IndisputableMonolith.Foundation.LogicAsFunctionalEquation.RealityStructure
The RealityStructure module introduces TruthEvaluableComparison as the minimal structure for evaluating statements about positive-ratio comparisons. Researchers deriving the Recognition Composition Law from mismatch magnitude would cite it to anchor the canonicality step. The module consists of a four-field definition in semantic language followed by direct implication lemmas that translate those fields into algebraic conditions (L1) through (L4).
claimA truth-evaluable comparison on positive ratios consists of four semantic fields that imply the algebraic identities (L1)--(L4) for the comparison operator.
background
This module belongs to the Foundation.LogicAsFunctionalEquation hierarchy and imports Canonicality. The upstream Canonicality module formalizes the paper's canonicality step: once a comparison operator is read as a magnitude of mismatch, the operator-level conditions used in LogicAsFunctionalEquation are the canonical structural content of that reading. TruthEvaluableComparison supplies the minimal structure needed to evaluate statements about positive-ratio comparisons, with its four fields stated in semantic language.
proof idea
This is a definition module. It declares the TruthEvaluableComparison structure and then establishes direct implications from its four semantic fields to the algebraic conditions (L1)--(L4) via lemmas such as truth_eval_implies_identity, truth_eval_implies_non_contradiction, truth_eval_implies_totality, truth_eval_implies_composition, and rcl_from_truth_evaluable_comparison.
why it matters in Recognition Science
The module supplies the base structure that CountOnceComparison and FiniteLogicalComparison build upon. CountOnceComparison uses it to formalize the affine combiner for counted-once comparisons, while FiniteLogicalComparison packages the sharpened theorem that finite logical comparison on positive ratios forces the RCL family. It completes the canonicality step that precedes the Recognition Composition Law in the Recognition Science framework.
scope and limits
- Does not derive the full RCL without the finite-pairwise-polynomial condition.
- Does not address comparisons on zero or negative ratios.
- Does not include the T0--T8 forcing chain or phi-ladder mass formula.
- Does not verify numerical constants such as the alpha band or G = phi^5 / pi.