IndisputableMonolith.Foundation.UniversalForcing.StrictRealization
This module defines a strict Law-of-Logic realization that carries only native law propositions and excludes any supplied orbit data. It is cited by work on the Universal Forcing theorem to supply the concrete structure needed for equivalence of forced arithmetic objects across realizations. The module consists entirely of definitions for the realization structure and its interpretation maps.
claimA structure whose fields are propositions $excluded_middle_law$, $composition_law$, and $invariance_law$, with no external orbit supplied.
background
The parent module UniversalForcing states that any two Law-of-Logic realizations have canonically equivalent forced arithmetic objects because those objects are initial Peano algebras. StrictRealization introduces the StrictLogicRealization structure whose three law fields are raw Props rather than derived theorems. Sibling definitions such as interpret, interpret_zero, and arith_equiv_logicNat then map this structure onto arithmetic objects without external orbit data.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the StrictLogicRealization structure required by AdmissibleClass to quantify the Universal Forcing theorem over the five domain realizations and by PositiveRatio to construct the strict continuous positive-ratio case. It therefore closes the strict-native branch of the forcing argument that begins in UniversalForcing.
scope and limits
- Does not instantiate the law propositions for any concrete domain.
- Does not supply orbit data or FreeOrbit constructions.
- Does not derive the law propositions from functional equations.
- Does not contain the Universal Forcing theorem itself.