Start with what Proteus does to the urine. This organism manufactures the enzyme urease, which cleaves urea into ammonia and carbon dioxide. The ammonia drives the urinary pH upward, making the urine strongly alkaline.
An alkaline, ammonia-laden environment is precisely the chemistry needed to crystallise magnesium ammonium phosphate, known as struvite or triple phosphate. Because they grow in the setting of infection, these are termed infection stones and are notorious for filling the renal pelvis as staghorn calculi.
The distractors fail because they require different conditions. Uric acid and xanthine calculi precipitate when the urine is acidic, the opposite of what Proteus creates. Calcium oxalate stones, although the commonest type, arise from metabolic factors and have no special tie to urease-splitting organisms. Hence the stone linked to Proteus is triple phosphate.
\[\boxed{\text{Triple phosphate (struvite)}}\]