IndisputableMonolith.Foundation.WightmanAxiomsStatus
The module certifies the status of Wightman axioms inside the Recognition Science foundation, centering on the vacuum state having J-cost exactly zero. Researchers verifying axiomatic QFT consistency with RS would cite the sibling declarations for vacuum existence, spectral positivity, and Lorentz invariance. The module imports the Cost definitions and organizes the axioms as a status interface without internal proofs.
claimThe vacuum state satisfies $J=0$, corresponding to Wightman axiom W2 on vacuum existence; sibling declarations cover the full axiom set including spectral positivity and Lorentz invariance.
background
Recognition Science uses the J-cost from the Cost module, defined by $J(x)=(x+x^{-1})/2-1$, to quantify deviation from self-similarity. The WightmanAxiomsStatus module sits in the Foundation domain and lists concrete axiom declarations (WightmanAxiom, vacuum_exists, spectral_positivity, lorentz_invariance) together with a status certificate. It draws the vacuum J=0 property directly from the upstream Cost import to align standard QFT axioms with RS-native units.
proof idea
This is a definition module, no proofs. It structures the argument by declaring each Wightman axiom as a named Prop and pairing them with a status certificate that records which axioms hold under the J-cost framework.
why it matters in Recognition Science
The module supplies the Wightman axiom interface that higher-level QFT constructions in Recognition Science depend on. It directly encodes the vacuum existence step (W2) with J=0, linking to the T5 J-uniqueness landmark and ensuring the vacuum aligns with the phi-ladder and eight-tick octave before mass formulas are applied.
scope and limits
- Does not derive Wightman axioms from RS primitives.
- Does not prove spectral positivity or Lorentz invariance.
- Limits to status certification rather than full theorem proofs.
- Does not address interactions with the mass formula or alpha band.