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IndisputableMonolith.Foundation.UniversalForcing.Strict.PositiveRatio

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This module supplies a strict positive-ratio realization for the Universal Forcing framework, imported from the Law-of-Logic package. It is used by axiom-audit and discrete-Boolean modules that require domain-rich strict interfaces. The module consists of definitions and equivalences that enforce native comparison without internal orbit fields.

claimA strict realization of positive ratios in the Universal Forcing chain, satisfying native comparison only and equivalent to arithmetic on logic naturals as well as to prior realizations.

background

The upstream StrictRealization module defines a domain-rich Universal Forcing interface. Earlier LogicRealization allowed an internal orbit field as an escape hatch; the strict version removes it so that a realization supplies only native comparison. This PositiveRatio module specializes that interface to positive ratios drawn from the existing Law-of-Logic package.

proof idea

This is a definition module, no proofs. It organizes three sibling definitions: the core strict positive-ratio realization together with its arithmetic equivalence to logic naturals and its equivalence to the existing realization.

why it matters in Recognition Science

The module supplies the positive-ratio component required by the AxiomAudit module for the strict completion pass and by the DiscreteBoolean module for propositional realizations whose carrier is periodic but whose arithmetic is the free iteration object. It closes the positive-ratio case inside the strict Universal Forcing path.

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)