IndisputableMonolith.Foundation.UniversalForcing.Invariance.TwoCases
The module shows continuous positive-ratio arithmetic is canonically equivalent to discrete Boolean arithmetic. Recognition Science researchers cite it to unify realizations under universal forcing. The module imports the continuous and discrete realization modules to frame the two-case invariance.
claimContinuous positive-ratio arithmetic is canonically equivalent to discrete Boolean arithmetic: continuous realization ≃ discrete realization.
background
This module sits in the invariance section of the Universal Forcing framework. It imports ContinuousRealization, the re-export of the continuous positive-ratio realization as a wrapper around LogicRealization.ofPositiveRatioComparison. It also imports DiscreteRealization, the re-export of the Boolean/propositional realization. The setting is that every Law-of-Logic realization carries canonically equivalent forced arithmetic.
proof idea
This is a definition module, no proofs. The module imports the continuous and discrete realizations to support the equivalence claim.
why it matters in Recognition Science
This module feeds the AxiomAudit for reproducible theorem surfaces and the general Universal forcing theorem, which states every Law-of-Logic realization carries canonically equivalent forced arithmetic. It fills the invariance step for the two realizations in the Recognition Science framework, supporting forced arithmetic independent of realization type.
scope and limits
- Does not derive physical constants or mass formulas.
- Does not address realizations beyond continuous and discrete cases.
- Does not contain the equivalence proof itself.