IndisputableMonolith.Foundation.RecoveredTowerAxiomAudit
This module audits the axiom recovery tower from foundational logic through arithmetic, integers, rationals, reals, and complex numbers. Researchers checking consistency between logic-derived structures and classical mathematics would cite it during foundation verification. The module aggregates five recovery imports with no additional declarations or proofs.
claimRecovered tower: logic layer to arithmetic operations, then integers, rationals, reals via Bourbaki completion of recovered rationals, and complex numbers as pairs of recovered reals equivalent to standard $ℂ$.
background
The module belongs to the Foundation layer and imports the five recovery files that build standard mathematics from the Law-of-Logic base. ArithmeticFromLogic recovers arithmetic; IntegersFromLogic and RationalsFromLogic extend to integers and rationals; RealsFromLogic recovers the reals by applying Mathlib's Bourbaki completion to the recovered rationals LogicRat; ComplexFromLogic constructs LogicComplex as pairs of those reals and proves carrier equivalence with Mathlib $ℂ$ without redeveloping analysis.
proof idea
This is an audit module, no proofs. It consists solely of the five module imports that expose the recovered structures for inspection.
why it matters in Recognition Science
The module supports the overall Recognition Science foundation by auditing the mathematical tower that later modules rely on for derivations such as the forcing chain T0-T8 and constants in RS-native units. With no downstream declarations yet, it serves as an internal consistency checkpoint before physical applications.
scope and limits
- Does not develop complex analysis or contour integration.
- Does not modify the Bourbaki completion engine for reals.
- Does not introduce new axioms beyond those in the imported recoveries.
- Does not contain theorems or proofs of its own.