In DHOST theories with Gauss-Bonnet and Weyl operators, gauge symmetry invariance conditions are identical to Hamiltonian constraints eliminating ghosts.
Davis,Symmetric variations of the metric and extrema of the action for pure gravity, General Relativity and Gravitation30(1998) 345?377
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AI--Assisted Exploration: DHOST Theories without Quantum Ghosts
In DHOST theories with Gauss-Bonnet and Weyl operators, gauge symmetry invariance conditions are identical to Hamiltonian constraints eliminating ghosts.