Optimized probes of CP-odd effects in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:mi>t</mml:mi><mml:mover accent="true"><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">¯</mml:mo></mml:mrow></mml:mover><mml:mi>h</mml:mi></mml:math> process at hadron colliders

We use machine learning (ML) and non-ML techniques to study optimized $CP$-odd observables, directly maximally sensitive the $i \tilde \kappa \bar t \gamma^5 h$ interaction at LHC prospective future hadron colliders using final state with a Higgs boson top quark pair, $pp\to t\bar h$, followed by semileptonic $t$ decays. perform phase-space optimization of manifestly observables ($\boldsymbol \omega$), sign $\tilde \kappa$, constructed from experimentally accessible momenta. identify simple linear combination $\boldsymbol \alpha\cdot \boldsymbol\omega$ that gives similar sensitivity as studied fully fledged ML models. Using $\boldsymbol\alpha\cdot we project expected sensitivities \kappa$ HL-LHC, HE-LHC, FCC-hh.