The Chiral Anomaly as Record Decoherence: Deriving the ABJ Coefficient from the K-Functional

We show that the Adler-Bell-Jackiw chiral anomaly is a natural consequence of the record sector K_rec of the K-functional framework. Chirality (the eigenvalue of γ₅) is a record observable: it takes discrete values ±1, is measured in every weak interaction, and its indefiniteness is penalized by K_rec. In a background gauge field, the K_rec gradient drives the fermion density matrix toward states of definite chirality. The rate of this drive is the chirality decoherence rate λ_chiral = e²/(16π²), determined by the one-loop coupling of the fermion to the gauge field environment. Combined with the Atiyah-Singer index theorem, this yields ∂_μ⟨J^μ_5⟩ = (e²/16π²) F_μν F̃^μν. The derivation extends to non-abelian gauge fields: for SU(N) with fermions in representation R, λ_chiral = g²C(R)/(16π²), recovering the standard non-abelian anomaly. The Adler-Bardeen theorem (exactness at one loop) is proven rigorously from CPTP monotonicity and the quantum Cramér-Rao bound: the chirality variance decays geometrically under sequential CPTP maps, with a rate determined by the single-step quantum Fisher information. A new prediction is derived: the chiral anomaly is suppressed near the Bekenstein bound, with λ_eff = (e²/16π²)(1 − S/S_Bek), providing a natural timing mechanism for baryogenesis after the cosmological bounce.