IndisputableMonolith.Foundation.LogicRealization
LogicRealization supplies the interface for any Law-of-Logic realization. Workers on Universal Forcing cite it as the common abstraction that turns identity and step data into arithmetic. The module keeps fields lean so each carrier can supply its own order or topology while the extracted arithmetic remains invariant. It is a definition module with no proofs.
claimA Law-of-Logic realization is a structure on a carrier $K$ equipped with a comparison cost $J:K→ℝ$, an identity element, a step/generator action, and the structural propositions required to extract an initial arithmetic object.
background
The module imports ArithmeticFromLogic and LogicAsFunctionalEquation. It introduces LogicRealization as the minimal interface: a carrier together with comparison cost, identity, and step data. The module doc-comment states that each realization supplies its own topology or order through the carried propositions, while the invariant target remains the arithmetic object extracted from the identity/step data.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
LogicRealization feeds ArithmeticOf, which extracts the initial Peano algebra from any realization. It also supports the self-reference construction in UniversalForcingSelfReference and the distinction-based instantiation in UniversalInstantiationFromDistinction. The module therefore supplies the common shape required by the Universal Forcing meta-theorem.
scope and limits
- Does not commit to any concrete topology or order on the carrier.
- Does not prove existence of realizations.
- Does not derive the arithmetic object inside this module.
- Does not address the T0-T8 forcing chain or Recognition Composition Law directly.
used by (3)
depends on (2)
declarations in this module (10)
-
structure
LogicRealization -
def
hasIdentityStep -
theorem
hasIdentityStep_of_nontrivial -
structure
FaithfulArithmeticInterpretation -
def
positiveRatioOrbitInterpret -
theorem
positiveRatioOrbitInterpret_val -
def
ofPositiveRatioComparison -
theorem
positiveRatio_hasIdentityStep -
theorem
positiveRatio_interpret_injective -
theorem
positiveRatio_faithful