{"abstract":"The bounded leftist ranks certificate reports an incorrect rank recurrence.","category":"Heap invariants","checks":7,"contract":"A leftist-tree certificate has nodes [key,left,right,stored_npl] with missing child=-1 and valid references. Null-path length of null is -1. Report local heap-edge violations, rank recurrence violations, leftist orientation violations, leaves, unary-right nodes, and root-to-right-spine length; spine traversal stops on repeated node.","contract_signature":"d","evaluation_group":"s3-heap-model-leftist-ranks","failed_approach":"The local patch uses [i for i,x in enumerate(a) if x[3]!=min(rank(x[1]),rank(x[2]))] and still violates the stated relation.","family":"s3-heap-leftist-ranks-rank_recurrence","id":"FA-39906","implementations":{"attempt":{"sha256":"4e2b2e9e1ceb6ae46321bfe4912406441a6111f997c0724e645d3e4ee139ab32","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    a=d['nodes']; root=d['root']\n    def rank(i): return -1 if i==-1 else a[i][3]\n    spine=[]; q=root\n    while q!=-1 and q not in spine:\n        spine.append(q); q=a[q][2]\n    return {'heap_edges': [[i,j] for i,x in enumerate(a) for j in x[1:3] if j!=-1 and a[j][0]<x[0]],\n    'rank_recurrence': [i for i,x in enumerate(a) if x[3]!=min(rank(x[1]),rank(x[2]))],\n    'orientation': [i for i,x in enumerate(a) if rank(x[1])<rank(x[2])],\n    'leaves': [i for i,x in enumerate(a) if x[1]==-1 and x[2]==-1],\n    'right_orphans': [i for i,x in enumerate(a) if x[1]==-1 and x[2]!=-1],\n    'spine_length': len(spine)}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'nodes': [], 'root': -1}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [], 'right_orphans': [], 'spine_length': 0}), ({'nodes': [[4, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [0], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[1, 1, 2, 1], [5, -1, -1, 0], [7, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1, 2], 'right_orphans': [], 'spine_length': 2}), ({'nodes': [[5, 1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[8, -1, 1, 1], [2, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 1]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1], 'right_orphans': [0], 'spine_length': 2}), ({'nodes': [[2, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3}), ({'nodes': [[3, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3})], [({'nodes': [], 'root': -1}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [], 'right_orphans': [], 'spine_length': 0}), ({'nodes': [[4, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [0], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[1, 1, 2, 1], [5, -1, -1, 0], [7, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1, 2], 'right_orphans': [], 'spine_length': 2}), ({'nodes': [[5, 1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[8, -1, 1, 1], [2, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 1]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1], 'right_orphans': [0], 'spine_length': 2}), ({'nodes': [[2, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3}), ({'nodes': [[4, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3})], [({'nodes': [], 'root': -1}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [], 'right_orphans': [], 'spine_length': 0}), ({'nodes': [[4, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [0], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[1, 1, 2, 1], [5, -1, -1, 0], [7, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1, 2], 'right_orphans': [], 'spine_length': 2}), ({'nodes': [[5, 1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[8, -1, 1, 1], [2, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 1]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1], 'right_orphans': [0], 'spine_length': 2}), ({'nodes': [[2, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3}), ({'nodes': [[5, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3})], [({'nodes': [], 'root': -1}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [], 'right_orphans': [], 'spine_length': 0}), ({'nodes': [[4, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [0], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[1, 1, 2, 1], [5, -1, -1, 0], [7, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1, 2], 'right_orphans': [], 'spine_length': 2}), ({'nodes': [[5, 1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[8, -1, 1, 1], [2, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 1]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1], 'right_orphans': [0], 'spine_length': 2}), ({'nodes': [[2, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3}), ({'nodes': [[6, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3})], [({'nodes': [], 'root': -1}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [], 'right_orphans': [], 'spine_length': 0}), ({'nodes': [[4, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [0], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[1, 1, 2, 1], [5, -1, -1, 0], [7, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1, 2], 'right_orphans': [], 'spine_length': 2}), ({'nodes': [[5, 1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[8, -1, 1, 1], [2, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 1]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1], 'right_orphans': [0], 'spine_length': 2}), ({'nodes': [[2, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3}), ({'nodes': [[7, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3})]][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":"ae94cd26ec07ad4d7099e06ff075939d124c1691607997dfe2e0b35e151ad154","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    a=d['nodes']; root=d['root']\n    def rank(i): return -1 if i==-1 else a[i][3]\n    spine=[]; q=root\n    while q!=-1 and q not in spine:\n        spine.append(q); q=a[q][2]\n    return {'heap_edges': [[i,j] for i,x in enumerate(a) for j in x[1:3] if j!=-1 and a[j][0]<x[0]],\n    'rank_recurrence': [i for i,x in enumerate(a) if x[3]!=1+max(rank(x[1]),rank(x[2]))],\n    'orientation': [i for i,x in enumerate(a) if rank(x[1])<rank(x[2])],\n    'leaves': [i for i,x in enumerate(a) if x[1]==-1 and x[2]==-1],\n    'right_orphans': [i for i,x in enumerate(a) if x[1]==-1 and x[2]!