Does persist trigger if the creature is destroyed by a state-based action due to having zero toughness?

Persist reads: "When this creature is put into a graveyard from the battlefield, if it had no -1/-1 counters on it, return it to the battlefield under its owner's control with a -1/-1 counter on it." The trigger condition is being put into the graveyard from the battlefield — that part is met — but the key issue is that persist, as a keyword, functions correctly only when the permanent dies (i.e., is destroyed or sacrificed). Wait — actually, let's be precise.

Persist's trigger watches for the creature being put into the graveyard from the battlefield (CR 702.79a). It does NOT require the creature to be "destroyed" specifically — the trigger fires whenever the creature hits the graveyard from the battlefield with no -1/-1 counters. A creature with 0 or less toughness is moved to the graveyard by a state-based action under CR 704.5f, which is NOT destruction — it is simply a state-based action. However, persist's trigger text does not say "when this creature is destroyed" — it says "when put into a graveyard from the battlefield."

Therefore, persist does trigger even when the creature is put into the graveyard due to having 0 or less toughness via state-based actions. The creature is still being put into the graveyard from the battlefield (CR 704.5f), satisfying the trigger condition in CR 702.79a, as long as it had no -1/-1 counters at the time it last existed on the battlefield.

Concrete example: You control Strangleroot Geist (2/1 with persist... actually undying, but for illustration) — instead, consider Murderous Redcap with no -1/-1 counters. Your opponent enchants it with a -0/-2 aura, reducing it to 0 toughness. State-based actions put it into the graveyard (CR 704.5f). Persist triggers, and Murderous Redcap returns to the battlefield with a -1/-1 counter, becoming a 1/0... which immediately dies again without retriggering.

In summary: persist does trigger on a 0-toughness state-based-action death. The trigger cares only that the creature was put into the graveyard from the battlefield with no -1/-1 counters, regardless of the cause (CR 702.79a, CR 704.5f).