IndisputableMonolith.Foundation.LogicAsFunctionalEquation.OperativeDomain
The OperativeDomain module defines the operative-domain structure as finite logical comparison on continuous positive ratios. Researchers deriving the Recognition Composition Law from logical comparison axioms would cite it to connect the discrete finite case to the continuous setting. The module is a definition module with no proofs; it imports FiniteLogicalComparison and exposes the structure for the main theorem chain.
claimAn operative-domain structure is finite logical comparison on the continuous positive-ratio setting $\mathbb{R}_{>0}$, where the finite-pairwise-polynomial condition is the algebraic content of logical comparison.
background
The module belongs to the LogicAsFunctionalEquation section of the foundation layer. It imports FiniteLogicalComparison, whose doc-comment states that finite logical comparison on positive ratios forces the RCL family and names the finite-pairwise-polynomial condition as the finite algebraic content of logical comparison.
The operative-domain structure is the continuous positive-ratio restriction of that comparison. The local theoretical setting is the sharpened theorem that scale-free comparison factors through positive ratios and counted-once finite comparison forces the RCL family.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module feeds the MainTheorem package, whose doc-comment collects the formal chain: scale-free comparison factors through positive ratios; no-hidden-state finite comparison gives counted-once composition; counted-once finite logical comparison forces the RCL family. It supplies the continuous positive-ratio step in the paper's headline derivation of the Recognition Composition Law from logical comparison.
scope and limits
- Does not prove that finite comparison forces the RCL family.
- Does not treat discrete or non-positive-ratio cases.
- Does not derive physical constants, dimensions, or the forcing chain T0-T8.
- Does not include the J-uniqueness or phi-ladder constructions.