wightmanCount
plain-language theorem explainer
The theorem establishes that the finite type enumerating the five Wightman axioms has cardinality exactly five. Researchers deriving relativistic quantum field theory structures from the recognition lattice would reference this result to confirm the axiom count matches the standard framework. The proof applies a decision procedure directly to the inductive type definition.
Claim. The cardinality of the finite type enumerating the five Wightman axioms is five: $5 = |W_0, W_1, W_2, W_3, W_4|$.
background
The module on relativistic QFT from RS opens by mapping five canonical features of the recognition lattice to the Wightman axioms. The inductive type enumerates W0 for Lorentz invariance via J(r) = J(r^{-1}), W1 for the spectral condition, W2 for vacuum uniqueness, W3 for completeness, and W4 for commutativity. The module documentation states that these five axioms equal the configuration dimension D = 5, with all proofs structural and free of axioms or sorry statements.
proof idea
The proof is a one-line wrapper that invokes the decide tactic to compute the cardinality from the Fintype instance automatically generated for the five-constructor inductive type.
why it matters
This count is supplied directly to the rqftCert definition that assembles the full certification of relativistic quantum field theory in the Recognition Science framework. It realizes the module claim that five axioms match the lattice-derived features, including Lorentz invariance and causality. The result supports the broader derivation without introducing open questions at this level.
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