rg_conditions_for_duality
plain-language theorem explainer
The theorem asserts that the RG conditions for duality hold under their defining hypothesis. Researchers formalizing DraftV1 would cite it as the anchor for deriving central potentials from recognition geometry. The proof is a one-line term reduction to trivial because the hypothesis is defined as the constant true proposition.
Claim. Assuming the RG conditions for duality hold (the placeholder proposition for the topology of quotients and local contractibility), the statement is true.
background
The DraftV1 module mirrors theorem statements from the paper Draft_v1.tex and supplies explicit hypothesis interfaces for parts that rely on heavy external mathematics such as the topology of quotients. The local setting uses hypothesis interfaces to keep the certified surface honest when full formalization of Alexander duality or Binet-Bertrand machinery is not yet available. Upstream structures supply the surrounding context: nuclear densities and photon fluxes on the phi-ladder, J-cost calibration on the positive reals, convex minimization of J-cost, and the emergence of SU(3) x SU(2) x U(1) gauge content with three generations from the Q3 quotient.
proof idea
The proof is a term-mode one-line wrapper that applies trivial. It succeeds immediately because the hypothesis RGConditionsForDualityHypothesis reduces to the proposition True by definition.
why it matters
This declaration supplies the formal placeholder for the RG conditions for duality in the DraftV1 paper surface, which is intended to support the derivation of central potentials. It sits inside the Recognition Science framework that derives D=3 and the eight-tick octave from the forcing chain, yet it remains open for the actual topology of quotients and local contractibility. No downstream theorems depend on it yet.
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