{"taskid":"9b90d918682fc656decddf7c56a20f266743cf37bb9c689885f83ffb3cae1c2ei0","node":"witness","claimid":"05614c2563cae40b5a47c883aff11590da3feda00f8bd8faac26aa93ff8954d7i0","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":"5c268d9edfa490055b9e5b5684cc252f2f6335c3f0baca4432a9776701f8292a"},"hash":"4dba8c30378d72da08e47d240995a73538b848888d98a69632448733d353dc22","contentType":"application/json;utf-8","attachment":"metafile://50616d9738d789344cb6f696194e6f5d5a2c82389c99a1fd396b59307ca8e364i0.md","childids":[]}