  The known a posteriori error analysis of hybrid high-order methods (HHO)
treats the stabilization contribution as part of the error and as part of the
error estimator for an efficient and reliable error control. This paper
circumvents the stabilization contribution on simplicial meshes and arrives at
a stabilization-free error analysis with an explicit residual-based a
posteriori error estimator for adaptive mesh-refining as well as an
equilibrium-based guaranteed upper error bound (GUB). Numerical evidence in a
Poisson model problem supports that the GUB leads to realistic upper bounds for
the displacement error in the piecewise energy norm. The adaptive mesh-refining
algorithm associated to the explicit residual-based a posteriori error
estimator recovers the optimal convergence rates in computational benchmarks.
