  We initiate the hunt for a definition of Hamiltonian constraint in Euclidean
Loop Quantum Gravity (LQG) which faithfully represents quantum Dirac algebra.
Borrowing key ideas from previous works on Hamiltonian constraint in LQG and
several toy models, we present some evidence that there exists such a continuum
Hamiltonian constraint operator which is well defined on a suitable
generalization of the Lewandowski-Marolf Habitat and is anomaly free off-shell.
