IndisputableMonolith.Foundation.RecoveredTowerAxiomAudit
RecoveredTowerAxiomAudit assembles the five recovery modules that reconstruct arithmetic, integers, rationals, reals and complexes from the Law-of-Logic layer. Researchers verifying consistency between recovered mathematics and classical structures would cite it as the single audit point for the full tower. The module performs this solely through imports with no new declarations or proofs.
claimThe recovered tower is the chain $ ext{LogicNat} o ext{LogicInt} o ext{LogicRat} o ext{LogicReal} o ext{LogicComplex}$ together with the carrier-level equivalences $ ext{LogicReal} o ext{Bourbaki completion of } ext{LogicRat}$ and $ ext{LogicComplex} o ext{Mathlib }\mathbb{C}$.
background
The module resides in the Foundation domain and imports ArithmeticFromLogic, IntegersFromLogic, RationalsFromLogic, RealsFromLogic and ComplexFromLogic. RealsFromLogic recovers the reals from the Law-of-Logic rational layer: "The construction uses Mathlib's Bourbaki completion of ℚ as the completion engine, while the input rationals are the recovered rationals LogicRat from Foundation.RationalsFromLogic." ComplexFromLogic builds the complex carrier over those reals: "We construct the carrier LogicComplex as pairs of recovered reals and prove the carrier-level equivalence with Mathlib's ℂ."
proof idea
this is a definition module, no proofs. The structure consists of five sequential module imports that close the tower from arithmetic through complexes.
why it matters in Recognition Science
The module confirms the recovered tower matches classical mathematics, supplying the intact number systems required by all higher Recognition Science derivations. It supports the parent chain from logic foundations to the J-uniqueness and phi-ladder steps by guaranteeing that downstream physics statements can be stated in the recovered carriers without additional translation axioms.
scope and limits
- Does not develop analytic properties or contour integration on LogicComplex.
- Does not connect the recovered tower to the J-cost function or phi-ladder.
- Does not audit specific axioms beyond carrier equivalence.
- Does not provide use sites for the recovered structures in physics derivations.