StableState
plain-language theorem explainer
StableState encodes binary values as real numbers fixed at 0 or 1. Researchers deriving Boolean fragments from pre-logical cost minima cite this structure when constructing arithmetic gates. The definition is a direct structure pairing a real field with a disjunctive constraint that enables later closure proofs.
Claim. A stable state is a real number $x$ such that $x=0$ or $x=1$.
background
The PreLogicalCost module treats pre-logical configuration values as real numbers constrained to the unit interval. StableState refines this to the exact endpoints 0 and 1 via the is_bit predicate. Sibling definitions such as PreState and IsStable supply the surrounding context for stability before operations are introduced.
proof idea
Direct structure definition with a bit field of type real and an is_bit field enforcing the disjunction bit = 0 or bit = 1. No tactics or lemmas are applied.
why it matters
This definition supplies the domain for band, bor, and bnot, which feed the theorem prelogical_boolean_fragment establishing that pre-logical arithmetic cost minima induce Boolean-style stable operations. It also supports stable_forms_boolean_algebra in the same module. The structure marks the pre-logical to logical transition in the Recognition Science foundation layer.
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