Riemann Hypothesis via Self-Dual Trace Confinement: A Conditional Closure

This paper gives a conditional Six Birds closure of the Riemann hypothesis by moving the question from classical analytic number theory to a formed-layer trace setting. The substrate is the saturated completed Selberg trace closure of the completed Riemann zeta function, equipped with the functional-equation involution and with a typed ledger of nontrivial zeros. A translation theorem T shows that the anti-invariant zero ledger of the completed zeta shell vanishes, AZ(ζ) = 0, if and only if every typed nontrivial zero has real part 1/2. The conditional landing chain uses the Selberg-class instance of Self-Dual Trace Confinement supplied by Tsiokos (2026): its recognition source gives domination records whose vanishing trace forces AZ(ζ) = 0, and theorem T converts that ledger collapse into the critical-line statement. Stated in the audit-closure language of Tsiokos (2026), the same conditional chain is recorded as a local refinement-stable audited-operational-realisability instance, Sel!ζ,tr ∈ RefStableAORref𝔖RH , whose typed-zero-ledger readout is the critical-line statement. Outside Six Birds, the result is the conditional theorem ΓSDTC-Selberg ⇒ RH on the typed zero ledger. This is not an unconditional proof of the Riemann hypothesis in standard ZFC. The shell's admissibility is a standing Foundations-II hypothesis, and the real-part coordinate of a typed zero is a representation parameter identified with the classical real part by construction-parameter assignment. The development is formalized in Lean as a mathlib-free mechanization.