IndisputableMonolith.Foundation.UniversalForcing.Strict.PositiveRatio
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
- Does not prove the full Universal Forcing theorem.
- Does not permit internal orbit fields in realizations.
- Does not address non-positive ratios or non-strict cases.
- Does not include numerical constants, mass formulas, or Berry thresholds.