The idea that everything that has happened will happen again, exactly, endlessly: held as physics by the Stoics, offered as a test of the soul by Nietzsche, and given a mathematical shadow by Poincare.
Documented
Stoic fire, Nietzsche's demon, Poincare's theorem
Documented triple ancestry. The Stoics taught ekpyrosis, the cosmos periodically consumed by fire and reborn identically. Nietzsche's Gay Science (1882, aphorism 341) introduced the demon's question, and his notebooks show he briefly chased scientific proof before settling for the thought as an existential filter. Poincare's recurrence theorem (1890) proved that a finite bounded mechanical system returns arbitrarily close to any initial state, given inconceivable time.
Assessment: All documented, three different claims wearing one name: a cosmology, a psychological gauntlet, and a theorem. Only the theorem is proven, and it does not say what the cosmologists want it to say.
Stories
The wheel that cultures keep inventing
The folk version is humanity's second-oldest model of time: yugas cycling, kalpas turning, the Mayan baktun, the seasons as rehearsal for eternity. Linear time, one beginning, one end, is the historical exception; the wheel is the rule, and eternal recurrence is the wheel with the metaphysics left in.
Assessment: Documented across civilizations as the default cosmology. Its psychological function is documented too: a cyclical cosmos tames death by promising returns, at the price of novelty. Every culture chose its poison.
Interesting claims
The quantum reruns
The interesting claim is the modern physics echo: in an eternal universe with finite entropy states, Boltzmann fluctuations must eventually reassemble this moment, you reading this sentence, infinitely many times; some eternal-inflation models imply identical Hubble volumes recurring without end. The Arrow of Time files its objection: entropy may forbid the bounded system the theorem requires.
Assessment: Documented as a consequence cosmologists actively argue about, unprovable on any human timescale. The recurrence literature is where physics meets Nietzsche's demon and both look uncomfortable. Genuine question, zero checkable content.
Sources and further reading
Nietzsche, The Gay Science, aphorism 341 (1882), the demon
Nietzsche's Nachlass notebooks, the abandoned proof attempt
Stoic fragments on ekpyrosis, via Diogenes Laertius and Nemesius
Poincare, Sur le probleme des trois corps (1890), the recurrence theorem
Boltzmann-fluctuation and eternal-inflation recurrence literature
Worth asking
If the offer arrived tonight, same life, no edits, infinite reruns, what would you change by morning?