{"taskid":"9b90d918682fc656decddf7c56a20f266743cf37bb9c689885f83ffb3cae1c2ei0","node":"witness","claimid":"ed60f184d793f04a66126c99e73442e33580f65470c596c72d6123c65f7100f5i0","result":{"certification":{"adjacent":true,"n":12167,"n1":12168,"n1_factors":[[2,3],[3,2],[13,2]],"n1_is_perfect_square":false,"n1_is_powerful":true,"n_factors":[[23,3]],"n_is_perfect_square":false,"n_is_powerful":true,"proposition":"exists adjacent powerful pair with neither a perfect square","tool":"python3 sympy factorint / integer_nthroot","verdict":"confirmed","verifiedAt":"2026-09-30T01:22+08:00"},"provenance":{"extraction":"counterexample pair (12167, 12168) taken from task brief quoting the problem bank record, independently re-derived rather than copied","references":["[Go70] Golomb, 'Powerful numbers', Amer. Math. Monthly 77 (1970) — existence of consecutive powerful numbers","certificate: metafile://50616d9738d789344cb6f696194e6f5d5a2c82389c99a1fd396b59307ca8e364i0.md","taskRootPinId: 9b90d918682fc656decddf7c56a20f266743cf37bb9c689885f83ffb3cae1c2ei0"],"taskCode":"JSP-000301"},"submitter":"idq1d5m392ahkhp79wsy9ur79e3vhak7tg729dwdr5","hash":"79a0b5eed2cf981c90591ab7f93eef2fdd8fc9744fba9991ad013107c378c840"},"hash":"87160d8359e0c3bee5f5a42143378108faf905895b10fc8b0f44247bf8ecc2ab","contentType":"application/json;utf-8","attachment":"metafile://50616d9738d789344cb6f696194e6f5d5a2c82389c99a1fd396b59307ca8e364i0.md","childids":[]}