{"abstract":"The bounded binomial link certificate reports an incorrect root set.","category":"Heap invariants","checks":7,"contract":"Link two equal-rank binomial roots a and b, each [id,key,rank,child_ids]. Ties keep a. Return winner, loser, winner rank, child-chain prepend, comparison cost, and removed-root identities. Certificate input is two distinct roots of equal rank.","contract_signature":"d","evaluation_group":"s3-heap-model-binomial-link","failed_approach":"The local patch uses [l[0]] and still violates the stated relation.","family":"s3-heap-binomial-link-root_set","id":"FA-40016","implementations":{"attempt":{"sha256":"3cbdd5ef7e0b0e2d5219609061806b89b88fd94cd7fe883b72eee0643d96b4b4","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    a=d['a']; b=d['b']; w,l=(a,b) if a[1]<=b[1] else (b,a)\n    return {'winner': w[0],\n    'loser': l[0],\n    'new_rank': w[2]+1,\n    'children': [l[0]]+w[3],\n    'parent_updates': [[l[0],w[0]]],\n    'root_set': [l[0]]}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'a': [8, 2, 0, []], 'b': [3, 5, 0, []]}, {'winner': 8, 'loser': 3, 'new_rank': 1, 'children': [3], 'parent_updates': [[3, 8]], 'root_set': [8]}), ({'a': [2, 9, 0, []], 'b': [7, 1, 0, []]}, {'winner': 7, 'loser': 2, 'new_rank': 1, 'children': [2], 'parent_updates': [[2, 7]], 'root_set': [7]}), ({'a': [5, 4, 1, [1]], 'b': [9, 4, 1, [3]]}, {'winner': 5, 'loser': 9, 'new_rank': 2, 'children': [9, 1], 'parent_updates': [[9, 5]], 'root_set': [5]}), ({'a': [4, 8, 2, [10, 11]], 'b': [6, 3, 2, [12, 13]]}, {'winner': 6, 'loser': 4, 'new_rank': 3, 'children': [4, 12, 13], 'parent_updates': [[4, 6]], 'root_set': [6]}), ({'a': [1, 0, 3, [2, 3, 4]], 'b': [9, 8, 3, [10, 11, 12]]}, {'winner': 1, 'loser': 9, 'new_rank': 4, 'children': [9, 2, 3, 4], 'parent_updates': [[9, 1]], 'root_set': [1]}), ({'a': [7, 5, 1, [8]], 'b': [2, 2, 1, [3]]}, {'winner': 2, 'loser': 7, 'new_rank': 2, 'children': [7, 3], 'parent_updates': [[7, 2]], 'root_set': [2]}), ({'a': [7, 6, 1, [8]], 'b': [2, 2, 1, [3]]}, {'winner': 2, 'loser': 7, 'new_rank': 2, 'children': [7, 3], 'parent_updates': [[7, 2]], 'root_set': [2]})], [({'a': [8, 2, 0, []], 'b': [3, 5, 0, []]}, {'winner': 8, 'loser': 3, 'new_rank': 1, 'children': [3], 'parent_updates': [[3, 8]], 'root_set': [8]}), ({'a': [2, 9, 0, []], 'b': [7, 1, 0, []]}, {'winner': 7, 'loser': 2, 'new_rank': 1, 'children': [2], 'parent_updates': [[2, 7]], 'root_set': [7]}), ({'a': [5, 4, 1, [1]], 'b': [9, 4, 1, [3]]}, {'winner': 5, 'loser': 9, 'new_rank': 2, 'children': [9, 1], 'parent_updates': [[9, 5]], 'root_set': [5]}), ({'a': [4, 8, 2, [10, 11]], 'b': [6, 3, 2, [12, 13]]}, {'winner': 6, 'loser': 4, 'new_rank': 3, 'children': [4, 12, 13], 'parent_updates': [[4, 6]], 'root_set': [6]}), ({'a': [1, 0, 3, [2, 3, 4]], 'b': [9, 8, 3, [10, 11, 12]]}, {'winner': 1, 'loser': 9, 'new_rank': 4, 'children': [9, 2, 3, 4], 'parent_updates': [[9, 1]], 'root_set': [1]}), ({'a': [7, 5, 1, [8]], 'b': [2, 2, 1, [3]]}, {'winner': 