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  1. Abstract The rate for Higgs ( $${\mathrm{H}} $$ H ) bosons production in association with either one ( $${\mathrm{t}} {\mathrm{H}} $$ t H ) or two ( $${\mathrm{t}} {{\overline{{{\mathrm{t}}}}}} {\mathrm{H}} $$ t t ¯ H ) top quarks is measured in final states containing multiple electrons, muons, or tau leptons decaying to hadrons and a neutrino, using proton–proton collisions recorded at a center-of-mass energy of $$13\,\text {TeV} $$ 13 TeV by the CMS experiment. The analyzed data correspond to an integrated luminosity of 137 $$\,\text {fb}^{-1}$$ fb - 1 . The analysis is aimed at events that contain $${\mathrm{H}} \rightarrowmore »{\mathrm{W}} {\mathrm{W}} $$ H → W W , $${\mathrm{H}} \rightarrow {\uptau } {\uptau } $$ H → τ τ , or $${\mathrm{H}} \rightarrow {\mathrm{Z}} {\mathrm{Z}} $$ H → Z Z decays and each of the top quark(s) decays either to lepton+jets or all-jet channels. Sensitivity to signal is maximized by including ten signatures in the analysis, depending on the lepton multiplicity. The separation among $${\mathrm{t}} {\mathrm{H}} $$ t H , $${\mathrm{t}} {{\overline{{{\mathrm{t}}}}}} {\mathrm{H}} $$ t t ¯ H , and the backgrounds is enhanced through machine-learning techniques and matrix-element methods. The measured production rates for the $${\mathrm{t}} {{\overline{{{\mathrm{t}}}}}} {\mathrm{H}} $$ t t ¯ H and $${\mathrm{t}} {\mathrm{H}} $$ t H signals correspond to $$0.92 \pm 0.19\,\text {(stat)} ^{+0.17}_{-0.13}\,\text {(syst)} $$ 0.92 ± 0.19 (stat) - 0.13 + 0.17 (syst) and $$5.7 \pm 2.7\,\text {(stat)} \pm 3.0\,\text {(syst)} $$ 5.7 ± 2.7 (stat) ± 3.0 (syst) of their respective standard model (SM) expectations. The corresponding observed (expected) significance amounts to 4.7 (5.2) standard deviations for $${\mathrm{t}} {{\overline{{{\mathrm{t}}}}}} {\mathrm{H}} $$ t t ¯ H , and to 1.4 (0.3) for $${\mathrm{t}} {\mathrm{H}} $$ t H production. Assuming that the Higgs boson coupling to the tau lepton is equal in strength to its expectation in the SM, the coupling $$y_{{\mathrm{t}}}$$ y t of the Higgs boson to the top quark divided by its SM expectation, $$\kappa _{{\mathrm{t}}}=y_{{\mathrm{t}}}/y_{{\mathrm{t}}}^{\mathrm {SM}}$$ κ t = y t / y t SM , is constrained to be within $$-0.9< \kappa _{{\mathrm{t}}}< -0.7$$ - 0.9 < κ t < - 0.7 or $$0.7< \kappa _{{\mathrm{t}}}< 1.1$$ 0.7 < κ t < 1.1 , at 95% confidence level. This result is the most sensitive measurement of the $${\mathrm{t}} {{\overline{{{\mathrm{t}}}}}} {\mathrm{H}} $$ t t ¯ H production rate to date.« less