Kiliani–Fischer synthesis of (+)-glyceraldehyde was performed three times to get a hexose. Determine the identity of the hexose based on the following experimental data:

(i) an optically inactive aldaric acid is formed by oxidation of the hexose with nitric acid

(ii) an optically active aldaric acid is formed when the hexose undergoes Wohl degradation followed by nitric acid oxidation

(iii) and D-threose is formed by a second Wohl degradation