_ethics_ok
plain-language theorem explainer
This definition supplies an explicit equivalence showing that the arithmetic structure induced by the strict ethical realization matches the natural numbers generated by the Law of Logic. Researchers auditing strict Universal Forcing completions would cite it to confirm domain-specific realizations preserve foundational arithmetic. The construction is a one-line wrapper that applies the orbit equivalence from the lightweight realization of the ethical case.
Claim. The carrier of the Peano structure in the arithmetic induced by the strict ethical realization is equivalent to the natural numbers forced by the Law of Logic: $(arith(R)).peano.carrier ≃ LogicNat$, where $R$ is the strict ethical realization, $arith$ extracts the arithmetic structure, and $LogicNat$ is the inductive type with identity and step constructors.
background
StrictLogicRealization supplies a domain-rich completion of universal forcing. The arith map extracts an arithmetic structure whose Peano carrier is the object of interest. LogicNat is the inductive type with constructors identity (the zero-cost multiplicative identity) and step (one iteration of the generator), forming the orbit under multiplication by the generator γ as the smallest subset of positive reals closed under that operation and containing 1.
proof idea
One-line wrapper that applies the orbitEquivLogicNat equivalence obtained from the lightweight realization of the strict ethical realization.
why it matters
This definition closes the ethics audit item in the strict Universal Forcing completion pass, confirming that the ethical realization (built from ActionState carrier and Nat cost with actionCost comparison) yields the expected LogicNat arithmetic. It supports the claim that strict realizations across domains align with the Law of Logic foundation. The module provides an audit surface for such domain-rich completions.
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