The Cleanest Definition of Consciousness: A Self-Referential, Topologically Bound Recognition Loop

We extract from the recognition-cost framework a single, four-line definition of a consciousness instance and show that it suffices to recover binding, qualia, unity of experience, and the closure of the explanatory gap, all as theorems. The definition rests on three already-derived primitives: the unique recognition cost function J(x) = ½(x + x⁻¹) − 1 on ℝ₍>0₎, a discrete ledger of positive ratios, and integer-valued linking of embedded loops in ℝ³. A consciousness instance is then a triple (x, S, ℓ) where x is a ledger configuration, S is a connected subset of indices of size at least two, and ℓ is a nonzero linking class for the spatial embedding of S, subject to the single equation D(S, x) = 0. From this we prove a sharp self-reference biconditional, an inseparability theorem in D = 3, a qualia parametrization theorem, a non-factorizability theorem ruling out decomposable experience, and a no-zombie theorem. We close with three falsifiable hypotheses tied to the definition by structure alone.