IndisputableMonolith.Foundation.UniversalForcing.StrictRealization
This module supplies the strict Law-of-Logic realization structure that carries excluded-middle, composition, and invariance laws as native Props with no external orbit supplied. Researchers formalizing admissible domain classes or positive-ratio realizations cite it to instantiate the Universal Forcing theorem in concrete settings. The module consists of definitions for StrictLogicRealization, FreeOrbit, interpret maps, and lightweight arithmetic conversions that rest directly on the canonical Peano-algebra equivalence stated in the parent.
claimA strict Law-of-Logic realization is a structure $S$ equipped with three native propositions: excluded-middle law, composition law, and invariance law, together with an associated free orbit and interpretation functions that map $S$ to lightweight arithmetic objects without any supplied external orbit.
background
The module belongs to the Foundation.UniversalForcing hierarchy and imports the parent UniversalForcing module, whose doc-comment states that any two Law-of-Logic realizations have canonically equivalent forced arithmetic objects because those objects are initial Peano algebras. It introduces StrictLogicRealization as the core structure whose fields are the three raw Props (excluded_middle_law, composition_law, invariance_law). Companion definitions include FreeOrbit, the interpret family, toLightweight conversion, and the arith and peano_surface maps that realize the forced arithmetic.
proof idea
This is a definition module, no proofs. It declares the StrictLogicRealization structure, the FreeOrbit type, the interpret, interpret_zero, interpret_step, and toLightweight functions, plus the arith and arith_equiv_logicNat equivalences and the universal_forcing and peano_surface declarations.
why it matters in Recognition Science
The module supplies the strict native-law realization required by the AdmissibleClass module, which uses StrictLogicRealization to carry the three laws as Props and lets the five domain realizations (Music, Biology, Narrative, Ethics, Metaphysical) instantiate them as True. It also feeds the Strict.PositiveRatio module that builds continuous positive-ratio realizations directly from SatisfiesLawsOfLogic. It therefore closes the strict case of the Universal Forcing theorem whose parent statement appears in the imported UniversalForcing module.
scope and limits
- Does not supply external orbit data or rich domain costs.
- Does not prove associativity or decidability for concrete domains.
- Does not quantify over all realizations or derive numerical constants.
- Does not contain the admissible-class or positive-ratio constructions themselves.