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On 2022 September 18, an alert by the IceCube Collaboration indicated that a ∼170 TeV neutrino arrived in directional coincidence with the blazar TXS 0506+056. This event adds to two previous pieces of evidence that TXS 0506+056 is a neutrino emitter, i.e., a neutrino alert from its direction on 2017 September 22, and a 3σsignature of a dozen neutrinos in 2014/2015. De Bruijn el al. showed that two previous neutrino emission episodes from this blazar could be due to a supermassive binary black hole (SMBBH) central engine where jet precession close to the final coalescence of the binary results in periodic emission. This model predicted a new emission episode consistent with the 2022 September 18 neutrino observation by IceCube. Here, we show that the neutrino cadence of TXS 0506+056 is consistent with an SMBBH origin. We find that the emission episodes are consistent with an SMBBH with mass ratiosq≲ 0.3 for a total black hole mass ofM_tot≳ 3 · 10⁸M_⊙. For the first time, we calculate the characteristic strain of the gravitational wave emission of the binary, and show that the merger could be detectable by LISA for black hole masses <5 · 10⁸M_⊙if the mass ratios are in the range 0.1 ≲q≲ 0.3. We predict that there can be a neutrino flare existing in the still-to-be-analyzed IceCube data peaking some time between 2019 August and 2021 January if a precessing jet is responsible for all three detected emission episodes. The next flare is expected to peak in the period 2023 January to 2026 August. Further observation will make it possible to constrain the mass ratio as a function of the total mass of the black hole more precisely and would open the window toward the preparation of the detection of SMBBH mergers.