{"abstract":"The bounded heap frontier certificate reports an incorrect ready.","category":"Heap invariants","checks":7,"contract":"A read-only best-first traversal of a valid binary min heap has already emitted parent slot p and a frontier of distinct slots. Insert p children that exist into the frontier, order by (key,index), and choose next. Return new frontier, chosen slot, child additions, traversal output key, preserved heap, and next frontier after selection. Initial frontier excludes p and its children.","contract_signature":"d","evaluation_group":"s3-heap-model-heap-frontier","failed_approach":"The local patch uses sorted(f+children,key=lambda i:(a[i],-i)) and still violates the stated relation.","family":"s3-heap-heap-frontier-ready","id":"FA-40951","implementations":{"attempt":{"sha256":"241d3d7d49726d6b4f17a84af7eb83bc53f040e6e83d68b5662d92ce3fd73047","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    a=d['keys']; p=d['parent']; f=d['frontier']; children=[i for i in (2*p+1,2*p+2) if i<len(a)]; ready=sorted(f+children,key=lambda i:(a[i],i)); nxt=ready[0] if ready else None\n    return {'ready': sorted(f+children,key=lambda i:(a[i],-i)),\n    'chosen': nxt,\n    'children': children,\n    'next_key': None if nxt is None else a[nxt],\n    'heap_after': a,\n    'frontier_after': ready[1:]}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'keys': [1], 'parent': 0, 'frontier': []}, {'ready': [], 'chosen': None, 'children': [], 'next_key': None, 'heap_after': [1], 'frontier_after': []}), ({'keys': [1, 7, 2], 'parent': 0, 'frontier': []}, {'ready': [2, 1], 'chosen': 2, 'children': [1, 2], 'next_key': 2, 'heap_after': [1, 7, 2], 'frontier_after': [1]}), ({'keys': [1, 4, 2, 7, 5, 3, 6], 'parent': 1, 'frontier': [2]}, {'ready': [2, 4, 3], 'chosen': 2, 'children': [3, 4], 'next_key': 2, 'heap_after': [1, 4, 2, 7, 5, 3, 6], 'frontier_after': [4, 3]}), ({'keys': [1, 4, 2, 7, 4, 3, 6], 'parent': 1, 'frontier': [2]}, {'ready': [2, 4, 3], 'chosen': 2, 'children': [3, 4], 'next_key': 2, 'heap_after': [1, 4, 2, 7, 4, 3, 6], 'frontier_after': [4, 3]}), ({'keys': [1, 3, 3, 5, 6, 7, 8], 'parent': 0, 'frontier': []}, {'ready': [1, 2], 'chosen': 1, 'children': [1, 2], 'next_key': 3, 'heap_after': [1, 3, 3, 5, 6, 7, 8], 'frontier_after': [2]}), ({'keys': [1, 2, 3, 4, 5, 6, 7, 8], 'parent': 3, 'frontier': [2, 4]}, {'ready': [2, 4, 7], 'chosen': 2, 'children': [7], 'next_key': 3, 'heap_after': [1, 2, 3, 4, 5, 6, 7, 8], 'frontier_after': [4, 7]}), ({'keys': [1, 2, 3, 4, 5, 6, 7, 9], 'parent': 3, 'frontier': [2, 4]}, {'ready': [2, 4, 7], 'chosen': 2, 'children': [7], 'next_key': 3, 'heap_after': [1, 2, 3, 4, 5, 6, 7, 9], 'frontier_after': [4, 7]})], [({'keys': [1], 'parent': 0, 'frontier': []}, {'ready': [], 'chosen': None, 'children': [], 'next_key': None, 'heap_after': [1], 'frontier_after': []}), ({'keys': [1, 7, 2], 'parent': 0, 'frontier': []}, {'ready': [2, 1], 'chosen': 2, 'children': [1, 2], 'next_key': 2, 'heap_after': [1, 7, 2], 'frontier_after': [1]}), ({'keys': [1, 4, 2, 7, 5, 3, 6], 'parent': 1, 'frontier': [2]}, {'ready': [2, 4, 3], 'chosen': 2, 'children': [3, 4], 'next_key': 