~てある
Curiosity
How do you say "the window is open" meaning "someone deliberately opened it and left it so"? How does it differ from intransitive te-iru?
Intuition
te-aru focuses on the result left by someone's intention. It uses a transitive verb but hides the doer, presenting only the resulting state with aru ("exist"). It pairs with intransitive + te-iru (a state that just is).
Visualization
oku (put) → oite (te-form) → oite aru (has been put / is placed). A transitive verb passes through the te-form into a resulting state.
Essence
Transitive te-form + aru (oite aru, kaite aru). The object is usually marked with ga (memo ga kaite aru). Contrast with intransitive te-iru (doa ga aite iru, "the door is open"): te-aru implies "someone did it." It connects to the preparatory te-oku (yoyaku shite aru).
Examples
Mini-quiz
Which expresses "a memo has been written (left in that state)"?