pith. sign in
module module high

IndisputableMonolith.Foundation.UniversalForcing.Strict.PositiveRatio

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Strict positive-ratio realization extracts the positive ratio case from the Law-of-Logic package into the strict realization framework. Researchers completing the domain-rich Universal Forcing theorem cite it when the realization must supply only native comparison without an internal orbit field. The module defines three objects that establish arithmetic equivalence to logic nat and strict equivalence to prior realizations.

claimThe strict positive-ratio realization is the structure supplying native comparison for the universal forcing theorem in the positive-ratio case, without an internal orbit field.

background

The upstream StrictRealization module defines the domain-rich Universal Forcing interface. Its doc-comment states that the earlier LogicRealization proves the lightweight theorem but permits an internal orbit as a field, while StrictLogicRealization removes that escape hatch so that a strict realization supplies only native comparison. This PositiveRatio module specializes the strict interface to the positive-ratio case drawn from the existing Law-of-Logic package.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module feeds the AxiomAudit surface for the strict, domain-rich Universal Forcing completion pass and the DiscreteBoolean realization, whose doc-comment notes that the carrier orbit is periodic but the strict forced arithmetic is the free iteration object derived from the native generator. It supplies the positive-ratio specialization required by those downstream strict modules.

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)