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Abstract We study 1+1 dimensional ϕ 4 theory using the recently proposed method of conformal truncation. Starting in the UV CFT of free field theory, we construct a complete basis of states with definite conformal Casimir, C $$ \mathcal{C} $$ . We use these states to express the Hamiltonian of the full interacting theory in lightcone quantization. After truncating to states with C ≤ C max $$ \mathcal{C}\le {\mathcal{C}}_{\max } $$ , we numerically diagonalize the Hamiltonian at strong coupling and study the resulting IR dynamics. We compute non-perturbative spectral densities of several local operators, which are equivalent to real-time, infinite-volume correlation functions. These spectral densities, which include the Zamolodchikov C-function along the full RG flow, are calculable at any value of the coupling. Near criticality, our numerical results reproduce correlation functions in the 2D Ising model.