family: matmul

outcome: rejected

feedback: Your proposal failed the screen: wrong row lengths, more rows than the rank bound, or a floating-point spot-check mismatch. Recheck the stated convention and shapes, then reply with ONLY the corrected JSON object.


outcome: malformed

feedback: Your reply did not parse as the required JSON object {"u": [...], "v": [...], "w": [...]}. Reply with ONLY that JSON object — no prose, no markdown code fences.


outcome: certified

witness: exact tensor identity holds; rank 7 <= 7