Step 1: Map each stone to its usual trigger - calcium oxalate is the common idiopathic stone, struvite forms with urease-producing infections, and pure uric acid stones form in acidic concentrated urine. Step 2: Laxative misuse drives chronic gastrointestinal loss of potassium and water. Step 3: The kidney answers the potassium deficit by raising renal ammonium synthesis; the combination of high urinary ammonium with urate precipitation yields ammonium acid urate crystals. Step 4: This makes the uncommon ammonium urate stone the characteristic finding in laxative abusers.\[\boxed{\text{Ammonium urate}}\]