IndisputableMonolith.Foundation.UniversalForcing.Invariance.TwoCases
Continuous positive-ratio arithmetic is canonically equivalent to discrete Boolean arithmetic. Researchers auditing the Recognition Science derivations cite this module to bridge the continuous and discrete realizations inside the Universal Forcing invariance. The module imports the positive-ratio wrapper from ContinuousRealization and the Boolean realization from DiscreteRealization to establish the link.
claimContinuous positive-ratio arithmetic is canonically equivalent to discrete Boolean arithmetic.
background
This module sits inside the Foundation.UniversalForcing.Invariance namespace. It imports ContinuousRealization, described as the continuous positive-ratio realization re-exported from the already-existing LogicRealization.ofPositiveRatioComparison wrapper under the Universal Forcing namespace, and DiscreteRealization, the re-export of the Boolean/propositional realization under the same module tree. The local setting is the program to demonstrate that distinct logic realizations produce canonically equivalent forced arithmetic.
proof idea
This is a definition module, no proofs. The structure consists solely of importing the two realization modules to support the equivalence claim stated in the module doc-comment.
why it matters in Recognition Science
This module feeds AxiomAudit, which supplies the reproducible theorem surface for the Universal Forcing Lean program, and Invariance.Universal, whose doc-comment states that every Law-of-Logic realization carries canonically equivalent forced arithmetic. It supplies the two-cases equivalence step required by the general invariance result.
scope and limits
- Does not define any new realizations or functions.
- Does not contain proof bodies or tactic applications.
- Does not reference physical constants or mass formulas.