pith. sign in
module module high

IndisputableMonolith.Foundation.UniversalForcing.Strict.PositiveRatio

show as:
view Lean formalization →

This module supplies the strict positive-ratio realization drawn from the Law-of-Logic package for domain-rich Universal Forcing. It removes internal orbit fields to enforce native comparison only. Researchers building axiom audits or discrete Boolean structures cite these definitions when closing arithmetic-to-logic paths. The module consists of three sibling definitions that establish the realization and its equivalences.

claimThe module defines the strict positive-ratio realization together with its arithmetic equivalence to logic naturals and its strict equivalence to existing realizations.

background

The module imports the StrictRealization interface, which supplies a domain-rich Universal Forcing setup. Upstream, the earlier LogicRealization proved the lightweight Universal Forcing theorem yet permitted an internal orbit field; StrictRealization removes that escape hatch so that a realization supplies only native comparison. The positive-ratio focus aligns with the forcing chain's J-uniqueness and self-similar fixed point.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module feeds the AxiomAudit module for the strict Universal Forcing completion pass and the DiscreteBoolean module for strict propositional realizations whose carrier orbit is periodic yet whose arithmetic remains the free iteration object. It closes the path from the existing Law-of-Logic package into the strict domain-rich setting.

scope and limits

used by (2)

From the project-wide theorem graph. These declarations reference this one in their body.

depends on (1)

Lean names referenced from this declaration's body.

declarations in this module (3)