IndisputableMonolith.Foundation.ModularLogicRealization
ModularLogicRealization supplies definitions for equality cost on finite carriers as the modular Law-of-Logic realization. Researchers extending Universal Forcing to ordered and audit settings cite it after the discrete Boolean case. The module consists entirely of definitions establishing finCost, modularInterpret, and modularRealization together with their invariants.
claimDefines $\mathrm{finCost}$ as equality cost on a finite carrier, $\mathrm{modulus} > 1$, $\mathrm{cycStep}$, $\mathrm{modularInterpret}$ with zero and step cases, and $\mathrm{modularRealization}$ obeying the modular arithmetic invariant.
background
The module imports DiscreteLogicRealization, the second Law-of-Logic realization that supplies a discrete Boolean/propositional carrier and serves as the first non-continuous test case for Universal Forcing.
It introduces finCost with self and symmetry properties, modulus with positivity and one_lt_modulus, cycStep, modularInterpret with zero and step lemmas, modularRealization, and the modular_arithmetic_invariant.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module feeds OrderedLogicRealization (ordered faithful realization for Universal Forcing) and UniversalForcingAudit (reproducible audit surface). It supplies the modular case in the sequence of logic realizations supporting the forcing chain.
scope and limits
- Does not contain any proved theorems.
- Does not treat continuous carriers.
- Does not reference the phi-ladder or J-cost.