2, 'loser': 7, 'new_rank': 2, 'children': [7, 3], 'parent_updates': [[7, 2]], 'root_set': [2]}), ({'a': [7, 7, 1, [8]], 'b': [2, 2, 1, [3]]}, {'winner': 2, 'loser': 7, 'new_rank': 2, 'children': [7, 3], 'parent_updates': [[7, 2]], 'root_set': [2]})], [({'a': [8, 2, 0, []], 'b': [3, 5, 0, []]}, {'winner': 8, 'loser': 3, 'new_rank': 1, 'children': [3], 'parent_updates': [[3, 8]], 'root_set': [8]}), ({'a': [2, 9, 0, []], 'b': [7, 1, 0, []]}, {'winner': 7, 'loser': 2, 'new_rank': 1, 'children': [2], 'parent_updates': [[2, 7]], 'root_set': [7]}), ({'a': [5, 4, 1, [1]], 'b': [9, 4, 1, [3]]}, {'winner': 5, 'loser': 9, 'new_rank': 2, 'children': [9, 1], 'parent_updates': [[9, 5]], 'root_set': [5]}), ({'a': [4, 8, 2, [10, 11]], 'b': [6, 3, 2, [12, 13]]}, {'winner': 6, 'loser': 4, 'new_rank': 3, 'children': [4, 12, 13], 'parent_updates': [[4, 6]], 'root_set': [6]}), ({'a': [1, 0, 3, [2, 3, 4]], 'b': [9, 8, 3, [10, 11, 12]]}, {'winner': 1, 'loser': 9, 'new_rank': 4, 'children': [9, 2, 3, 4], 'parent_updates': [[9, 1]], 'root_set': [1]}), ({'a': [7, 5, 1, [8]], 'b': [2, 2, 1, [3]]}, {'winner': 2, 'loser': 7, 'new_rank': 2, 'children': [7, 3], 'parent_updates': [[7, 2]], 'root_set': [2]}), ({'a': [7, 8, 1, [8]], 'b': [2, 2, 1, [3]]}, {'winner': 2, 'loser': 7, 'new_rank': 2, 'children': [7, 3], 'parent_updates': [[7, 2]], 'root_set': [2]})], [({'a': [8, 2, 0, []], 'b': [3, 5, 0, []]}, {'winner': 8, 'loser': 3, 'new_rank': 1, 'children': [3], 'parent_updates': [[3, 8]], 'root_set': [8]}), ({'a': [2, 9, 0, []], 'b': [7, 1, 0, []]}, {'winner': 7, 'loser': 2, 'new_rank': 1, 'children': [2], 'parent_updates': [[2, 7]], 'root_set': [7]}), ({'a': [5, 4, 1, [1]], 'b': [9, 4, 1, [3]]}, {'winner': 5, 'loser': 9, 'new_rank': 2, 'children': [9, 1], 'parent_updates': [[9, 5]], 'root_set': [5]}), ({'a': [4, 8, 2, [10, 11]], 'b': [6, 3, 2, [12, 13]]}, {'winner': 6, 'loser': 4, 'new_rank': 3, 'children': [4, 12, 13], 'parent_updates': [[4, 6]], 'root_set': [6]}), ({'a': [1, 0, 3, [2, 3, 4]], 'b': [9, 8, 3, [10, 11, 12]]}, {'winner': 1, 'loser': 9, 'new_rank': 4, 'children': [9, 2, 3, 4], 'parent_updates': [[9, 1]], 'root_set': [1]}), ({'a': [7, 5, 1, [8]], 'b': [2, 2, 1, [3]]}, {'winner': 2, 'loser': 7, 'new_rank': 2, 'children': [7, 3], 'parent_updates': [[7, 2]], 'root_set': [2]}), ({'a': [7, 9, 1, [8]], 'b': [2, 2, 1, [3]]}, {'winner': 2, 'loser': 7, 'new_rank': 2, 'children': [7, 3], 'parent_updates': [[7, 2]], 'root_set': [2]})], [({'a': [8, 2, 0, []], 'b': [3, 5, 0, []]}, {'winner': 8, 'loser': 3, 'new_rank': 1, 'children': [3], 'parent_updates': [[3, 8]], 'root_set': [8]}), ({'a': [2, 9, 0, []], 'b': [7, 1, 0, []]}, {'winner': 7, 'loser': 2, 'new_rank': 1, 'children': [2], 'parent_updates': [[2, 7]], 'root_set': [7]}), ({'a': [5, 4, 1, [1]], 'b': [9, 4, 1, [3]]}, {'winner': 5, 'loser': 9, 'new_rank': 2, 'children': [9, 1], 'parent_updates': [[9, 5]], 'root_set': [5]}), ({'a': [4, 8, 2, [10, 11]], 'b': [6, 3, 2, [12, 13]]}, {'winner': 