WightmanAxiomW
plain-language theorem explainer
The declaration defines an inductive enumeration of five Wightman axioms tied to recognition lattice properties including Lorentz invariance via J symmetry and commutativity at the light cone. Axiomatic QFT researchers cite it when verifying that the RS framework reproduces the standard structural axioms without additional assumptions. The definition proceeds by direct enumeration of five constructors deriving Fintype for immediate cardinality checks.
Claim. Let $W$ be the finite set of five Wightman axioms consisting of Lorentz invariance ($W_0$), the spectral condition ($W_1$), vacuum uniqueness ($W_2$), completeness ($W_3$), and commutativity ($W_4$).
background
The module opens the structural correspondence between the recognition science lattice and relativistic QFT by listing five canonical features: Lorentz invariance expressed as $J(r)=J(r^{-1})$, CPT symmetry from $J$ symmetry, unitarity from total $J$ conservation with defect zero, causality from $J=0$ on the light cone, and locality from couplings restricted to adjacent lattice sites. These map directly onto the five Wightman axioms. The module states that five Wightman axioms (W0-W4) equal configuration dimension $D=5$.
proof idea
Inductive definition with five constructors, one per axiom, automatically deriving DecidableEq, Repr, BEq, and Fintype instances. No lemmas or tactics are invoked; the structure is primitive and supplies the finite type needed for downstream cardinality theorems.
why it matters
This supplies the axiom set used by the RQFTCert structure to certify that the recognition lattice yields exactly five axioms, satisfying both the count of five and the relation five equals $D$ plus two. It fills the opening step in deriving relativistic QFT from RS and directly supports the count theorems wightmanCount and wightman_5_eq_Dp2. The definition closes the structural opening listed in the module documentation.
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