m_c_at_MZ_GeV
plain-language theorem explainer
The definition supplies the constant 0.78 GeV as the RS-anchored MS-bar charm quark mass at the Z-boson scale, serving as the fixed input m_0 for two-loop QCD mass running in the scorecard. Heavy-quark phenomenologists comparing Recognition Science rung-15 predictions against PDG data would cite this anchor when evolving from M_Z down to the charm scale. It is introduced by direct numerical assignment drawn from the gap-corrected massAtAnchor evaluation at the canonical yardstick.
Claim. The RS-anchored MS-bar charm quark mass at the $M_Z$ scale is defined to be $0.78$ GeV.
background
The Charm Quark MS-bar Mass Scorecard module states the PDG value m_c(m_c) = 1.27 ± 0.02 GeV and places the RS prediction at sector rung c = 15 for the up-type second generation. It uses the gap-corrected mass formula from Masses.RSBridge.Anchor.massAtAnchor to obtain the structural value at the anchor scale, then applies two-loop alpha_s and mass running between M_Z and m_c. This definition supplies the numerical starting mass at M_Z for that running engine.
proof idea
Direct numerical assignment of the approximate value 0.78 with no lemmas or computation steps.
why it matters
This constant is the input anchor for m_c_predicted and m_c_predicted_pos, which close the two-loop running comparison to PDG data. It bridges the RS structural mass formula at the canonical yardstick to the empirical scorecard, keeping the module free of sorrys and axioms. The placement at rung 15 and the M_Z anchor align with the phi-ladder mass formula used across the Recognition framework.
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