IndisputableMonolith.Foundation.LogicAsFunctionalEquation.BooleanRatioBridge
This module defines a finite weighted Boolean reality over Fin n and embeds it into positive ratios. It supports the logic-as-functional-equation chain by realizing scale-free comparison factors through counted-once composition. The module supplies definitions and an embedding lemma that extend the imported MainTheorem package.
claimLet $B$ be a finite weighted Boolean reality over $Fin n$ with positive weight function $w$. The ratio of any two events equals $w(e_1)/w(e_2)$, and finite Boolean logic embeds into the positive reals under this weighting.
background
The module operates inside the Foundation.LogicAsFunctionalEquation development and imports the MainTheorem package. That package assembles the headline 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. FiniteBooleanReality encodes a finite collection of Boolean events equipped with positive weights; eventWeight and eventRatio extract those weights and compute their ratios to realize the embedding.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the finite Boolean bridge required by the MainTheorem package to reach the RCL family. It realizes the scale-free comparison step in positive ratios for the finite case, closing one link in the forcing chain from logic to the functional equation.
scope and limits
- Does not treat infinite or continuous Boolean structures.
- Does not prove the Recognition Composition Law itself.
- Does not incorporate the phi-ladder or physical constants.
- Does not provide numerical verification of the embedding.