IndisputableMonolith.Foundation.UniversalForcing.Strict.Ordered
Module defines the strict ordered integer realization for the universal forcing chain. It extends the discrete boolean carrier by adding ordered integer costs and arithmetic equivalences to the native generator. Researchers tracing the forcing from boolean to modular levels cite this step. The module organizes definitions around periodic orbits with free iteration arithmetic.
claimThe strict ordered integer realization supplies a periodic carrier orbit on the integers whose forced arithmetic is the free iteration object derived from the native generator.
background
The module belongs to the Strict subfolder of UniversalForcing and imports DiscreteBoolean. That upstream module states: 'Strict Boolean/propositional realization. The carrier orbit is periodic, but the strict forced arithmetic is the free iteration object derived from the native generator, not the finite image inside Bool.' The present module introduces integer cost functions together with the main realization object and its arithmetic equivalence to logic natural numbers.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module is imported by the Modular realization, which applies the same pattern to ZMod n. It supplies the ordered integer layer in the sequence of strict realizations that build the forcing chain.
scope and limits
- Does not realize forcing on finite boolean images.
- Does not supply the modular arithmetic layer.
- Does not address non-strict or continuous carriers.
- Does not contain the full T0-T8 forcing chain.