IndisputableMonolith.Foundation.UniversalForcing.Strict.PositiveRatio
The module supplies a strict positive-ratio realization drawn from the Law-of-Logic package for domain-rich Universal Forcing. Researchers auditing axioms or building discrete Boolean models cite it when they need native comparison without internal orbits. It consists of three sibling definitions establishing arithmetic-logic equivalence under the strict interface imported from StrictRealization.
claimA strict positive-ratio realization $R$ satisfies native comparison only, with arithmetic-logic equivalence $R_{ ext{arith}} o R_{ ext{logicNat}}$ and strict equivalence to the existing package realization.
background
StrictRealization provides the domain-rich Universal Forcing interface. Its doc states that the earlier LogicRealization proves the lightweight theorem but permits an internal orbit field, while StrictLogicRealization removes that escape hatch and supplies only native comparison. This module specializes the strict interface to the positive-ratio case imported from the Law-of-Logic package.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module feeds AxiomAudit (audit surface for strict Universal Forcing completion) and DiscreteBoolean (strict Boolean realization whose forced arithmetic is the free iteration object). It supplies the positive-ratio case required for the strict path in the forcing chain.
scope and limits
- Does not prove the full Universal Forcing theorem.
- Does not admit internal orbit fields in realizations.
- Does not cover non-positive ratio cases.
- Does not address non-strict realizations.