IndisputableMonolith.Foundation.LogicAsFunctionalEquation.OperativeDomain
OperativeDomain defines the operative-domain structure as finite logical comparison on the continuous positive-ratio setting. It supplies the domain layer that lets the FiniteLogicalComparison result apply inside the logic-as-functional-equation chain. The module organizes the structure definition together with satisfaction and identification lemmas that connect directly to the main theorem package.
claimAn operative-domain structure is finite logical comparison on the continuous positive-ratio setting, written as the domain in which scale-free comparison reduces to positive ratios and forces the Recognition Composition Law family.
background
The module belongs to the LogicAsFunctionalEquation package inside the Foundation domain. It imports FiniteLogicalComparison, whose documentation states that finite logical comparison on positive ratios forces the RCL family, with the finite-pairwise-polynomial condition retained as the finite algebraic content of logical comparison. The operative-domain structure is introduced precisely as the continuous positive-ratio setting for this comparison, per the module documentation.
proof idea
This is a definition module, no proofs. It packages the operative domain structure and the lemmas operative_domain_satisfies_logic, operative_domain_identification, and rcl_logic_reality_chain that inherit their content from the upstream FiniteLogicalComparison result.
why it matters in Recognition Science
The module supplies the operative domain to the MainTheorem package, which assembles the formal chain closest to the paper headline: scale-free comparison factors through positive ratios, no-hidden-state finite comparison yields counted-once composition, and counted-once finite logical comparison forces the RCL family. It therefore fills the positive-ratio step required by the sharpened theorem on logic as functional equation.
scope and limits
- Does not extend beyond positive ratios.
- Does not remove the finite-pairwise-polynomial condition.
- Does not address hidden-state or infinite comparisons.
- Does not derive J-uniqueness or the phi fixed point.