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IndisputableMonolith.Foundation.UniversalForcing.AxiomAudit

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The AxiomAudit module consolidates five realization imports to verify that universal forcing axioms produce equivalent arithmetic across carriers. Foundation researchers cite it when confirming axiom invariance in the Recognition Science derivation chain. It organizes the categorical, order, modular, metaphysical, and two-case invariance modules without adding proofs or new content.

claimThe forcing axioms are realized with equivalent forced arithmetic in the categorical (Lawvere-style) carrier, the order realization on $ℤ$, the modular realization on $ℤ/nℤ$, and the two-case continuous/discrete invariance, with the source of distinguishability represented by the universal generator class.

background

In the Universal Forcing construction, multiple carriers must yield the same forced arithmetic to support the Recognition Science derivation from T0-T8. The imported modules supply the carriers: CategoricalRealization re-exports the canonical categorical/Lawvere-style realization; Invariance.TwoCases gives the first non-trivial invariance kernel where continuous positive-ratio realizations and the discrete Boolean realization have canonically equivalent forced arithmetic; MetaphysicalRealization supplies the structural, theology-neutral formalization that if all realizations have equivalent forced arithmetic then the source of distinguishability is the universal generator class; ModularRealization uses the $ℤMod n$ carrier with equality cost; OrderRealization uses the $ℤ$ carrier with equality cost and unit step.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

This module feeds the invariance and metaphysical results in the Universal Forcing paper by auditing the axiom base across realizations. It directly supports the claim that equivalent forced arithmetic across carriers isolates the universal generator class as the mathematical source of distinguishability, as stated in the MetaphysicalRealization doc-comment.

scope and limits

depends on (5)

Lean names referenced from this declaration's body.