2, 'heap_after': [1, 4, 2, 7, 5, 3, 6], 'frontier_after': [4, 3]}), ({'keys': [1, 4, 2, 7, 4, 3, 6], 'parent': 1, 'frontier': [2]}, {'ready': [2, 4, 3], 'chosen': 2, 'children': [3, 4], 'next_key': 2, 'heap_after': [1, 4, 2, 7, 4, 3, 6], 'frontier_after': [4, 3]}), ({'keys': [1, 3, 3, 5, 6, 7, 8], 'parent': 0, 'frontier': []}, {'ready': [1, 2], 'chosen': 1, 'children': [1, 2], 'next_key': 3, 'heap_after': [1, 3, 3, 5, 6, 7, 8], 'frontier_after': [2]}), ({'keys': [1, 2, 3, 4, 5, 6, 7, 8], 'parent': 3, 'frontier': [2, 4]}, {'ready': [2, 4, 7], 'chosen': 2, 'children': [7], 'next_key': 3, 'heap_after': [1, 2, 3, 4, 5, 6, 7, 8], 'frontier_after': [4, 7]}), ({'keys': [1, 2, 3, 4, 5, 6, 7, 10], 'parent': 3, 'frontier': [2, 4]}, {'ready': [2, 4, 7], 'chosen': 2, 'children': [7], 'next_key': 3, 'heap_after': [1, 2, 3, 4, 5, 6, 7, 10], 'frontier_after': [4, 7]})], [({'keys': [1], 'parent': 0, 'frontier': []}, {'ready': [], 'chosen': None, 'children': [], 'next_key': None, 'heap_after': [1], 'frontier_after': []}), ({'keys': [1, 7, 2], 'parent': 0, 'frontier': []}, {'ready': [2, 1], 'chosen': 2, 'children': [1, 2], 'next_key': 2, 'heap_after': [1, 7, 2], 'frontier_after': [1]}), ({'keys': [1, 4, 2, 7, 5, 3, 6], 'parent': 1, 'frontier': [2]}, {'ready': [2, 4, 3], 'chosen': 2, 'children': [3, 4], 'next_key': 2, 'heap_after': [1, 4, 2, 7, 5, 3, 6], 'frontier_after': [4, 3]}), ({'keys': [1, 4, 2, 7, 4, 3, 6], 'parent': 1, 'frontier': [2]}, {'ready': [2, 4, 3], 'chosen': 2, 'children': [3, 4], 'next_key': 2, 'heap_after': [1, 4, 2, 7, 4, 3, 6], 'frontier_after': [4, 3]}), ({'keys': [1, 3, 3, 5, 6, 7, 8], 'parent': 0, 'frontier': []}, {'ready': [1, 2], 'chosen': 1, 'children': [1, 2], 'next_key': 3, 'heap_after': [1, 3, 3, 5, 6, 7, 8], 'frontier_after': [2]}), ({'keys': [1, 2, 3, 4, 5, 6, 7, 8], 'parent': 3, 'frontier': [2, 4]}, {'ready': [2, 4, 7], 'chosen': 2, 'children': [7], 'next_key': 3, 'heap_after': [1, 2, 3, 4, 5, 6, 7, 8], 'frontier_after': [4, 7]}), ({'keys': [1, 2, 3, 4, 5, 6, 7, 11], 'parent': 3, 'frontier': [2, 4]}, {'ready': [2, 4, 7], 'chosen': 2, 'children': [7], 'next_key': 3, 'heap_after': [1, 2, 3, 4, 5, 6, 7, 11], 'frontier_after': [4, 7]})], [({'keys': [1], 'parent': 0, 'frontier': []}, {'ready': [], 'chosen': None, 'children': [], 'next_key': None, 'heap_after': [1], 'frontier_after': []}), ({'keys': [1, 7, 2], 'parent': 0, 'frontier': []}, {'ready': [2, 1], 'chosen': 2, 'children': [1, 2], 'next_key': 2, 'heap_after': [1, 7, 2], 'frontier_after': [1]}), ({'keys': [1, 4, 2, 7, 5, 3, 6], 'parent': 1, 'frontier': [2]}, {'ready': [2, 4, 3], 'chosen': 2, 'children': [3, 4], 'next_key': 2, 'heap_after': [1, 4, 2, 7, 5, 3, 6], 'frontier_after': [4, 3]}), ({'keys': [1, 4, 2, 7, 4, 3, 6], 'parent': 1, 'frontier': [2]}, {'ready': [2, 4, 3], 'chosen': 2, 'children': [3, 4], 'next_key': 2, 'heap_after': [1, 4, 2, 7, 4, 3, 6], 'frontier_after': [4, 3]}), ({'keys': [1, 3, 3, 5, 6, 7, 8], 'parent': 0, 'frontier': []}, {'ready': [1, 2], 'chosen': 1, 'children': [1, 2], 'next_key': 3, 'heap_after': [1, 3, 3, 5, 6, 7, 8], 'frontier_after': [2]}), ({'keys': [1, 2, 3, 4, 5, 6, 7, 8], 'parent': 3, 