<p>We employ an ADM deparametrization strategy to discuss the radial canonical formalism of asymptotically AdS₃ gravity. It leads to the identification of a radial ‘time’ before quantization, which is the volume time, canonically conjugate to York time. Holographically, this allows to interpret the semi-classical path integral of <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <mi>T</mi> <mover accent="true"> <mi>T</mi> <mo stretchy="true">¯</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">\( T\overline{T} \)</EquationSource> </InlineEquation> theory as a Schrödinger wavefunctional satisfying a Schrödinger evolution equation in volume time, and the <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math display="inline"> <mi>T</mi> <mover accent="true"> <mi>T</mi> <mo stretchy="true">¯</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">\( T\overline{T} \)</EquationSource> </InlineEquation> operator expectation value in terms of the Hamiltonian that generates volume time translations — both consistent with cut-off holography. We make use of the canonical perspective to construct the rotating BTZ solution from the Hamilton-Jacobi equation, with a finite cut-off energy spectrum that has a known holographic <InlineEquation ID="IEq4"> <EquationSource Format="MATHML"><math display="inline"> <mi>T</mi> <mover accent="true"> <mi>T</mi> <mo stretchy="true">¯</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">\( T\overline{T} \)</EquationSource> </InlineEquation> interpretation, as well as semi-classical Wheeler-DeWitt states for that solution.</p>