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module module high

IndisputableMonolith.Foundation.AbsoluteFloorClosure

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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

used by (2)

From the project-wide theorem graph. These declarations reference this one in their body.

depends on (2)

Lean names referenced from this declaration's body.

declarations in this module (8)