'frontier': [2, 4]}, {'ready': [2, 4, 7], 'chosen': 2, 'children': [7], 'next_key': 3, 'heap_after': [1, 2, 3, 4, 5, 6, 7, 8], 'frontier_after': [4, 7]}), ({'keys': [1, 2, 3, 4, 5, 6, 7, 12], 'parent': 3, 'frontier': [2, 4]}, {'ready': [2, 4, 7], 'chosen': 2, 'children': [7], 'next_key': 3, 'heap_after': [1, 2, 3, 4, 5, 6, 7, 12], 'frontier_after': [4, 7]})], [({'keys': [1], 'parent': 0, 'frontier': []}, {'ready': [], 'chosen': None, 'children': [], 'next_key': None, 'heap_after': [1], 'frontier_after': []}), ({'keys': [1, 7, 2], 'parent': 0, 'frontier': []}, {'ready': [2, 1], 'chosen': 2, 'children': [1, 2], 'next_key': 2, 'heap_after': [1, 7, 2], 'frontier_after': [1]}), ({'keys': [1, 4, 2, 7, 5, 3, 6], 'parent': 1, 'frontier': [2]}, {'ready': [2, 4, 3], 'chosen': 2, 'children': [3, 4], 'next_key': 2, 'heap_after': [1, 4, 2, 7, 5, 3, 6], 'frontier_after': [4, 3]}), ({'keys': [1, 4, 2, 7, 4, 3, 6], 'parent': 1, 'frontier': [2]}, {'ready': [2, 4, 3], 'chosen': 2, 'children': [3, 4], 'next_key': 2, 'heap_after': [1, 4, 2, 7, 4, 3, 6], 'frontier_after': [4, 3]}), ({'keys': [1, 3, 3, 5, 6, 7, 8], 'parent': 0, 'frontier': []}, {'ready': [1, 2], 'chosen': 1, 'children': [1, 2], 'next_key': 3, 'heap_after': [1, 3, 3, 5, 6, 7, 8], 'frontier_after': [2]}), ({'keys': [1, 2, 3, 4, 5, 6, 7, 8], 'parent': 3, 'frontier': [2, 4]}, {'ready': [2, 4, 7], 'chosen': 2, 'children': [7], 'next_key': 3, 'heap_after': [1, 2, 3, 4, 5, 6, 7, 8], 'frontier_after': [4, 7]}), ({'keys': [1, 2, 3, 4, 5, 6, 7, 13], 'parent': 3, 'frontier': [2, 4]}, {'ready': [2, 4, 7], 'chosen': 2, 'children': [7], 'next_key': 3, 'heap_after': [1, 2, 3, 4, 5, 6, 7, 13], 'frontier_after': [4, 7]})]][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":"dc5c05564937fce8afe5a1102367f26b2b5a3815192bc3b4b9586b8527ce7c29","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    a=d['keys']; p=d['parent']; f=d['frontier']; children=[i for i in (2*p+1,2*p+2) if i<len(a)]; ready=sorted(f+children,key=lambda i:(a[i],i)); nxt=ready[0] if ready else None\n    return {'ready': sorted(f+children),\n    'chosen': nxt,\n    'children': children,\n    'next_key': None if nxt is None else a[nxt],\n    'heap_after': a,\n    'frontier_after': ready[1:]}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'keys': [1], 'parent': 0, 'frontier': []}, {'ready': [], 'chosen': None, 'children': [], 'next_key': None, 'heap_after': [1], 'frontier_after': []}), ({'keys': [1, 7, 2], 'parent': 0, 'frontier': []}, {'ready': [2, 1], 'chosen': 2, 'children': [1, 2], 'next_key': 2, 'heap_after': [1, 7, 2], 'frontier_after': [1]}), ({'keys': [1, 4, 2, 7, 5, 3, 6], 'parent': 1, 'frontier': [2]}, {'ready': [2, 4, 3], 'chosen': 2, 'children': [3, 4], 'next_key': 2, 'heap_after': [1, 4, 2, 7, 5, 3, 6], 'frontier_after': [4, 3]}), ({'keys': [1, 4, 2, 7, 4, 3, 6], 'parent': 1, 'frontier': [2]}, {'ready': [2, 4, 3], 'chosen': 2, 'children': [3, 4], 'next_key': 2, 'heap_after': [1, 4, 2, 7, 4, 3, 6], 'frontier_after': [4, 3]}), ({'keys': [1, 3, 3, 5, 6, 7, 8], 'parent': 0, 'frontier': []}, {'ready': [1, 2], 'chosen': 1, 'children': [1, 2], 'next_key': 3, 'heap_after': [1, 