IndisputableMonolith.Physics.Proton_Charge_Radius_RS
RS-native packaging of the proton charge radius via a domain cost, a positive canonical threshold, and an inhabited certificate type. Nuclear and particle theorists comparing Recognition ladder predictions to the proton-radius discrepancy would cite it. The module is mostly definitions and elementary positivity lemmas over the imported cost and constants layers.
claimThe module defines a domain cost $C$, proves $C\ge 0$ and evaluates it at a distinguished point, introduces a canonical threshold $\theta>0$, and packages a proton charge-radius certificate type that is inhabited.
background
Recognition Science works in RS-native units fixed by the golden ratio $\varphi$ and the cost functional $J$ forced by the Recognition Composition Law. The Constants import supplies the fundamental tick $\tau_0=1$; the Cost import supplies the non-negative $J$-cost used throughout the monolith.
This physics module specializes that cost language to a one-dimensional domain cost for the proton charge radius. Sibling definitions introduce domainCost (with an evaluation identity and a non-negativity lemma) and a strictly positive canonicalThreshold. The certificate type ProtonChargeRadCert then asserts that the RS radius relation holds relative to that threshold; cert and cert_inhabited witness that the certificate is realizable.
The local setting is therefore a thin physics façade: no new forcing-chain step, only a named cost-threshold pair and a certificate wrapper that downstream radius comparisons can inhabit.
proof idea
Definition-heavy module rather than a deep proof development. Non-negativity of the domain cost and positivity of the canonical threshold are short lemmas over the imported Cost and Constants layers. The certificate is assembled as a structure (or Prop bundle) and shown inhabited by a concrete witness cert, so the module closes with existence rather than a multi-step derivation.
why it matters in Recognition Science
Gives the monolith a named, certifiable handle on the proton charge radius inside RS units, so later comparison lemmas can quote a single inhabited certificate instead of re-deriving the cost-threshold pair. No downstream edges are recorded yet; the module stands as a physics leaf ready for radius-puzzle or form-factor work. It sits downstream of the cost uniqueness (T5) and $\varphi$-ladder infrastructure only indirectly, through the Cost and Constants imports, and does not itself advance T0–T8.
scope and limits
- Does not derive the numerical proton radius from first principles inside this file.
- Does not compare RS predictions to CODATA or muonic-hydrogen data.
- Does not prove uniqueness of the canonical threshold beyond positivity.
- Does not extend the certificate to neutron or nuclear radii.
- Does not discharge any forcing-chain step T0–T8.