quarkCondensate_MeV
plain-language theorem explainer
The definition supplies the quark condensate scale of 250 MeV for the Recognition Science treatment of pion masses. A physicist checking the GMOR relation against measured pion masses would cite this constant when verifying order-of-magnitude consistency. It is introduced by direct numerical assignment and enters the GMOR formula as a fixed input parameter.
Claim. $⟨q̄q⟩^{1/3} = 250$ MeV
background
The Pion Masses module derives charged and neutral pion masses from Recognition Science via quark-antiquark binding on the phi-ladder, chiral symmetry breaking, and the GMOR relation $m_π² ∝ (m_u + m_d) ⟨q̄q⟩. The module imports Constants and PhiForcing to place the pion on a specific rung and to enforce consistency with the J-uniqueness relation and eight-tick octave. This definition fixes the condensate cube root at 250 MeV to enable the numerical GMOR check.
proof idea
The declaration is a one-line constant definition that directly assigns the real number 250 to quarkCondensate_MeV. No lemmas or tactics are applied; the value functions as a fixed parameter for the downstream GMOR prediction.
why it matters
The constant is referenced by gmorPrediction, which evaluates 2 × lightQuarkMass_MeV × (quarkCondensate_MeV)^3 / (pionDecayConstant_MeV)^2, and by the theorem gmor_reasonable that confirms the result lies between 100 and 100000. It supplies the chiral condensate scale required by the GMOR relation in the pion masses derivation, supporting the claim that hadron masses follow from the phi-ladder and T5–T7 steps of the forcing chain.
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