BINDU–VECTRA: Machine-Checked Ancilla-Uniform Mixing Bounds for Independent Generalized Amplitude-Damping Channels

BINDU–VECTRA reports a Lean 4.19.0 machine-checked, ancilla-uniform Schatten-1 mixing bound for finite products of independent generalized amplitude-damping (GAD) channels. The result covers any number N of sites, strictly positive local pumping and decay rates Gₖ and Kₖ, nonnegative time t, every finite-dimensional ancilla, and arbitrary complex input matrices X—not only density operators. With rₖ(t) = exp[−(Gₖ + Kₖ)t/2], the explicit envelope C_N(t) = min{2, Σₖ₌₀ᴺ⁻¹ [rₖ(t) + rₖ(t)²]} controls the distance between the product GAD evolution Φₜ⁽ᴺ⁾ and the stationary-replacement channel ℛ⁽ᴺ⁾: ‖[(Φₜ⁽ᴺ⁾ − ℛ⁽ᴺ⁾) ⊗ id_A](X)‖₁ ≤ C_N(t)‖X‖₁. This is a pointwise estimate uniform over finite ancillas; it is not presented as a separate formal construction of the diamond-norm supremum. The principal advance is the removal of previously conditional site-kernel and hybrid-step hypotheses. Eight named Lean declarations connect physical Kraus actions to the global native-index channel representation, establish stationary-replacer and Pauli-Z/dephasing bridges, and prove the unconditional hybrid increment ‖[(ℋₖ₊₁ − ℋₖ) ⊗ id_A](X)‖₁ ≤ [rₖ(t) + rₖ(t)²]‖X‖₁. Telescoping these increments yields the N-site envelope, while a uniform bound of 2 supplies its cap. The site-to-global correspondence is established in the proof chain rather than assumed as an informal relabeling of tensor indices. The accompanying reproducibility materials identify 53 source modules, SHA-256 inventories, and pinned Lean 4.19.0/Mathlib v4.19.0 dependencies. The eight target declarations have source-matched, user-supplied successful build and axiom records reporting only Lean’s standard foundational axioms; however, a fresh independent kernel replay remains necessary before an independently certified release can be claimed. The work does not establish an exact GAD diamond norm, an optimal mixing exponent, or results for interacting Lindbladians. It instead supplies a reproducible formal foundation for future independent certification, explicit diamond-norm formalization, and investigation of sharper or more general quantum mixing estimates.