IndisputableMonolith.Foundation.RecoveredTowerAxiomAudit
RecoveredTowerAxiomAudit imports the five recovery modules to audit axiom consistency in the logic-derived number tower. Foundation researchers cite it when verifying that LogicNat through LogicComplex satisfy standard axioms without extra hypotheses. The module consists solely of import declarations with no new declarations or proofs.
claimThe recovered tower comprises the structures LogicNat, LogicInt, LogicRat, LogicReal (Bourbaki completion of LogicRat), and LogicComplex (pairs of recovered reals equivalent to Mathlib ℂ).
background
The module belongs to the Foundation domain and imports ArithmeticFromLogic, IntegersFromLogic, RationalsFromLogic, RealsFromLogic, and ComplexFromLogic. RealsFromLogic recovers the real numbers from the Law-of-Logic rational layer using Mathlib's Bourbaki completion on LogicRat. ComplexFromLogic constructs LogicComplex as pairs of recovered reals and proves carrier-level equivalence with Mathlib ℂ. The setting is sequential recovery of classical number systems from the Recognition Science logic layer.
proof idea
This is a definition module, no proofs. The structure consists of five module imports that expose the recovered arithmetic, integer, rational, real, and complex layers for axiom auditing.
why it matters in Recognition Science
The module verifies the axiom base for the recovered tower that supports the forcing chain T0-T8 and downstream mass formulas. It feeds the parent foundation constructions used in higher Recognition Science derivations, though no explicit used_by edges are recorded.
scope and limits
- Does not introduce new number constructions or operations.
- Does not contain theorems or proofs about the recovered structures.
- Does not extend the tower to analysis, geometry, or physics.
- Does not list or discharge specific axioms beyond the import chain.