IndisputableMonolith.Foundation.UniversalForcing.DiscreteRealization
This module supplies the discrete Boolean realization of the Law-of-Logic as a propositional carrier. It acts as the first non-continuous test case inside the Universal Forcing framework. Researchers verifying invariance kernels cite it to confirm that forced arithmetic remains canonically equivalent across carrier types. The module consists of targeted definitions establishing the carrier and its arithmetic equivalence.
claimA discrete propositional carrier realizing the Law-of-Logic, with forced arithmetic canonically isomorphic to that induced by continuous positive-ratio carriers.
background
Universal Forcing requires any two LogicRealizations to induce isomorphic forced arithmetic. The upstream DiscreteLogicRealization module introduces the second such realization as a discrete Boolean/propositional carrier and marks it as the first non-continuous test case. This module concretizes that carrier inside the foundation layer, providing the discrete counterpart to continuous positive-ratio realizations for direct comparison.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the discrete case required by the TwoCases invariance kernel, which shows that continuous positive-ratio realizations and the discrete Boolean realization have canonically equivalent forced arithmetic. It also feeds UniversalForcingSelfReference, where the meta-theorem is shown to fit the Law-of-Logic structural shape, closing the framework reflexively. It completes the non-continuous test case in the forcing chain.
scope and limits
- Does not assume continuity of the carrier.
- Does not compute explicit numerical values for forced constants.
- Does not address higher-dimensional realizations beyond the discrete case.
- Does not prove the full meta-theorem of Universal Forcing.