No, we cannot.
Though many of the products we’ve made have serial numbers on them, we don’t maintain a database of these numbers to cross-reference by product and date of manufacture. Nor do we have any such file for current products. At present, the serial numbers are used in the manufacturing process only.
You can use the serial number to identify your particular scope for personal purposes (e.g., noting for insurance records, etc.). Just be aware that we will not be able to provide any information for you based on a serial number.