6, 'loser': 4, 'new_rank': 3, 'children': [4, 12, 13], 'parent_updates': [[4, 6]], 'root_set': [6]}), ({'a': [1, 0, 3, [2, 3, 4]], 'b': [9, 8, 3, [10, 11, 12]]}, {'winner': 1, 'loser': 9, 'new_rank': 4, 'children': [9, 2, 3, 4], 'parent_updates': [[9, 1]], 'root_set': [1]}), ({'a': [7, 5, 1, [8]], 'b': [2, 2, 1, [3]]}, {'winner': 2, 'loser': 7, 'new_rank': 2, 'children': [7, 3], 'parent_updates': [[7, 2]], 'root_set': [2]}), ({'a': [7, 10, 1, [8]], 'b': [2, 2, 1, [3]]}, {'winner': 2, 'loser': 7, 'new_rank': 2, 'children': [7, 3], 'parent_updates': [[7, 2]], 'root_set': [2]})]][N-1]\ncheck('regression certificate 1', solve(cases[0][0]), cases[0][1])\ncheck('regression certificate 2', solve(cases[1][0]), cases[1][1])\ncheck('regression certificate 3', solve(cases[2][0]), cases[2][1])\ncheck('regression certificate 4', solve(cases[3][0]), cases[3][1])\ncheck('regression certificate 5', solve(cases[4][0]), cases[4][1])\ncheck('regression certificate 6', solve(cases[5][0]), cases[5][1])\ncheck('variant-dependent certificate', solve(cases[6][0]), cases[6][1])\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"950636cfd7c32623abd09e39b7c93269db908f645d3807a76b5538d49469c12f","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    a=d['a']; b=d['b']; w,l=(a,b) if a[1]<=b[1] else (b,a)\n    return {'winner': w[0],\n    'loser': l[0],\n    'new_rank': w[2]+1,\n    'children': [l[0]]+w[3],\n    'parent_updates': [[l[0],w[0]]],\n    'root_set': [a[0],b[0]]}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'a': [8, 2, 0, []], 'b': [3, 5, 0, []]}, {'winner': 8, 'loser': 3, 'new_rank': 1, 'children': [3], 'parent_updates': [[3, 8]], 'root_set': [8]}), ({'a': [2, 9, 0, []], 'b': [7, 1, 0, []]}, {'winner': 7, 'loser': 2, 'new_rank': 1, 'children': [2], 'parent_updates': [[2, 7]], 'root_set': [7]}), ({'a': [5, 4, 1, [1]], 'b': [9, 4, 1, [3]]}, {'winner': 5, 'loser': 9, 'new_rank': 2, 'children': [9, 1], 'parent_updates': [[9, 5]], 'root_set': [5]}), ({'a': [4, 8, 2, [10, 11]], 'b': [6, 3, 2, [12, 13]]}, {'winner': 6, 'loser': 4, 'new_rank': 3, 'children': [4, 12, 13], 'parent_updates': [[4, 6]], 'root_set': [6]}), ({'a': [1, 0, 3, [2, 3, 4]], 'b': [9, 8, 3, [10, 11, 12]]}, {'winner': 1, 'loser': 9, 'new_rank': 4, 'children': [9, 2, 3, 4], 'parent_updates': [[9, 1]], 'root_set': [1]}), ({'a': [7, 5, 1, [8]], 'b': [2, 2, 1, [3]]}, {'winner': 2, 'loser': 7, 'new_rank': 2, 'children': [7, 3], 'parent_updates': [[7, 2]], 'root_set': [2]}), ({'a': [7, 6, 1, [8]], 'b': [2, 2, 1, [3]]}, {'winner': 2, 'loser': 7, 'new_rank': 2, 'children': [7, 3], 'parent_updates': [[7, 2]], 'root_set': [2]})], [({'a': [8, 2, 0, []], 'b': [3, 5, 0, []]}, {'winner': 8, 'loser': 3, 'new_rank': 1, 'children': [3], 'parent_updates': [[3, 8]], 'root_set': [8]}), ({'a': [2, 9, 0, []], 'b': [7, 1, 0, []]}, {'winner': 7, 'loser': 2, 'new_rank': 1, 'children': [2], 'parent_updates': [[2, 7]], 'root_set': [7]}), ({'a': [5, 4, 1, [1]], 'b': [9, 4, 1, [3]]}, {'winner': 