Sloth
Wild sloths typically achieve 20 to 30 years of unhurried existence, with captive specimens occasionally reaching 40. The Monteverde Sloth Sanctuary recorded one individual, designated 'Patient Margaret', who lived to 43 years whilst maintaining what staff described as 'absolute commitment to her sedentary principles.'
Glacier
Antarctic ice cores contain glacial ice exceeding 800,000 years of age, with some formations dating to 2.7 million years. The Greenland Ice Sheet has persisted for approximately three million years, though researchers at the Nordic Institute for Glacial Permanence note with some concern that this figure may require downward revision within the century.
Individual glaciers may form, advance, retreat, and vanish within mere centuries, but the concept of glaciation has demonstrated remarkable staying power.
VERDICT
The mathematics prove insurmountable. A sloth's lifetime represents a rounding error in glacial timescales. The glacier secures this criterion through the simple advantage of existing before sloths evolved and likely persisting after they have departed, climate change permitting.