Final answer:
Anti-P is the biphasic auto-antibody associated with paroxysmal cold hemoglobinuria, identifiable through the Donath-Landsteiner test.
Step-by-step explanation:
The biphasic auto-antibody is the Anti-P antibody. Antibodies like Anti-P can react at different temperatures and are involved in paroxysmal cold hemoglobinuria, a condition where the individual's immune system mistakenly attacks and destroys red blood cells. In the biphasic hemolysin test, also known as the Donath-Landsteiner test, this antibody is identifiable because it binds to red blood cells in the cold and then causes red blood cell lysis when warmed.