Solution graph eq52: ∀ x y, (D1 (D2 u) x y) ^ 2 - D1 (D1 u) x y * D2 (D2 u) x y = f x * (u x y) ^ k

The graph reads left to right. Problem — the original equation. Idea — a solution plan the agent formulated before trying. Variant — an attempt to solve along the idea; a successful variant ends in a ★ final solution. A variant is carried out by an implementation: subtasks whose solutions (fragments) are assembled into the final solution — only some fragments make it into the result. A dead end is a variant that produced no solution: its whole branch (implementation, subtasks, fragments) is not part of the result. Completeness is a separate branch: the argument that there are no other solutions.