Punctiliousness is a habit of paying extremely close attention to rules and details, and following them to a T. Your tendency to arrive five minutes early, no matter what? That's your punctiliousness at work.
The word punctiliousness goes back to the Italian puntiglio, "fine point." People who take note of life's fine points and small details, from a library book's due date to the beach rules about leashing their dog, possess the quality of punctiliousness. You could also use the words fastidiousness and meticulousness to capture this characteristic.