rqftCert
plain-language theorem explainer
The rqftCert definition supplies a concrete certificate that the Recognition Science lattice realizes exactly five Wightman axioms by matching their count both to five and to D plus two. A physicist deriving QFT axioms from the J-cost lattice would cite this to confirm the structural correspondence between RS features and the Wightman set. The construction is a direct record instantiation that pulls the two required cardinalities from prior counting results.
Claim. Let $W$ denote the finite set of Wightman axioms realized on the recognition lattice. A certificate $C$ exists such that $|W| = 5$ and $|W| = 3 + 2$.
background
The module opens the derivation of relativistic QFT from Recognition Science by listing five lattice-derived features: Lorentz invariance expressed as $J(r) = J(r^{-1})$, CPT symmetry, unitarity via total conservation, causality with vanishing $J$ on the light cone, and locality restricted to adjacent sites. These five features are identified with the five Wightman axioms W0-W4, whose total count equals the configuration dimension $D = 5$. The structure RQFTCert packages the two cardinality statements needed to certify this identification.
proof idea
The definition is a direct record construction that supplies the five_axioms field from the theorem establishing cardinality five and the five_Dp2 field from the theorem establishing equality to three plus two.
why it matters
This definition closes the structural certificate for the five Wightman axioms inside the RS-derived QFT, confirming that the axiom count equals both five and $D+2$. It supports the module claim that the recognition lattice yields the canonical Wightman set without additional hypotheses. No downstream theorems are listed, so the result stands as a self-contained count that anchors the S1 structural opening.
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