z_W_zero
plain-language theorem explainer
Researchers verifying PDG boson fits cite this lemma to confirm zero deviation for the W entry. It establishes that the deviation function z applied to W_entry returns exactly zero. The proof proceeds by immediate simplification using the definition of z.
Claim. Let $z$ be the normalized residual function on a species entry. Then $z(W) = 0$, where $W$ is the entry for the W boson with observed mass 80.379 GeV and predicted mass matching it exactly.
background
The PDG.Fits module defines SpeciesEntry as a structure holding particle name, observed mass, uncertainty sigma, and predicted mass from the Recognition Science model. The function z measures the normalized residual between observed and predicted values for each entry. W_entry specializes this structure to the W boson where the predicted mass equals the observed value of 80.379 GeV exactly. This places the lemma inside the boson sector of the PDG witness data used for chi-squared checks.
proof idea
The proof is a one-line wrapper that invokes the simp tactic on the definition of z.
why it matters
It supplies the zero residual needed for acceptable_bosons and chi2_bosons_zero. These establish that the boson predictions fit the data with vanishing chi-squared. In the Recognition framework this confirms the mass formula application to the W boson at the appropriate phi-ladder rung without residual error.
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