of order $10^{14}$ Gauss. Status is structural (zero sorry, zero axiom).
The certificate packages three local predicates on a domain cost and a threshold. The domain cost is the module-level cost pairing (mass/energy style arguments); its diagonal vanishing and nonnegativity mirror the global recognition cost $J$, which is nonnegative on recognition events (ObserverForcing: "The cost of any recognition event is non-negative," via $J$-cost nonnegativity). The canonical threshold is the positive cutoff used by the module's structural comparison.
Imports are Mathlib, Constants, and Cost, so the arithmetic lives in real analysis with the RS cost primitives.
proof idea
No proof body: this is a structure declaration. The three fields are Prop-valued requirements (diagonal identity of domain cost, nonnegativity on the positive quadrant, positivity of the canonical threshold). Inhabitation is deferred to the sibling cert, which fills the fields with domainCost_at_eq, domainCost_nonneg, and canonicalThreshold_pos.
why it matters
Gives a single named type for the module-11 structural obligations so downstream code can treat "module 11 is certified" as one object. Used by the concrete inhabitant cert and by cert_inhabited : Nonempty RSAstro011Cert. That pattern keeps the magnetar-scale claim ($\phi^{72}$ Gauss $\sim 10^{14}$ Gauss) behind an explicit, checkable interface rather than scattered lemmas. It sits in the astrophysics layer that applies forced RS constants ($\phi$, cost nonnegativity from the forcing/observer side) to extreme-field scales; it does not itself derive the exponent 72.
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