How would you explain superposition to a smart twelve year old, no analogies allowed

[BretHart88]

Every explanation of superposition leans on the same tired coin flip or Schrodinger's cat setup, and both analogies actually mislead more than they clarify because they imply the particle has a definite state we just don't know yet, when the actual physics says something stranger, the particle exists in a combination of states until measurement forces one outcome

Try explaining it using only the actual math or the actual experimental behavior, no cats, no coins, no dice

Bonus points if your explanation would survive a physicist reading over your shoulder

[SašaJelenič]

A quantum system's state is a probability distribution across every possible outcome simultaneously, measurement collapses that distribution to a single value, and nothing about the particle was secretly fixed before that collapse happened