IndisputableMonolith.Foundation.AbsoluteFloorClosure
This module closes the absolute-floor program for any universe of discourse K by supplying a named witness that equates the absolute floor property with bare distinguishability. Researchers tracing the Recognition Science foundation would cite it when moving from meta-level distinguishability facts to the promotion of non-triviality. The module assembles two imported routes into mutual implications and an if-and-only-if statement without introducing new axioms.
claimFor a carrier $K$, the absolute floor is witnessed by the equivalence between the absolute-floor property and bare distinguishability, i.e., the existence of distinct $x, y : K$ with $x ≠ y$.
background
The module operates in the Foundation layer of Recognition Science and imports two sibling modules that together implement the absolute-floor program. SelfBootstrapDistinguishability records the meta-level facts that a formal language already distinguishes propositions, while DistinguishabilityFromSpecifiability shows that any non-trivial specification is equivalent to a non-singleton carrier. Together they supply the two routes (A and B) needed to close the floor without positing an object-level non-singleton carrier from nothing. The module itself introduces the named witness AbsoluteFloorWitness together with the conversion functions bare_distinguishability_of_absolute_floor, absolute_floor_of_bare_distinguishability, and the equivalence absolute_floor_iff_bare_distinguishability.
proof idea
This is a definition module whose structure consists of a central witness definition followed by two conversion lemmas and their equivalence. The conversions are obtained directly from the imported Route A and Route B results; no additional tactics beyond the imported lemmas are required.
why it matters in Recognition Science
The module supplies the absolute-floor closure that NonTrivialityFromDistinguishability uses to promote the non_trivial field of SatisfiesLawsOfLogic from a posit to a corollary. It also feeds RealityFromDistinction, the master forcing-chain theorem that derives the entire T0-T8 sequence, spacetime, and the phi-derived constants from the single bare distinction ∃x y : K, x ≠ y. It therefore completes the formal prerequisite for the self-bootstrap argument in the Recognition Science chain.
scope and limits
- Does not derive an object-level non-singleton carrier from nothing.
- Does not address physical interpretations or constants beyond the formal distinction.
- Does not contain the full forcing chain to D = 3 or the phi-ladder.
- Does not replace the non_trivial posit in SatisfiesLawsOfLogic; it only supplies the supporting equivalence.