IndisputableMonolith.Foundation.WightmanAxiomsStatus
This module defines the status of Wightman axioms within Recognition Science foundations, centering on the vacuum state satisfying J=0 for W2 vacuum existence. Researchers verifying QFT consistency with the J-cost framework would cite it. The module consists of axiom definitions, counts, and certificates imported from the Cost module.
claimThe vacuum state satisfies $J=0$ (W2: vacuum existence).
background
Recognition Science builds from the J-cost functional equation and the T0-T8 forcing chain, with J(x) = (x + x^{-1})/2 - 1. This module imports Mathlib and IndisputableMonolith.Cost to introduce WightmanAxiom as the type for QFT axioms, along with wightmanAxiomCount, vacuum_exists, spectral_positivity, and lorentz_invariance. The DOC_COMMENT states the vacuum state has J = 0 (W2: vacuum existence).
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module prepares Wightman axioms for integration into the Recognition framework and supports downstream certification via WightmanStatusCert. It directly encodes the W2 vacuum existence axiom using J-cost from the upstream Cost module, linking to T5 J-uniqueness where J=0 identifies the vacuum.
scope and limits
- Does not prove spectral positivity or Lorentz invariance.
- Does not derive the full Wightman axiom set from RS primitives.
- Does not connect axioms to specific mass spectra or constants.