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def definition def or abbrev high

pionNeutralMass_MeV

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Neutral pion mass is fixed at 134.9768 MeV from PDG 2024. Hadron mass modelers and Recognition Science ladder calculations cite this anchor when computing electromagnetic splittings against the charged pion. The entry is a direct numerical definition with no computation or lemmas.

claimThe neutral pion mass is $134.9768$ MeV.

background

Pion masses arise in Recognition Science from quark-antiquark binding on the phi-ladder and explicit chiral symmetry breaking. The module sets the neutral pion (ūu-dd̄ state) at rung 12 relative to coherence energy, with the GMOR relation linking mass squared to quark masses and condensate. This definition supplies the PDG 2024 numerical value used for all subsequent difference and ratio calculations in the module.

proof idea

Direct definition that assigns the constant 134.9768 with no lemmas or tactics.

why it matters in Recognition Science

Supplies the neutral reference for downstream theorems establishing that the charged pion is heavier, the electromagnetic mass difference is 4.6 MeV, and the relative difference is 3.4 percent. It anchors the phi-ladder prediction m_π/m_e ≈ 273 and the rung-12 placement inside the eight-tick octave. The entry closes the experimental input for P-013 derivations.

scope and limits

formal statement (Lean)

  51def pionNeutralMass_MeV : ℝ := 134.9768

proof body

Definition body.

  52
  53/-- Charged pion mass in eV. -/

used by (6)

From the project-wide theorem graph. These declarations reference this one in their body.