Solution graph eq45
\[u_y\,u_{xy} - u_x\,u_{yy} = u_{yyy}\]
boundary layer; test problem 4
Partially solved
Families found: 2 / 11
Judge: Solutions verified
Solution process: strong
Lean: 12 / 23
Partially solved. Some of the reference solution families were found: 2 of 11. Completeness is not established; this conclusion matches the reference.
How to read the graph
The graph shows how the agent solved the problem, left to right. The answer is in the ★ solution nodes; everything to their left is how it was obtained.
- Problem
- the original equation, the root of the graph.
- Idea N
- a solution plan the agent formulated before trying.
- Variant N
- an attempt along idea N: “✓ gave a solution” or “dead end” (no solution; the whole branch is hidden by the filter).
- ★ Solution N
- the final solution of variant N — a finished answer. “matches reference” — the judge matched it to a solution family of the handbook; “Lean ✓” — its formal part compiles.
- Completeness → Step N
- the argument that there are no other solutions: steps and their solutions; ∎ Completeness conclusion — the result of this branch, if the agent stated one.
- Subtasks, fragments
- (toggle) how a variant was carried out: subtasks and their solutions; green fragments made it into the final solution.
- Judge
- (toggle) LLM-judge nodes: checks of solutions, comparison with the reference, the verdict.
Click a node to see its text, Lean code and check result; “Where it leads” in the panel is the node’s subtree.
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Prompts and raw model outputs are not shown; reference solutions and the judge's retelling of them are hidden.