IndisputableMonolith.Foundation.SelfBootstrapDistinguishability
The SelfBootstrapDistinguishability module establishes that the two-element type carries a definitional distinction, allowing distinguishability to bootstrap from basic logical carriers without external postulates. It would be cited by researchers closing the absolute-floor program in Recognition Science. The module structures its content as a collection of definitions and lemmas on the two-element type and propositions that together certify self-distinguishability.
claimThe two-element type $2$ carries a definitional distinction, meaning its elements satisfy a non-trivial inequality that holds by definition; this property lifts from the Boolean type to propositions and yields a self-bootstrap certificate on any inhabited carrier.
background
The module sits in the Foundation domain and imports only Mathlib. It introduces the two-element type as the starting carrier for distinguishability, with lemmas showing that Bool elements are distinguishable, that this lifts to propositions (where the meta-language already separates distinct propositions), and that an object witness forces the distinction. The local setting is the logical precondition for the absolute floor: distinguishability reduces to non-trivial specifiability on an inhabited carrier rather than an RS-specific physical assumption.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the distinguishability foundation required by AbsoluteFloorClosure, whose documentation states: 'The closure is deliberately modest: distinguishability is equivalent to non-trivial specifiability on an inhabited carrier, and the meta-language already distinguishes propositions. The remaining floor is therefore not an RS-specific physical postulate; it is the precondition that there is a'. It thereby anchors the base of the forcing chain (T0 onward) by showing that the meta-language already supplies the required distinction.
scope and limits
- Does not interpret distinguishability as a physical process.
- Does not extend the result to infinite or continuous carriers.
- Does not claim that the absolute floor is fully closed.
- Does not address interaction with the J-cost or phi-ladder.