IndisputableMonolith.Foundation.AbsoluteFloorClosure
The AbsoluteFloorClosure module supplies a named witness for the absolute floor on any universe of discourse K, closing the base case of the absolute-floor program. Researchers tracing the Recognition Science forcing chain would cite it to ground non-triviality before the J-cost and phi-ladder steps. The module achieves this by importing Route A (self-bootstrap meta-facts) and Route B (specification-to-carrier equivalence) to establish the equivalence with bare distinguishability.
claimFor a universe of discourse $K$, AbsoluteFloorWitness$(K)$ holds if and only if there exist distinct $x,y \in K$ (i.e., the carrier is non-singleton).
background
The module belongs to the Foundation domain and forms the closure step of the absolute-floor program. It imports DistinguishabilityFromSpecifiability, whose doc states that a non-trivial specification is equivalent to a non-singleton carrier, and SelfBootstrapDistinguishability, whose doc records the meta-level facts that the formal language already distinguishes propositions. These supply the two routes needed to name the absolute-floor witness without positing it separately.
proof idea
This is a definition module, no proofs. It defines AbsoluteFloorWitness together with the equivalence lemmas bare_distinguishability_of_absolute_floor, absolute_floor_of_bare_distinguishability, and absolute_floor_iff_bare_distinguishability by direct combination of the two imported routes.
why it matters in Recognition Science
The module feeds NonTrivialityFromDistinguishability (which promotes the non_trivial field of SatisfiesLawsOfLogic from posit to corollary) and RealityFromDistinction (the master theorem deriving the full T0-T8 chain, spacetime, light cone, and phi-derived constants from one distinction). It thereby closes the absolute-floor base case required by the Law-of-Logic forcing chain.
scope and limits
- Does not derive a non-singleton carrier from an empty starting point.
- Does not reach J-uniqueness, the phi fixed point, or the eight-tick octave.
- Does not compute constants such as alpha or G.
- Does not address spatial dimension D=3 or the mass ladder.