Solve the 12-coin balance puzzle

Using a balance scale with no weights and exactly three weighings, you have 12 visually identical coins, one of which is counterfeit and either heavier or lighter (unknown). Provide a weighing strategy that always identifies the counterfeit coin and whether it is heavier or lighter. Present the full decision tree: for each weighing, which coins go on each pan and how the next step depends on outcomes (left heavy, right heavy, or balance). Prove correctness and minimality of three weighings.