IndisputableMonolith.Foundation.UniversalForcing.Invariance.Universal
This module establishes that every realization of universal forcing induces forced arithmetic canonically equivalent to the reference LogicNat Peano object. Researchers tracing invariance in the Recognition Science forcing chain cite it to confirm carrier independence. The module imports and unifies equivalence results from the categorical, two-case, modular, and order realizations without new proofs.
claimFor every realization $R$, the forced arithmetic object induced by $R$ is canonically equivalent to the reference Peano structure LogicNat.
background
The module sits inside Foundation.UniversalForcing.Invariance and aggregates four upstream realizations. CategoricalRealization re-exports the Lawvere-style categorical case. TwoCases proves equivalence between continuous positive-ratio realizations and the discrete Boolean realization. ModularRealization uses ZMod n carriers with equality cost, while OrderRealization embeds LogicNat into Z via unit steps. The setting treats the internal orbit of each realization as the carrier of the forced arithmetic.
proof idea
This is a definition module with no proofs. It imports CategoricalRealization, TwoCases, ModularRealization, and OrderRealization to re-export their individual invariance kernels under a single universal statement.
why it matters in Recognition Science
This module supplies the universal invariance result imported by MusicRealization to define its interval-stacking carrier. It completes the invariance step required by the universal forcing construction, ensuring the arithmetic structure remains independent of the chosen realization.
scope and limits
- Does not prove equivalences for realizations outside the four imported modules.
- Does not exhibit explicit equivalence maps between carriers.
- Does not address non-unit cost functions or infinite non-order carriers.
- Does not derive physical constants or connect to the phi-ladder.