lambda_rec_unique
lambda_rec_unique defines the proposition asserting existence and uniqueness of a real number x satisfying LawfulNormalizer x. Researchers on URC adapters cite it when establishing the trivial normalizer at 1 under abstract stationarity obligations. The definition directly applies the ExistsUnique quantifier to the predicate from the LawfulNormalizer structure.
claimThere exists a unique real number $x$ such that $x=1$ and the EL property holds.
background
LawfulNormalizer is a structure on a real $x$ that requires the fixed condition $x=1$ together with the EL_prop. This predicate supplies the content for the uniqueness claim inside the URCAdapters layer. The module imports Mathlib and assembles adapters that draw on forcing self-reference structures and mechanism design results to encode stationarity and scaling invariance.
proof idea
The declaration is a direct definition that applies the ExistsUnique constructor from Mathlib to the LawfulNormalizer predicate on reals. No lemmas are applied and no tactics are used beyond the structure definition itself.
why it matters in Recognition Science
It supplies the target proposition proved by the sibling lemma lawful_normalizer_exists_unique, which exhibits the witness at 1 using EL stationarity and confirms uniqueness. The definition stands in for the concrete lambda_rec bridge in the URC adapter layer until the ethics alignment hook is added. It aligns with the self-similar fixed point step in the Recognition Science forcing chain.
scope and limits
- Does not compute explicit normalizer values beyond the fixed point at 1.
- Does not discharge the EL_prop obligation in isolation.
- Does not incorporate the ethics alignment hook referenced in the documentation.
- Does not generalize the normalizer to non-trivial lambda values.
formal statement (Lean)
9def lambda_rec_unique : Prop := ExistsUnique (fun x : ℝ => LawfulNormalizer x)
proof body
Definition body.
10
11end URC
12
13namespace IndisputableMonolith
14namespace URCAdapters
15
16/-- Prop-level witness: a trivial normalizer at λ=1 satisfies stationarity and scaling invariance
17 under our current abstract obligations; this stands in for the concrete λ_rec bridge and will be
18 refined when the ethics alignment hook is exposed. -/