3, 3, 5, 6, 7, 8], 'frontier_after': [2]}), ({'keys': [1, 2, 3, 4, 5, 6, 7, 8], 'parent': 3, 'frontier': [2, 4]}, {'ready': [2, 4, 7], 'chosen': 2, 'children': [7], 'next_key': 3, 'heap_after': [1, 2, 3, 4, 5, 6, 7, 8], 'frontier_after': [4, 7]}), ({'keys': [1, 2, 3, 4, 5, 6, 7, 9], 'parent': 3, 'frontier': [2, 4]}, {'ready': [2, 4, 7], 'chosen': 2, 'children': [7], 'next_key': 3, 'heap_after': [1, 2, 3, 4, 5, 6, 7, 9], 'frontier_after': [4, 7]})], [({'keys': [1], 'parent': 0, 'frontier': []}, {'ready': [], 'chosen': None, 'children': [], 'next_key': None, 'heap_after': [1], 'frontier_after': []}), ({'keys': [1, 7, 2], 'parent': 0, 'frontier': []}, {'ready': [2, 1], 'chosen': 2, 'children': [1, 2], 'next_key': 2, 'heap_after': [1, 7, 2], 'frontier_after': [1]}), ({'keys': [1, 4, 2, 7, 5, 3, 6], 'parent': 1, 'frontier': [2]}, {'ready': [2, 4, 3], 'chosen': 2, 'children': [3, 4], 'next_key': 2, 'heap_after': [1, 4, 2, 7, 5, 3, 6], 'frontier_after': [4, 3]}), ({'keys': [1, 4, 2, 7, 4, 3, 6], 'parent': 1, 'frontier': [2]}, {'ready': [2, 4, 3], 'chosen': 2, 'children': [3, 4], 'next_key': 2, 'heap_after': [1, 4, 2, 7, 4, 3, 6], 'frontier_after': [4, 3]}), ({'keys': [1, 3, 3, 5, 6, 7, 8], 'parent': 0, 'frontier': []}, {'ready': [1, 2], 'chosen': 1, 'children': [1, 2], 'next_key': 3, 'heap_after': [1, 3, 3, 5, 6, 7, 8], 'frontier_after': [2]}), ({'keys': [1, 2, 3, 4, 5, 6, 7, 8], 'parent': 3, 'frontier': [2, 4]}, {'ready': [2, 4, 7], 'chosen': 2, 'children': [7], 'next_key': 3, 'heap_after': [1, 2, 3, 4, 5, 6, 7, 8], 'frontier_after': [4, 7]}), ({'keys': [1, 2, 3, 4, 5, 6, 7, 10], 'parent': 3, 'frontier': [2, 4]}, {'ready': [2, 4, 7], 'chosen': 2, 'children': [7], 'next_key': 3, 'heap_after': [1, 2, 3, 4, 5, 6, 7, 10], 'frontier_after': [4, 7]})], [({'keys': [1], 'parent': 0, 'frontier': []}, {'ready': [], 'chosen': None, 'children': [], 'next_key': None, 'heap_after': [1], 'frontier_after': []}), ({'keys': [1, 7, 2], 'parent': 0, 'frontier': []}, {'ready': [2, 1], 'chosen': 2, 'children': [1, 2], 'next_key': 2, 'heap_after': [1, 7, 2], 'frontier_after': [1]}), ({'keys': [1, 4, 2, 7, 5, 3, 6], 'parent': 1, 'frontier': [2]}, {'ready': [2, 4, 3], 'chosen': 2, 'children': [3, 4], 'next_key': 2, 'heap_after': [1, 4, 2, 7, 5, 3, 6], 'frontier_after': [4, 3]}), ({'keys': [1, 4, 2, 7, 4, 3, 6], 'parent': 1, 'frontier': [2]}, {'ready': [2, 4, 3], 'chosen': 2, 'children': [3, 4], 'next_key': 2, 'heap_after': [1, 4, 2, 7, 4, 3, 6], 'frontier_after': [4, 3]}), ({'keys': [1, 3, 3, 5, 6, 7, 8], 'parent': 0, 'frontier': []}, {'ready': [1, 2], 'chosen': 1, 'children': [1, 2], 'next_key': 3, 'heap_after': [1, 3, 3, 5, 6, 7, 8], 'frontier_after': [2]}), ({'keys': [1, 2, 3, 4, 5, 6, 7, 8], 'parent': 3, 'frontier': [2, 4]}, {'ready': [2, 4, 7], 'chosen': 2, 'children': [7], 'next_key': 3, 'heap_after': [1, 2, 3, 4, 5, 6, 7, 8], 'frontier_after': [4, 7]}), ({'keys': [1, 2, 3, 4, 5, 6, 7, 11], 'parent': 3, 'frontier': [2, 4]}, {'ready': [2, 4, 7], 'chosen': 2, 'children': [7], 'next_key': 3, 'heap_after': [1, 2, 3, 4, 5, 6, 7, 11], 'frontier_after': [4, 7]})], [({'keys': [1], 'parent': 0, 'frontier': []}, {'ready': [], 