IndisputableMonolith.Foundation.SelfBootstrapDistinguishability
The SelfBootstrapDistinguishability module shows that the two-element type Bool carries a definitional distinction between its constructors. It supplies the base case for bootstrapping distinguishability in the Recognition Science foundation and is cited by the absolute floor closure certificate. The module proceeds via direct definitions on Bool followed by lifting lemmas to the meta-language for propositions.
claimThe type $Bool$ carries a definitional distinction between its constructors, which lifts to the statement that the meta-language distinguishes propositions on an inhabited carrier.
background
Recognition Science requires a minimal floor of distinguishability to close the absolute floor program. This module introduces bool_distinguishable as the statement that the two constructors of Bool are distinct. It also defines distinguishability_lifted_from_bool and meta_language_distinguishes_props. The downstream AbsoluteFloorClosure states that distinguishability is equivalent to non-trivial specifiability on an inhabited carrier, and the meta-language already distinguishes propositions.
proof idea
The module consists of a sequence of definitions and short lemmas. It begins with the direct definition of distinguishability on Bool from its inductive structure, applies lifting lemmas to propositions, and concludes with the self-distinguishing claim for the meta-language.
why it matters in Recognition Science
This module supplies the base case for the joint certificate in AbsoluteFloorClosure. By establishing that the meta-language distinguishes propositions, it shows that the remaining floor is not an RS-specific physical postulate but the precondition that there is a formal system. It completes the self-bootstrap step before the forcing chain T0-T8.
scope and limits
- Does not assert distinguishability for types other than Bool.
- Does not derive physical constants or the forcing chain.
- Does not address non-inhabited carriers.