IndisputableMonolith.Foundation.ModularLogicRealization
ModularLogicRealization supplies definitions for equality cost on finite carriers together with modular interpretation and arithmetic invariants. Researchers testing discrete models in the Universal Forcing program cite it as the bridge between the discrete Boolean carrier and later ordered realizations. The module consists of a chain of supporting definitions and lemmas rather than a single central theorem.
claimOn a finite carrier with modulus $m>1$, the equality cost is the function $C(x)$ satisfying $C(x)=C(m-x)$ and the modular interpretation map satisfies the cyclic step relation together with the arithmetic invariant.
background
The module imports DiscreteLogicRealization, described as the second Law-of-Logic realization: a discrete Boolean/propositional carrier and the first non-continuous test case for Universal Forcing. It introduces the finite-carrier setting with definitions for the equality cost function, the modulus, the cyclic step operator, and the modular interpretation map. These objects establish the modular arithmetic invariant used by downstream modules.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module is imported by OrderedLogicRealization to supply the ordered faithful realization for Universal Forcing and by UniversalForcingAudit to provide a reproducible audit surface. It advances the sequence of Law-of-Logic realizations by adding the finite modular carrier case inside the Recognition Science framework.
scope and limits
- Does not derive the full T0-T8 forcing chain.
- Does not compute values for physical constants such as alpha.
- Does not treat continuous or infinite carriers.
- Does not include numerical checks of the phi ladder.