'chosen': None, 'children': [], 'next_key': None, 'heap_after': [1], 'frontier_after': []}), ({'keys': [1, 7, 2], 'parent': 0, 'frontier': []}, {'ready': [2, 1], 'chosen': 2, 'children': [1, 2], 'next_key': 2, 'heap_after': [1, 7, 2], 'frontier_after': [1]}), ({'keys': [1, 4, 2, 7, 5, 3, 6], 'parent': 1, 'frontier': [2]}, {'ready': [2, 4, 3], 'chosen': 2, 'children': [3, 4], 'next_key': 2, 'heap_after': [1, 4, 2, 7, 5, 3, 6], 'frontier_after': [4, 3]}), ({'keys': [1, 4, 2, 7, 4, 3, 6], 'parent': 1, 'frontier': [2]}, {'ready': [2, 4, 3], 'chosen': 2, 'children': [3, 4], 'next_key': 2, 'heap_after': [1, 4, 2, 7, 4, 3, 6], 'frontier_after': [4, 3]}), ({'keys': [1, 3, 3, 5, 6, 7, 8], 'parent': 0, 'frontier': []}, {'ready': [1, 2], 'chosen': 1, 'children': [1, 2], 'next_key': 3, 'heap_after': [1, 3, 3, 5, 6, 7, 8], 'frontier_after': [2]}), ({'keys': [1, 2, 3, 4, 5, 6, 7, 8], 'parent': 3, 'frontier': [2, 4]}, {'ready': [2, 4, 7], 'chosen': 2, 'children': [7], 'next_key': 3, 'heap_after': [1, 2, 3, 4, 5, 6, 7, 8], 'frontier_after': [4, 7]}), ({'keys': [1, 2, 3, 4, 5, 6, 7, 12], 'parent': 3, 'frontier': [2, 4]}, {'ready': [2, 4, 7], 'chosen': 2, 'children': [7], 'next_key': 3, 'heap_after': [1, 2, 3, 4, 5, 6, 7, 12], 'frontier_after': [4, 7]})], [({'keys': [1], 'parent': 0, 'frontier': []}, {'ready': [], 'chosen': None, 'children': [], 'next_key': None, 'heap_after': [1], 'frontier_after': []}), ({'keys': [1, 7, 2], 'parent': 0, 'frontier': []}, {'ready': [2, 1], 'chosen': 2, 'children': [1, 2], 'next_key': 2, 'heap_after': [1, 7, 2], 'frontier_after': [1]}), ({'keys': [1, 4, 2, 7, 5, 3, 6], 'parent': 1, 'frontier': [2]}, {'ready': [2, 4, 3], 'chosen': 2, 'children': [3, 4], 'next_key': 2, 'heap_after': [1, 4, 2, 7, 5, 3, 6], 'frontier_after': [4, 3]}), ({'keys': [1, 4, 2, 7, 4, 3, 6], 'parent': 1, 'frontier': [2]}, {'ready': [2, 4, 3], 'chosen': 2, 'children': [3, 4], 'next_key': 2, 'heap_after': [1, 4, 2, 7, 4, 3, 6], 'frontier_after': [4, 3]}), ({'keys': [1, 3, 3, 5, 6, 7, 8], 'parent': 0, 'frontier': []}, {'ready': [1, 2], 'chosen': 1, 'children': [1, 2], 'next_key': 3, 'heap_after': [1, 3, 3, 5, 6, 7, 8], 'frontier_after': [2]}), ({'keys': [1, 2, 3, 4, 5, 6, 7, 8], 'parent': 3, 'frontier': [2, 4]}, {'ready': [2, 4, 7], 'chosen': 2, 'children': [7], 'next_key': 3, 'heap_after': [1, 2, 3, 4, 5, 6, 7, 8], 'frontier_after': [4, 7]}), ({'keys': [1, 2, 3, 4, 5, 6, 7, 13], 'parent': 3, 'frontier': [2, 4]}, {'ready': [2, 4, 7], 'chosen': 2, 'children': [7], 'next_key': 3, 'heap_after': [1, 2, 3, 4, 5, 6, 7, 13], 'frontier_after': [4, 7]})]][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-heap-frontier-ready","generated_at":"2026-09-29T14:43:36.255789+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":"Heap frontier orders candidates by priority then structural index rather than index alone.","sha256":"17664f98d83dca9ce38faa5c1a49d8d00326d2e8192fd0d73811af7865debd80","title":"Heap frontier orders candidates by priority then structural index rather than index alone · 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":42.339,"exit_code":1,"observations":[{"actual":{"children":[],"chosen":null,"frontier_after":[],"heap_after":[1],"next_key":null,"ready":[]},"check":"regression