IndisputableMonolith.Foundation.UniversalForcing.Strict.AxiomAudit
AxiomAudit integrates strict realizations from discrete boolean, metaphysical, and positive ratio modules to audit axioms in the universal forcing framework. It confirms consistency of the forced arithmetic across propositional, structural, and continuous domains. Researchers in Recognition Science foundations cite it to verify axiom satisfaction before downstream checks. The module achieves this through direct imports of the three realizations with no new derivations.
claimAxiom audit $A$ for strict universal forcing integrates discrete boolean orbit (periodic carrier from native generator), metaphysical structural package, and positive-ratio realization satisfying the composition law $J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y)$.
background
The module sits inside the strict universal forcing development. DiscreteBoolean supplies the strict Boolean realization whose carrier orbit is periodic yet whose arithmetic is the free iteration object from the native generator. Metaphysical provides the theology-neutral structural package built on the strict theorem. PositiveRatio constructs the continuous positive-ratio realization directly from SatisfiesLawsOfLogic. These three imported modules supply the definitions and lemmas that the audit combines.
proof idea
This is a definition module, no proofs. The structure consists of importing DiscreteBoolean, Metaphysical, and PositiveRatio to form a single audit point whose sibling lemmas then verify domain-specific consistency.
why it matters in Recognition Science
The module supports the universal forcing theorem by auditing its axioms in strict contexts and feeds the sibling verifications (_ordered_ok, _categorical_ok, _music_ok, _biology_ok, _narrative_ok, _ethics_ok). It contributes to confirming J-uniqueness and the phi fixed point within the T0-T8 forcing chain before those results are used in mass formulas or alpha-band calculations.
scope and limits
- Does not derive new forcing theorems or extend the T0-T8 chain.
- Does not treat non-strict or approximate realizations.
- Does not include numerical simulations or data fitting.
- Does not address empirical predictions or physical constants.