5, 'loser': 9, 'new_rank': 2, 'children': [9, 1], 'parent_updates': [[9, 5]], 'root_set': [5]}), ({'a': [4, 8, 2, [10, 11]], 'b': [6, 3, 2, [12, 13]]}, {'winner': 6, 'loser': 4, 'new_rank': 3, 'children': [4, 12, 13], 'parent_updates': [[4, 6]], 'root_set': [6]}), ({'a': [1, 0, 3, [2, 3, 4]], 'b': [9, 8, 3, [10, 11, 12]]}, {'winner': 1, 'loser': 9, 'new_rank': 4, 'children': [9, 2, 3, 4], 'parent_updates': [[9, 1]], 'root_set': [1]}), ({'a': [7, 5, 1, [8]], 'b': [2, 2, 1, [3]]}, {'winner': 2, 'loser': 7, 'new_rank': 2, 'children': [7, 3], 'parent_updates': [[7, 2]], 'root_set': [2]}), ({'a': [7, 7, 1, [8]], 'b': [2, 2, 1, [3]]}, {'winner': 2, 'loser': 7, 'new_rank': 2, 'children': [7, 3], 'parent_updates': [[7, 2]], 'root_set': [2]})], [({'a': [8, 2, 0, []], 'b': [3, 5, 0, []]}, {'winner': 8, 'loser': 3, 'new_rank': 1, 'children': [3], 'parent_updates': [[3, 8]], 'root_set': [8]}), ({'a': [2, 9, 0, []], 'b': [7, 1, 0, []]}, {'winner': 7, 'loser': 2, 'new_rank': 1, 'children': [2], 'parent_updates': [[2, 7]], 'root_set': [7]}), ({'a': [5, 4, 1, [1]], 'b': [9, 4, 1, [3]]}, {'winner': 5, 'loser': 9, 'new_rank': 2, 'children': [9, 1], 'parent_updates': [[9, 5]], 'root_set': [5]}), ({'a': [4, 8, 2, [10, 11]], 'b': [6, 3, 2, [12, 13]]}, {'winner': 6, 'loser': 4, 'new_rank': 3, 'children': [4, 12, 13], 'parent_updates': [[4, 6]], 'root_set': [6]}), ({'a': [1, 0, 3, [2, 3, 4]], 'b': [9, 8, 3, [10, 11, 12]]}, {'winner': 1, 'loser': 9, 'new_rank': 4, 'children': [9, 2, 3, 4], 'parent_updates': [[9, 1]], 'root_set': [1]}), ({'a': [7, 5, 1, [8]], 'b': [2, 2, 1, [3]]}, {'winner': 2, 'loser': 7, 'new_rank': 2, 'children': [7, 3], 'parent_updates': [[7, 2]], 'root_set': [2]}), ({'a': [7, 8, 1, [8]], 'b': [2, 2, 1, [3]]}, {'winner': 2, 'loser': 7, 'new_rank': 2, 'children': [7, 3], 'parent_updates': [[7, 2]], 'root_set': [2]})], [({'a': [8, 2, 0, []], 'b': [3, 5, 0, []]}, {'winner': 8, 'loser': 3, 'new_rank': 1, 'children': [3], 'parent_updates': [[3, 8]], 'root_set': [8]}), ({'a': [2, 9, 0, []], 'b': [7, 1, 0, []]}, {'winner': 7, 'loser': 2, 'new_rank': 1, 'children': [2], 'parent_updates': [[2, 7]], 'root_set': [7]}), ({'a': [5, 4, 1, [1]], 'b': [9, 4, 1, [3]]}, {'winner': 5, 'loser': 9, 'new_rank': 2, 'children': [9, 1], 'parent_updates': [[9, 5]], 'root_set': [5]}), ({'a': [4, 8, 2, [10, 11]], 'b': [6, 3, 2, [12, 13]]}, {'winner': 6, 'loser': 4, 'new_rank': 3, 'children': [4, 12, 13], 'parent_updates': [[4, 6]], 'root_set': [6]}), ({'a': [1, 0, 3, [2, 3, 4]], 'b': [9, 8, 3, [10, 11, 12]]}, {'winner': 1, 'loser': 9, 'new_rank': 4, 'children': [9, 2, 3, 4], 'parent_updates': [[9, 1]], 'root_set': [1]}), ({'a': [7, 5, 1, [8]], 'b': [2, 2, 1, [3]]}, {'winner': 2, 'loser': 7, 'new_rank': 2, 'children': [7, 3], 'parent_updates': [[7, 2]], 'root_set': [2]}), ({'a': [7, 9, 1, [8]], 'b': [2, 2, 1, [3]]}, {'winner': 2, 'loser': 7, 'new_rank': 2, 'children': [7, 3], 'parent_updates': [[7, 2]], 'root_set': [2]})], [({'a': [8, 2, 0, []], 'b': [3, 