{"abstract":"The reduction disagrees with its explicit aggregation oracle.","category":"Numerical aggregation","checks":8,"contract":"Concatenate ordered integer blocks logically and sum products of neighboring observations. Empty blocks are identity; there is exactly one cross-boundary product between consecutive nonempty blocks.","contract_signature":"blocks","evaluation_group":"s3-na-adjacent-product-block-reduction","failed_approach":"Replacing the carried endpoint by zero also breaks adjacency across empty blocks.","family":"s3-numerical-aggregation-adjacent-product-block-reduction-adjacent-empty-reset","id":"FA-13926","implementations":{"attempt":{"sha256":"71a740971e5da68295c0c18b072ae4d6e016bd39ff792e184f2c085d742110ca","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nfrom collections import Counter, defaultdict\nimport math\nimport itertools\nN = 1\nobservations = []\ndef solve(blocks):\n    total=0\n    last=None\n    for block in blocks:\n        if not block:\n            last=0\n            continue\n        total+=sum(a*b for a,b in zip(block,block[1:]))\n        if last is not None: total+=last*block[0]\n        last=block[-1]\n    return total\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([[1, 2], [3, 4]],)), 20)\ncheck('regression 2', solve(*([[2], [], [-3], [5]],)), -21)\ncheck('regression 3', solve(*([],)), 0)\ncheck('regression 4', solve(*([[0, 4], [3, 0]],)), 12)\ncheck('regression 5', solve(*([[-2, -1], [3, -4, 5]],)), -33)\ncheck('regression 6', solve(*([[], [7], []],)), 0)\ncheck('regression 7', solve(*([[2, 3, 4]],)), 18)\ncheck(\"variable interblock product\",solve([[N],[N+1]]),N*(N+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":"91ed023df952f4ea6cb535b23a2b09c0f0907affd351181bf5b796ddf1a0ecd1","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nfrom collections import Counter, defaultdict\nimport math\nimport itertools\nN = 1\nobservations = []\ndef solve(blocks):\n    total=0\n    last=None\n    for block in blocks:\n        if not block:\n            last=None\n            continue\n        total+=sum(a*b for a,b in zip(block,block[1:]))\n        if last is not None: total+=last*block[0]\n        last=block[-1]\n    return total\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([[1, 2], [3, 4]],)), 20)\ncheck('regression 2', solve(*([[2], [], [-3], [5]],)), -21)\ncheck('regression 3', solve(*([],)), 0)\ncheck('regression 4', solve(*([[0, 4], [3, 0]],)), 12)\ncheck('regression 5', solve(*([[-2, -1], [3, -4, 5]],)), -33)\ncheck('regression 6', solve(*([[], [7], []],)), 0)\ncheck('regression 7', solve(*([[2, 3, 4]],)), 18)\ncheck(\"variable interblock product\",solve([[N],[N+1]]),N*(N+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":"Small offline integer/rational inputs only; no performance, statistical inference, or production-library conformance claim. 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-numerical-aggregation-adjacent-product-block-reduction-adjacent-empty-reset","generated_at":"2026-09-29T14:39:12.219008+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Exact bounded examples isolate a reduction defect without floating-point or external-service effects.","root_cause":"An empty block clears the carried neighbor.","sha256":"8b5a5c67e9e5df54e0e4a7d318a318b09f1fe64e5f9164b77b3adfd12ea91b36","title":"Adjacent product block reduction: An empty block clears the carried neighbor. · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":44.746,"exit_code":1,"observations":[{"actual":20,"check":"regression 1","expected":20,"passed":true},{"actual":-15,"check":"regression 2","expected":-21,"passed":false},{"actual":0,"check":"regression 3","expected":0,"passed":true},{"actual":12,"check":"regression 4","expected":12,"passed":true},{"actual":-33,"check":"regression 5","expected":-33,"passed":true},{"actual":0,"check":"regression 6","expected":0,"passed":true},{"actual":18,"check":"regression 7","expected":18,"passed":true},{"actual":2,"check":"variable interblock product","expected":2,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": 20, \"expected\": 20, \"passed\": true}, {\"check\": \"regression 2\", \"actual\": -15, \"expected\": -21, \"passed\": false}, {\"check\": \"regression 3\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"regression 4\", \"actual\": 12, \"expected\": 12, \"passed\": true}, {\"check\": \"regression 5\", \"actual\": -33, \"expected\": -33, \"passed\": true}, {\"check\": \"regression 6\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"regression 7\", \"actual\": 18, \"expected\": 18, \"passed\": true}, {\"check\": \"variable interblock product\", \"actual\": 2, \"expected\": 2, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":42.17,"exit_code":1,"observations":[{"actual":20,"check":"regression 1","expected":20,"passed":true},{"actual":-15,"check":"regression 2","expected":-21,"passed":false},{"actual":0,"check":"regression 3","expected":0,"passed":true},{"actual":12,"check":"regression 4","expected":12,"passed":true},{"actual":-33,"check":"regression 5","expected":-33,"passed":true},{"actual":0,"check":"regression 6","expected":0,"passed":true},{"actual":18,"check":"regression 7","expected":18,"passed":true},{"actual":2,"check":"variable interblock product","expected":2,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": 20, \"expected\": 20, \"passed\": true}, {\"check\": \"regression 2\", \"actual\": -15, \"expected\": -21, \"passed\": false}, {\"check\": \"regression 3\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"regression 4\", \"actual\": 12, \"expected\": 12, \"passed\": true}, {\"check\": \"regression 5\", \"actual\": -33, \"expected\": -33, \"passed\": true}, {\"check\": \"regression 6\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"regression 7\", \"actual\": 18, \"expected\": 18, \"passed\": true}, {\"check\": \"variable interblock product\", \"actual\": 2, \"expected\": 2, \"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."}}