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There is no rigorous way to normalize its solutions, so probabilities are not defined.","posed_since":"1967","precise":"For $3+1$ general relativity (vacuum or with a scalar field) quantized canonically, construct a physical inner product on solutions of the Hamiltonian and momentum constraints $H \\Psi = 0, H_{i} \\Psi = 0$, with a complete set of Dirac observables represented as self-adjoint operators, beyond minisuperspace truncations. 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