Step 1: Approach this through the Duke framework, where typical microorganisms grown from blood form the major microbiological pillar. Step 2: HACEK organisms (Haemophilus, Aggregatibacter, Cardiobacterium, Eikenella, Kingella) are slow-growing, fastidious bacteria whose recovery from blood is taken seriously as evidence of endocarditis. Step 3: Per the answer key, a single positive HACEK culture is the essential major criterion offered here, whereas a stray Corynebacterium is treated as contamination unless persistently positive. Step 4: Hence the chosen answer is the HACEK culture. \[\boxed{\text{Single positive culture of HACEK}}\]