certificate 1","expected":{"children":[],"chosen":null,"frontier_after":[],"heap_after":[1],"next_key":null,"ready":[]},"passed":true},{"actual":{"children":[1,2],"chosen":2,"frontier_after":[1],"heap_after":[1,7,2],"next_key":2,"ready":[2,1]},"check":"regression certificate 2","expected":{"children":[1,2],"chosen":2,"frontier_after":[1],"heap_after":[1,7,2],"next_key":2,"ready":[2,1]},"passed":true},{"actual":{"children":[3,4],"chosen":2,"frontier_after":[4,3],"heap_after":[1,4,2,7,5,3,6],"next_key":2,"ready":[2,4,3]},"check":"regression certificate 3","expected":{"children":[3,4],"chosen":2,"frontier_after":[4,3],"heap_after":[1,4,2,7,5,3,6],"next_key":2,"ready":[2,4,3]},"passed":true},{"actual":{"children":[3,4],"chosen":2,"frontier_after":[4,3],"heap_after":[1,4,2,7,4,3,6],"next_key":2,"ready":[2,4,3]},"check":"regression certificate 4","expected":{"children":[3,4],"chosen":2,"frontier_after":[4,3],"heap_after":[1,4,2,7,4,3,6],"next_key":2,"ready":[2,4,3]},"passed":true},{"actual":{"children":[1,2],"chosen":1,"frontier_after":[2],"heap_after":[1,3,3,5,6,7,8],"next_key":3,"ready":[2,1]},"check":"regression certificate 5","expected":{"children":[1,2],"chosen":1,"frontier_after":[2],"heap_after":[1,3,3,5,6,7,8],"next_key":3,"ready":[1,2]},"passed":false},{"actual":{"children":[7],"chosen":2,"frontier_after":[4,7],"heap_after":[1,2,3,4,5,6,7,8],"next_key":3,"ready":[2,4,7]},"check":"regression certificate 6","expected":{"children":[7],"chosen":2,"frontier_after":[4,7],"heap_after":[1,2,3,4,5,6,7,8],"next_key":3,"ready":[2,4,7]},"passed":true},{"actual":{"children":[7],"chosen":2,"frontier_after":[4,7],"heap_after":[1,2,3,4,5,6,7,9],"next_key":3,"ready":[2,4,7]},"check":"variant-dependent certificate","expected":{"children":[7],"chosen":2,"frontier_after":[4,7],"heap_after":[1,2,3,4,5,6,7,9],"next_key":3,"ready":[2,4,7]},"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression certificate 1\", \"actual\": {\"ready\": [], \"chosen\": null, \"children\": [], \"next_key\": null, \"heap_after\": [1], \"frontier_after\": []}, \"expected\": {\"ready\": [], \"chosen\": null, \"children\": [], \"next_key\": null, \"heap_after\": [1], \"frontier_after\": []}, \"passed\": true}, {\"check\": \"regression certificate 2\", \"actual\": {\"ready\": [2, 1], \"chosen\": 2, \"children\": [1, 2], \"next_key\": 2, \"heap_after\": [1, 7, 2], \"frontier_after\": [1]}, \"expected\": {\"ready\": [2, 1], \"chosen\": 2, \"children\": [1, 2], \"next_key\": 2, \"heap_after\": [1, 7, 2], \"frontier_after\": [1]}, \"passed\": true}, {\"check\": \"regression certificate 3\", \"actual\": {\"ready\": [2, 4, 3], \"chosen\": 2, \"children\": [3, 4], \"next_key\": 2, \"heap_after\": [1, 4, 2, 7, 5, 3, 6], \"frontier_after\": [4, 3]}, \"expected\": {\"ready\": [2, 4, 3], \"chosen\": 2, \"children\": [3, 4], \"next_key\": 2, \"heap_after\": [1, 4, 2, 7, 5, 3, 6], \"frontier_after\": [4, 3]}, \"passed\": true}, {\"check\": \"regression certificate 4\", \"actual\": {\"ready\": [2, 4, 3], \"chosen\": 2, \"children\": [3, 