TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Components: The titanium compound is an organic chelate titanium complex having an organic acid as a ligand. The phosphorus compound is a compound having formula (RO)3P=O. The mass content of titanium element in the composition is greater than 1 ppm to less than or equal to 30 ppm, and the mass content of phosphorus element in the composition is greater than 50 ppm to less than or equal to 90 ppm. The amount of terminal COOH groups contained in the composition is less than or equal to 25 eq/t. The content of the phosphorus compound in the addition solution is 1-10% by mass with respect to a total mass of the addition solution.R=1-3C alkyl.    TECHNOLOGY FOCUS - POLYMERS - Preferred Composition: The composition (C1) further comprises at least one metal ( greater than or equal to 50 parts per million (ppm) by mass) selected from an alkali metal, an alkaline earth metal, an iron-group metal, manganese, tin, lead, and zinc. Preferred Method: The method further involves adding a compound containing at least one metal selected from an alkali metal, an alkaline earth metal, an iron-group metal, manganese, tin, lead, and zinc to the reaction liquid before the addition of the phosphorus compound. The addition of the phosphorus compound is performed by adding an addition solution, which is prepared by dissolving the phosphorus compound in a solution containing the diol component at 25 degrees C, to the reaction liquid before step (i) is terminated. The polymerization temperature is less than or equal to 280 degrees C; and the method further involves performing solid-state polymerization of the condensation polymerization product obtained in step (ii). The solid-state polymerization is performed under a pressure of 1-1000 Pa, or is performed in a nitrogen atmosphere. EXAMPLE - High purity terephthalic acid (4.7 tons) and ethylene glycol (1.8 tons) were mixed over 90 minutes to form slurry and was continuously supplied to a first esterification reactor. VERTEC AC-420 (RTM: ethylene glycol solution of a citric acid chelate titanium complex having citric acid coordinated to Ti (titanium) metal) was supplied continuously. Reaction was carried out at a reactor inside temperature of 250 degrees C and an average retention time of 4.3 hours with stirring. The citric acid chelate titanium complex was continuously added in a manner that the addition amount of Ti element was 9 ppm. The acid value of the resulting oligomer was 600 eq/t. The resulting reaction mixture was transferred to a second esterification reactor tank, and reacted with stirring at a reactor inside temperature of 250 degrees C and an average retention time of 1.2 hours, so that an oligomer having an acid value of 200 eq/t was obtained. The inside of the second esterification reactor tank was parted into three zones. At a second zone, an ethylene glycol solution of magnesium acetate was continuously supplied in a manner that the addition amount of magnesium (Mg) element was 75 ppm. After that, at a third zone, an ethylene glycol solution of trimethyl phosphate was continuously supplied in a manner that the addition amount of P (phosphorus) element was 65 ppm. In this manner, an esterification reaction product was obtained. The ethylene glycol solution of trimethyl phosphate was prepared by adding a 25 degrees C trimethyl phosphate liquid to a 25 degrees C ethylene glycol liquid, and stirring at 25 degrees C for 2 hours (where the phosphate compound content in the solution was 3.8% by mass). The esterification reaction product obtained was supplied continuously to a first condensation polymerization reactor tank. Condensation polymerization (transesterification reaction) was carried out with stirring at a reaction temperature of 270 degrees C, a reactor inside pressure of 20 Torr, and an average retention time of 1.8 hours. Further, the reaction product was transferred from the first condensation polymerization reactor tank to a second condensation polymerization reactor tank. In this reactor tank, reaction (transesterification reaction) was carried out with stirring at a reactor inside temperature of 276 degrees C, a reactor inside pressure of 5 Torr, and a retention time of 1.2 hours. After that, the reaction product was transferred from the second condensation polymerization reactor tank to a third condensation polymerization reactor tank. In this reactor tank, reaction (transesterification reaction) was carried out at a reactor inside temperature of 278 degrees C, a reactor inside pressure of 1.5 Torr and retention time of 1.5 hours, so that a reaction product (polyethylene terephthalate (PET)) was obtained. Then, the resulting reaction product was extruded into cold water in a strand form and immediately cut, so that polyester resin composition pellets were prepared. The pellets obtained were subjected to heat treatment under a reduced pressure of 50 Pa at 210 degrees C for 30 hours with a rotary vacuum polymerization apparatus. After that, 25 degrees C nitrogen gas was passed through the vacuum polymerization apparatus to cool the pellets to 25 degrees C. In this way, a polyester resin composition was obtained. The composition contained a titanium content of 9 ppm, magnesium content of 75 ppm, and phosphorus content of 60 ppm; and showed a Log R of 6.5, and retention half-life of elongation at break (hour) of 3000.