Step 1: The clinical setting is a cirrhotic with ascites who develops infection of that fluid, called spontaneous bacterial peritonitis. The fastest bedside diagnostic tool is a tap of the fluid sent for a cell count.
Step 2: The defining laboratory cut-off is a neutrophil count exceeding 250 per cubic millimetre in the ascitic fluid. Crossing this number signals acute infection and is enough to start antibiotics even before culture returns.
Step 3: Check why the distractors fail. Infection drives white cells up, so a very low white cell count below 100 is not supportive. Lactate actually rises above 25 mg/dL in active infection, so a low lactate is wrong. The pH falls in infection, so a high pH over 7.35 also points away from disease.
Step 4: Only the raised neutrophil count fits the diagnosis.
\[\boxed{\text{Neutrophils} > 250/\text{mm}^3}\]