4], \"next_key\": 2, \"heap_after\": [1, 4, 2, 7, 4, 3, 6], \"frontier_after\": [4, 3]}, \"expected\": {\"ready\": [2, 4, 3], \"chosen\": 2, \"children\": [3, 4], \"next_key\": 2, \"heap_after\": [1, 4, 2, 7, 4, 3, 6], \"frontier_after\": [4, 3]}, \"passed\": true}, {\"check\": \"regression certificate 5\", \"actual\": {\"ready\": [2, 1], \"chosen\": 1, \"children\": [1, 2], \"next_key\": 3, \"heap_after\": [1, 3, 3, 5, 6, 7, 8], \"frontier_after\": [2]}, \"expected\": {\"ready\": [1, 2], \"chosen\": 1, \"children\": [1, 2], \"next_key\": 3, \"heap_after\": [1, 3, 3, 5, 6, 7, 8], \"frontier_after\": [2]}, \"passed\": false}, {\"check\": \"regression certificate 6\", \"actual\": {\"ready\": [2, 4, 7], \"chosen\": 2, \"children\": [7], \"next_key\": 3, \"heap_after\": [1, 2, 3, 4, 5, 6, 7, 8], \"frontier_after\": [4, 7]}, \"expected\": {\"ready\": [2, 4, 7], \"chosen\": 2, \"children\": [7], \"next_key\": 3, \"heap_after\": [1, 2, 3, 4, 5, 6, 7, 8], \"frontier_after\": [4, 7]}, \"passed\": true}, {\"check\": \"variant-dependent certificate\", \"actual\": {\"ready\": [2, 4, 7], \"chosen\": 2, \"children\": [7], \"next_key\": 3, \"heap_after\": [1, 2, 3, 4, 5, 6, 7, 9], \"frontier_after\": [4, 7]}, \"expected\": {\"ready\": [2, 4, 7], \"chosen\": 2, \"children\": [7], \"next_key\": 3, \"heap_after\": [1, 2, 3, 4, 5, 6, 7, 9], \"frontier_after\": [4, 7]}, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":43.17,"exit_code":1,"observations":[{"actual":{"children":[],"chosen":null,"frontier_after":[],"heap_after":[1],"next_key":null,"ready":[]},"check":"regression certificate 1","expected":{"children":[],"chosen":null,"frontier_after":[],"heap_after":[1],"next_key":null,"ready":[]},"passed":true},{"actual":{"children":[1,2],"chosen":2,"frontier_after":[1],"heap_after":[1,7,2],"next_key":2,"ready":[1,2]},"check":"regression certificate 2","expected":{"children":[1,2],"chosen":2,"frontier_after":[1],"heap_after":[1,7,2],"next_key":2,"ready":[2,1]},"passed":false},{"actual":{"children":[3,4],"chosen":2,"frontier_after":[4,3],"heap_after":[1,4,2,7,5,3,6],"next_key":2,"ready":[2,3,4]},"check":"regression certificate 3","expected":{"children":[3,4],"chosen":2,"frontier_after":[4,3],"heap_after":[1,4,2,7,5,3,6],"next_key":2,"ready":[2,4,3]},"passed":false},{"actual":{"children":[3,4],"chosen":2,"frontier_after":[4,3],"heap_after":[1,4,2,7,4,3,6],"next_key":2,"ready":[2,3,4]},"check":"regression certificate 4","expected":{"children":[3,4],"chosen":2,"frontier_after":[4,3],"heap_after":[1,4,2,7,4,3,6],"next_key":2,"ready":[2,4,3]},"passed":false},{"actual":{"children":[1,2],"chosen":1,"frontier_after":[2],"heap_after":[1,3,3,5,6,7,8],"next_key":3,"ready":[1,2]},"check":"regression certificate 5","expected":{"children":[1,2],"chosen":1,"frontier_after":[2],"heap_after":[1,3,3,5,6,7,8],"next_key":3,"ready":[1,2]},"passed":true},{"actual":{"children":[7],"chosen":2,"frontier_after":[4,7],"heap_after":[1,2,3,4,5,6,7,8],"next_key":3,"ready":[2,4,7]},"check":"regression certificate 