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We carry out in full generality and without fixing specific boundary conditions, the symmetry and charge analysis near a generic null surface for two and three dimensional ($2d$ and $3d$) gravity theories. In $2d$ and $3d$ there are respectively two and three charges which are generic functions over the codimension one null surface. The integrability of charges and their algebra depend on the state-dependence of symmetry generators which is a priori not specified. We establish the existence of infinitely many choices that render the surface charges integrable. We show that there is a choice, the ``fundamental basis'', where the null boundary symmetry algebra is the Heisenberg $\oplus$Diff($d-2$) algebra. We expect this result to be true for $d>3$ when there is no Bondi news through the null surface.
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