5, 0, []]}, {'winner': 8, 'loser': 3, 'new_rank': 1, 'children': [3], 'parent_updates': [[3, 8]], 'root_set': [8]}), ({'a': [2, 9, 0, []], 'b': [7, 1, 0, []]}, {'winner': 7, 'loser': 2, 'new_rank': 1, 'children': [2], 'parent_updates': [[2, 7]], 'root_set': [7]}), ({'a': [5, 4, 1, [1]], 'b': [9, 4, 1, [3]]}, {'winner': 5, 'loser': 9, 'new_rank': 2, 'children': [9, 1], 'parent_updates': [[9, 5]], 'root_set': [5]}), ({'a': [4, 8, 2, [10, 11]], 'b': [6, 3, 2, [12, 13]]}, {'winner': 6, 'loser': 4, 'new_rank': 3, 'children': [4, 12, 13], 'parent_updates': [[4, 6]], 'root_set': [6]}), ({'a': [1, 0, 3, [2, 3, 4]], 'b': [9, 8, 3, [10, 11, 12]]}, {'winner': 1, 'loser': 9, 'new_rank': 4, 'children': [9, 2, 3, 4], 'parent_updates': [[9, 1]], 'root_set': [1]}), ({'a': [7, 5, 1, [8]], 'b': [2, 2, 1, [3]]}, {'winner': 2, 'loser': 7, 'new_rank': 2, 'children': [7, 3], 'parent_updates': [[7, 2]], 'root_set': [2]}), ({'a': [7, 10, 1, [8]], 'b': [2, 2, 1, [3]]}, {'winner': 2, 'loser': 7, 'new_rank': 2, 'children': [7, 3], 'parent_updates': [[7, 2]], 'root_set': [2]})]][N-1]\ncheck('regression certificate 1', solve(cases[0][0]), cases[0][1])\ncheck('regression certificate 2', solve(cases[1][0]), cases[1][1])\ncheck('regression certificate 3', solve(cases[2][0]), cases[2][1])\ncheck('regression certificate 4', solve(cases[3][0]), cases[3][1])\ncheck('regression certificate 5', solve(cases[4][0]), cases[4][1])\ncheck('regression certificate 6', solve(cases[5][0]), cases[5][1])\ncheck('variant-dependent certificate', solve(cases[6][0]), cases[6][1])\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":"A stipulated offline diagnostic model; it does not implement a production allocator, concurrency protocol, or complete heap library. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"s3-heap-binomial-link-root_set","generated_at":"2026-09-29T14:43:26.982694+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"This isolates an internal heap representation or priority-structure invariant using deterministic finite records.","root_cause":"Binomial link removes the loser from the root collection.","sha256":"2e8c8cceafdcfb41c9df9ef7c788f7b2dc8adb37f89dfa0e0c78ca04aed4919f","title":"Binomial link removes the loser from the root collection · case 01","variant":1,"variant_policy":"Six explicit regression certificates are retained; a seventh changes structural size, position, priority, or bounds with N.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":40.092,"exit_code":1,"observations":[{"actual":{"children":[3],"loser":3,"new_rank":1,"parent_updates":[[3,8]],"root_set":[3],"winner":8},"check":"regression certificate 1","expected":{"children":[3],"loser":3,"new_rank":1,"parent_updates":[[3,8]],"root_set":[8],"winner":8},"passed":false},{"actual":{"children":[2],"loser":2,"new_rank":1,"parent_updates":[[2,7]],"root_set":[2],"winner":7},"check":"regression certificate 