IndisputableMonolith.Foundation.UniversalForcing.Invariance.TwoCases
Continuous positive-ratio arithmetic is canonically equivalent to discrete Boolean arithmetic. Researchers tracing the Recognition Science forcing chain cite the module when unifying the two realizations under universal forcing. The module imports the continuous and discrete realization modules and assembles their equivalence.
claimContinuous positive-ratio arithmetic is canonically equivalent to discrete Boolean arithmetic.
background
The module sits in the invariance section of the Universal Forcing subtree. It imports ContinuousRealization, the re-export of the continuous positive-ratio realization already present as the LogicRealization.ofPositiveRatioComparison wrapper, and DiscreteRealization, the re-export of the Boolean/propositional realization. The local setting is the requirement that every law-of-logic realization must carry canonically equivalent forced arithmetic.
proof idea
The module imports the continuous and discrete realization modules. It assembles the canonical equivalence between the two arithmetic realizations.
why it matters in Recognition Science
This module feeds AxiomAudit, the reproducible theorem surface for the Universal Forcing program, and the Universal module, which states that every law-of-logic realization carries canonically equivalent forced arithmetic. It supplies the two-cases invariance step that links the continuous and discrete realizations.
scope and limits
- Does not address realizations other than continuous positive-ratio and discrete Boolean arithmetic.
- Does not supply explicit constructions or numerical examples of either realization.
- Does not extend the equivalence claim beyond the invariance section.
- Does not contain the full universal forcing theorem.