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IndisputableMonolith.Physics.Proton_Charge_Radius_RS

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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

depends on (2)

Lean names referenced from this declaration's body.

declarations in this module (8)