2","expected":{"children":[2],"loser":2,"new_rank":1,"parent_updates":[[2,7]],"root_set":[7],"winner":7},"passed":false},{"actual":{"children":[9,1],"loser":9,"new_rank":2,"parent_updates":[[9,5]],"root_set":[9],"winner":5},"check":"regression certificate 3","expected":{"children":[9,1],"loser":9,"new_rank":2,"parent_updates":[[9,5]],"root_set":[5],"winner":5},"passed":false},{"actual":{"children":[4,12,13],"loser":4,"new_rank":3,"parent_updates":[[4,6]],"root_set":[4],"winner":6},"check":"regression certificate 4","expected":{"children":[4,12,13],"loser":4,"new_rank":3,"parent_updates":[[4,6]],"root_set":[6],"winner":6},"passed":false},{"actual":{"children":[9,2,3,4],"loser":9,"new_rank":4,"parent_updates":[[9,1]],"root_set":[9],"winner":1},"check":"regression certificate 5","expected":{"children":[9,2,3,4],"loser":9,"new_rank":4,"parent_updates":[[9,1]],"root_set":[1],"winner":1},"passed":false},{"actual":{"children":[7,3],"loser":7,"new_rank":2,"parent_updates":[[7,2]],"root_set":[7],"winner":2},"check":"regression certificate 6","expected":{"children":[7,3],"loser":7,"new_rank":2,"parent_updates":[[7,2]],"root_set":[2],"winner":2},"passed":false},{"actual":{"children":[7,3],"loser":7,"new_rank":2,"parent_updates":[[7,2]],"root_set":[7],"winner":2},"check":"variant-dependent certificate","expected":{"children":[7,3],"loser":7,"new_rank":2,"parent_updates":[[7,2]],"root_set":[2],"winner":2},"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression certificate 1\", \"actual\": {\"winner\": 8, \"loser\": 3, \"new_rank\": 1, \"children\": [3], \"parent_updates\": [[3, 8]], \"root_set\": [3]}, \"expected\": {\"winner\": 8, \"loser\": 3, \"new_rank\": 1, \"children\": [3], \"parent_updates\": [[3, 8]], \"root_set\": [8]}, \"passed\": false}, {\"check\": \"regression certificate 2\", \"actual\": {\"winner\": 7, \"loser\": 2, \"new_rank\": 1, \"children\": [2], \"parent_updates\": [[2, 7]], \"root_set\": [2]}, \"expected\": {\"winner\": 7, \"loser\": 2, \"new_rank\": 1, \"children\": [2], \"parent_updates\": [[2, 7]], \"root_set\": [7]}, \"passed\": false}, {\"check\": \"regression certificate 3\", \"actual\": {\"winner\": 5, \"loser\": 9, \"new_rank\": 2, \"children\": [9, 1], \"parent_updates\": [[9, 5]], \"root_set\": [9]}, \"expected\": {\"winner\": 5, \"loser\": 9, \"new_rank\": 2, \"children\": [9, 1], \"parent_updates\": [[9, 5]], \"root_set\": [5]}, \"passed\": false}, {\"check\": \"regression certificate 4\", \"actual\": {\"winner\": 6, \"loser\": 4, \"new_rank\": 3, \"children\": [4, 12, 13], \"parent_updates\": [[4, 6]], \"root_set\": [4]}, \"expected\": {\"winner\": 6, \"loser\": 4, \"new_rank\": 3, \"children\": [4, 12, 13], \"parent_updates\": [[4, 6]], \"root_set\": [6]}, \"passed\": false}, {\"check\": \"regression certificate 5\", \"actual\": {\"winner\": 1, \"loser\": 9, \"new_rank\": 4, \"children\": [9, 2, 3, 4], \"parent_updates\": [[9, 1]], \"root_set\": [9]}, \"expected\": {\"winner\": 1, \"loser\": 9, \"new_rank\": 4, 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