We report ALMA observations of NGC 1052 to quest mass accretion in a gas-poor active galactic nucleus (AGN). We detected CO emission representing a rotating ring-like circumnuclear disk (CND) seen edge-on with the gas mass of $5.3 times 10^{5}$ M$_{odot}$. The CND has smaller gas mass than that in typical Seyfert galaxies with circumnuclear star formation and is too gas-poor to drive mass accretion onto the central engine. The continuum emission casts molecular absorption features of CO, HCN, HCO$^+$, SO, SO$_2$, CS, CN, and H$_2$O, with H$^{13}$CN and HC$^{15}$N and vibrationally-excited (v$_2 = 1$) HCN and HCO$^+$. Broader absorption line widths than CND emission line widths imply presence of a geometrically thick molecular torus with a radius of $2.4 pm 1.3$ pc and a thickness ratio of $0.7 pm 0.3$. We estimate the H$_2$ column density of $(3.3 pm 0.7) times 10^{25}$ cm$^{-2}$ using H$^{12}$CN, H$^{13}$CN, and HCO$^{+}$ absorption features and adopting abundance ratio of $^{12}$C-to-$^{13}$C and a HCO$^{+}$-to-H$_2$, and derived the torus gas mass of $(1.3 pm 0.3) times 10^7$ M$_{odot}$, which is $sim 9$% of the central black-hole mass. The molecular gas in the torus is clumpy with the estimated covering factor of $0.17^{+0.06}_{-0.03}$. The gas density of clumps inside the torus is inferred to be $(6.4 pm 1.3) times 10^7$ cm$^{-3}$, which meets the excitation conditions of H$_2$O maser. Specific angular momentum in the torus exceeds a flat-rotation curve extrapolated from that of the CND, indicating a Keplerian rotation inside a 14.4-pc sphere of influence.
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