=-1],\n    'spine_length': len(spine)}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'nodes': [], 'root': -1}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [], 'right_orphans': [], 'spine_length': 0}), ({'nodes': [[4, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [0], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[1, 1, 2, 1], [5, -1, -1, 0], [7, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1, 2], 'right_orphans': [], 'spine_length': 2}), ({'nodes': [[5, 1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[8, -1, 1, 1], [2, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 1]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1], 'right_orphans': [0], 'spine_length': 2}), ({'nodes': [[2, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3}), ({'nodes': [[3, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3})], [({'nodes': [], 'root': -1}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [], 'right_orphans': [], 'spine_length': 0}), ({'nodes': [[4, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [0], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[1, 1, 2, 1], [5, -1, -1, 0], [7, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1, 2], 'right_orphans': [], 'spine_length': 2}), ({'nodes': [[5, 1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[8, -1, 1, 1], [2, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 1]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1], 'right_orphans': [0], 'spine_length': 2}), ({'nodes': [[2, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3}), ({'nodes': [[4, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3})], [({'nodes': [], 'root': -1}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [], 'right_orphans': [], 'spine_length': 0}), ({'nodes': [[4, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [0], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[1, 1, 2, 1], [5, -1, -1, 0], [7, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1, 2], 'right_orphans': [], 'spine_length': 2}), ({'nodes': [[5, 1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[8, -1, 1, 1], [2, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 1]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1], 'right_orphans': [0], 'spine_length': 2}), ({'nodes': [[2, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3}), ({'nodes': [[5, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3})], [({'nodes': [], 'root': -1}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [], 'right_orphans': [], 'spine_length': 0}), ({'nodes': [[4, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [0], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[1, 1, 2, 1], [5, -1, -1, 0], [7, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1, 2], 'right_orphans': [], 'spine_length': 2}), ({'nodes': [[5, 1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[8, -1, 1, 1], [2, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 1]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1], 'right_orphans': [0], 'spine_length': 2}), ({'nodes': [[2, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3}), ({'nodes': [[6, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3})], [({'nodes': [], 'root': -1}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [], 'right_orphans': [], 'spine_length': 0}), ({'nodes': [[4, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [0], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[1, 1, 2, 1], [5, -1, -1, 0], [7, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1, 2], 'right_orphans': [], 'spine_length': 2}), ({'nodes': [[5, 1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[8, -1, 1, 1], [2, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 1]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1], 'right_orphans': [0], 'spine_length': 2}), ({'nodes': [[2, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3}), ({'nodes': [[7, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3})]][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-leftist-ranks-rank_recurrence","generated_at":"2026-09-29T14:43:26.079081+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":"Null-path length counts the shortest path through an absent child including the current node.","sha256":"3df6417fbeab506022b1c666e4bf8c34a2a63167f617bf46ec0527398ad84433","title":"Leftist null-path rank is derived from the taller child · 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":42.065,"exit_code":1,"observations":[{"actual":{"heap_edges":[],"leaves":[],"orientation":[],"rank_recurrence":[],"right_orphans":[],"spine_length":0},"check":"regression certificate 1","expected":{"heap_edges":[],"leaves":[],"orientation":[],"rank_recurrence":[],"right_orphans":[],"spine_length":0},"passed":true},{"actual":{"heap_edges":[],"leaves":[0],"orientation":[],"rank_recurrence":[0],"right_orphans":[],"spine_length":1},"check":"regression certificate 2","expected":{"heap_edges":[],"leaves":[0],"orientation":[],"rank_recurrence":[],"right_orphans":[],"spine_length":1},"passed":false},{"actual":{"heap_edges":[],"leaves":[1,2],"orientation":[],"rank_recurrence":[0,1,2],"right_orphans":[],"spine_length":2},"check":"regression certificate 3","expected":{"heap_edges":[],"leaves":[1,2],"orientation":[],"rank_recurrence":[],"right_orphans":[],"spine_length":2},"passed":false},{"actual":{"heap_edges":[],"leaves":[1],"orientation":[],"rank_recurrence":[0,1],"right_orphans":[],"spine_length":1},"check":"regression certificate 4","expected":{"heap_edges":[],"leaves":[1],"orientation":[],"rank_recurrence":[],"right_orphans":[],"spine_length":1},"passed":false},{"actual":{"heap_edges":[[0,1]],"leaves":[1],"orientation":[0],"rank_recurrence":[0,1],"right_orphans":[0],"spine_length":2},"check":"regression certificate 5","expected":{"heap_edges":[[0,1]],"leaves":[1],"orientation":[0],"rank_recurrence":[0],"right_orphans":[0],"spine_length":2},"passed":false},{"actual":{"heap_edges":[[0,2]],"leaves":[1,3,4],"orientation":[0],"rank_recurrence":[0,1,2,3,4],"right_orphans":[],"spine_length":3},"check":"regression certificate 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