6","expected":{"children":[7],"chosen":2,"frontier_after":[4,7],"heap_after":[1,2,3,4,5,6,7,8],"next_key":3,"ready":[2,4,7]},"passed":true},{"actual":{"children":[7],"chosen":2,"frontier_after":[4,7],"heap_after":[1,2,3,4,5,6,7,9],"next_key":3,"ready":[2,4,7]},"check":"variant-dependent certificate","expected":{"children":[7],"chosen":2,"frontier_after":[4,7],"heap_after":[1,2,3,4,5,6,7,9],"next_key":3,"ready":[2,4,7]},"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression certificate 1\", \"actual\": {\"ready\": [], \"chosen\": null, \"children\": [], \"next_key\": null, \"heap_after\": [1], \"frontier_after\": []}, \"expected\": {\"ready\": [], \"chosen\": null, \"children\": [], \"next_key\": null, \"heap_after\": [1], \"frontier_after\": []}, \"passed\": true}, {\"check\": \"regression certificate 2\", \"actual\": {\"ready\": [1, 2], \"chosen\": 2, \"children\": [1, 2], \"next_key\": 2, \"heap_after\": [1, 7, 2], \"frontier_after\": [1]}, \"expected\": {\"ready\": [2, 1], \"chosen\": 2, \"children\": [1, 2], \"next_key\": 2, \"heap_after\": [1, 7, 2], \"frontier_after\": [1]}, \"passed\": false}, {\"check\": \"regression certificate 3\", \"actual\": {\"ready\": [2, 3, 4], \"chosen\": 2, \"children\": [3, 4], \"next_key\": 2, \"heap_after\": [1, 4, 2, 7, 5, 3, 6], \"frontier_after\": [4, 3]}, \"expected\": {\"ready\": [2, 4, 3], \"chosen\": 2, \"children\": [3, 4], \"next_key\": 2, \"heap_after\": [1, 4, 2, 7, 5, 3, 6], \"frontier_after\": [4, 3]}, \"passed\": false}, {\"check\": \"regression certificate 4\", \"actual\": {\"ready\": [2, 3, 4], \"chosen\": 2, \"children\": [3, 4], \"next_key\": 2, \"heap_after\": [1, 4, 2, 7, 4, 3, 6], \"frontier_after\": [4, 3]}, \"expected\": {\"ready\": [2, 4, 3], \"chosen\": 2, \"children\": [3, 4], \"next_key\": 2, \"heap_after\": [1, 4, 2, 7, 4, 3, 6], \"frontier_after\": [4, 3]}, \"passed\": false}, {\"check\": \"regression certificate 5\", \"actual\": {\"ready\": [1, 2], \"chosen\": 1, \"children\": [1, 2], \"next_key\": 3, \"heap_after\": [1, 3, 3, 5, 6, 7, 8], \"frontier_after\": [2]}, \"expected\": {\"ready\": [1, 2], \"chosen\": 1, \"children\": [1, 2], \"next_key\": 3, \"heap_after\": [1, 3, 3, 5, 6, 7, 8], \"frontier_after\": [2]}, \"passed\": true}, {\"check\": \"regression certificate 6\", \"actual\": {\"ready\": [2, 4, 7], \"chosen\": 2, \"children\": [7], \"next_key\": 3, \"heap_after\": [1, 2, 3, 4, 5, 6, 7, 8], \"frontier_after\": [4, 7]}, \"expected\": {\"ready\": [2, 4, 7], \"chosen\": 2, \"children\": [7], \"next_key\": 3, \"heap_after\": [1, 2, 3, 4, 5, 6, 7, 8], \"frontier_after\": [4, 7]}, \"passed\": true}, {\"check\": \"variant-dependent certificate\", \"actual\": {\"ready\": [2, 4, 7], \"chosen\": 2, \"children\": [7], \"next_key\": 3, \"heap_after\": [1, 2, 3, 4, 5, 6, 7, 9], \"frontier_after\": [4, 7]}, \"expected\": {\"ready\": [2, 4, 7], \"chosen\": 2, \"children\": [7], \"next_key\": 3, \"heap_after\": [1, 2, 3, 4, 5, 6, 7, 9], \"frontier_after\": [4, 7]}, \"passed\": true}], \"passed\": false}\n"}},"member_only":{"stages":["fixed"],"fields":["implementations.fixed","verification.fixed","harness","repair"],"note":"The verified repair, its recorded checks, the repair description, and the scoring harness are available to members."}}