{"abstract":"The power exponent converges to 1 or 10 and the fair probabilities do not sum to one.","category":"Betting odds conversion","checks":8,"contract":"Remove the bookmaker margin from decimal prices (implied p = 1/d, book = sum p > 1 assumed). multiplicative: p / book. additive: p - (book - 1) / n; if any result is negative return \"additive infeasible\". power: p ** k with k found by 60 bisection steps on [1, 10] so that the powered probabilities sum to 1 (k = midpoint of the final bracket). Any other method returns \"invalid method\". Return the fair probabilities formatted \"%.4f\".","evaluation_group":"w2-odds-conversion-margin-removal-methods","failed_approach":"Searching k on [0, 1] cannot reduce probabilities whose sum already exceeds one.","family":"w2-odds-conversion-margin-removal-methods-power-bracket-update","id":"FA-84436","implementations":{"attempt":{"sha256":"5e59dc26f4de37ea2814e36dca6cf8162412cc4e0e7347152fbe4b5b21b82aee","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(prices, method):\n    ps = [1 / float(d) for d in prices]\n    book = sum(ps)\n    n = len(ps)\n    if method == 'multiplicative':\n        fair = [p / book for p in ps]\n    elif method == 'additive':\n        fair = [p - (book - 1) / n for p in ps]\n        if any(x < 0 for x in fair):\n            return 'additive infeasible'\n    elif method == 'power':\n        lo, hi = 0.0, 1.0\n        for _ in range(60):\n            mid = (lo + hi) / 2\n            if sum(p ** mid for p in ps) > 1:\n                lo = mid\n            else:\n                hi = mid\n        k = (lo + hi) / 2\n        fair = [p ** k for p in ps]\n    else:\n        return 'invalid method'\n    return ['%.4f' % x for x in fair]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ndef run(args):\n    try:\n        return solve(*args)\n    except Exception as exc:\n        return 'raised ' + type(exc).__name__\ncases = [[('control multiplicative', (['1.80', '2.00'], 'multiplicative'), ['0.5263', '0.4737']),\n  ('control additive', (['1.80', '2.00'], 'additive'), ['0.5278', '0.4722']),\n  ('control power', (['1.80', '2.00'], 'power'), ['0.5285', '0.4715']),\n  ('boundary additive longshot',\n   (['1.01', '15.00', '100.00', '100.00'], 'additive'),\n   'additive infeasible'),\n  ('boundary unknown method', (['1.80', '2.00'], 'shin'), 'invalid method'),\n  ('regression: power bracket update', (['3.67', '1.10'], 'power'), ['0.1360', '0.8640']),\n  ('variant scenario 1', (['1.16', '6.38'], 'power'), ['0.8562', '0.1438']),\n  ('variant scenario 2', (['2.05', '14.07', '2.09'], 'additive'), ['0.4754', '0.0586', '0.4660'])],\n [('control multiplicative', (['1.80', '2.00'], 'multiplicative'), ['0.5263', '0.4737']),\n  ('control additive', (['1.80', '2.00'], 'additive'), ['0.5278', '0.4722']),\n  ('control power', (['1.80', '2.00'], 'power'), ['0.5285', '0.4715']),\n  ('boundary additive longshot',\n   (['1.01', '15.00', '100.00', '100.00'], 'additive'),\n   'additive infeasible'),\n  ('boundary unknown method', (['1.80', '2.00'], 'shin'), 'invalid method'),\n  ('regression: power bracket update',\n   (['5.55', '2.14', '2.00'], 'power'),\n   ['0.1375', '0.4144', '0.4482']),\n  ('variant scenario 1',\n   (['2.01', '2.51', '6.12', '10.10'], 'additive'),\n   ['0.4579', '0.3588', '0.1238', '0.0594']),\n  ('variant scenario 2', (['1.57', '1.97'], 'shin'), 'invalid method')],\n [('control multiplicative', (['1.80', '2.00'], 'multiplicative'), ['0.5263', '0.4737']),\n  ('control additive', (['1.80', '2.00'], 'additive'), ['0.5278', '0.4722']),\n  ('control power', (['1.80', '2.00'], 'power'), ['0.5285', '0.4715']),\n  ('boundary additive longshot',\n   (['1.01', '15.00', '100.00', '100.00'], 'additive'),\n   'additive infeasible'),\n  ('boundary unknown method', (['1.80', '2.00'], 'shin'), 'invalid method'),\n  ('regression: power bracket update',\n   (['6.44', '3.05', '2.57', '6.36'], 'power'),\n   ['0.1488', '0.3196', '0.3808', '0.1507']),\n  ('variant scenario 1',\n   (['2.82', '5.29', '5.54', '2.56'], 'additive'),\n   ['0.3259', '0.1603', '0.1518', '0.3619']),\n  ('variant scenario 2', (['1.27', '11.62', '4.64'], 'shin'), 'invalid method')],\n [('control multiplicative', (['1.80', '2.00'], 'multiplicative'), ['0.5263', '0.4737']),\n  ('control additive', (['1.80', '2.00'], 'additive'), ['0.5278', '0.4722']),\n  ('control power', (['1.80', '2.00'], 'power'), ['0.5285', '0.4715']),\n  ('boundary additive longshot',\n   (['1.01', '15.00', '100.00', '100.00'], 'additive'),\n   'additive infeasible'),\n  ('boundary unknown method', (['1.80', '2.00'], 'shin'), 'invalid method'),\n  ('regression: power bracket update',\n   (['2.85', '3.58', '3.18', '8.34'], 'power'),\n   ['0.3331', '0.2622', '0.2969', '0.1079']),\n  ('variant scenario 1', (['1.68', '4.49', '3.51'], 'additive'), ['0.5610', '0.1884', '0.2506']),\n  ('variant scenario 2', (['2.30', '1.48'], 'additive'), ['0.3796', '0.6204'])],\n [('control multiplicative', (['1.80', '2.00'], 'multiplicative'), ['0.5263', '0.4737']),\n  ('control additive', (['1.80', '2.00'], 'additive'), ['0.5278', '0.4722']),\n  ('control power', (['1.80', '2.00'], 'power'), ['0.5285', '0.4715']),\n  ('boundary additive longshot',\n   (['1.01', '15.00', '100.00', '100.00'], 'additive'),\n   'additive infeasible'),\n  ('boundary unknown method', (['1.80', '2.00'], 'shin'), 'invalid method'),\n  ('regression: power bracket update',\n   (['3.00', '5.62', '3.12', '2.96'], 'power'),\n   ['0.2887', '0.1420', '0.2762', '0.2931']),\n  ('variant scenario 1',\n   (['2.72', '54.78', '4.16', '2.80', '6.54'], 'multiplicative'),\n   ['0.3235', '0.0161', '0.2115', '0.3143', '0.1346']),\n  ('variant scenario 2',\n   (['4.03', '4.17', '5.00', '12.68', '4.10'], 'power'),\n   ['0.2458', '0.2374', '0.1978', '0.0775', '0.2415'])]]\nfor label, args, expected in cases[N - 1]:\n    check(label, run(args), expected)\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":"4480d183e5414768e05c87ca4f5d106063d93234a309243fba99d77c4a2ac1e9","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(prices, method):\n    ps = [1 / float(d) for d in prices]\n    book = sum(ps)\n    n = len(ps)\n    if method == 'multiplicative':\n        fair = [p / book for p in ps]\n    elif method == 'additive':\n        fair = [p - (book - 1) / n for p in ps]\n        if any(x < 0 for x in fair):\n            return 'additive infeasible'\n    elif method == 'power':\n        lo, hi = 1.0, 10.0\n        for _ in range(60):\n            mid = (lo + hi) / 2\n            if sum(p ** mid for p in ps) > 1:\n                hi = mid\n            else:\n                lo = mid\n        k = (lo + hi) / 2\n        fair = [p ** k for p in ps]\n    else:\n        return 'invalid method'\n    return ['%.4f' % x for x in fair]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ndef run(args):\n    try:\n        return solve(*args)\n    except Exception as exc:\n        return 'raised ' + type(exc).__name__\ncases = [[('control multiplicative', (['1.80', '2.00'], 'multiplicative'), ['0.5263', '0.4737']),\n  ('control additive', (['1.80', '2.00'], 'additive'), ['0.5278', '0.4722']),\n  ('control power', (['1.80', '2.00'], 'power'), ['0.5285', '0.4715']),\n  ('boundary additive longshot',\n   (['1.01', '15.00', '100.00', '100.00'], 'additive'),\n   'additive infeasible'),\n  ('boundary unknown method', (['1.80', '2.00'], 'shin'), 'invalid method'),\n  ('regression: power bracket update', (['3.67', '1.10'], 'power'), ['0.1360', '0.8640']),\n  ('variant scenario 1', (['1.16', '6.38'], 'power'), ['0.8562', '0.1438']),\n  ('variant scenario 2', (['2.05', '14.07', '2.09'], 'additive'), ['0.4754', '0.0586', '0.4660'])],\n [('control multiplicative', (['1.80', '2.00'], 'multiplicative'), ['0.5263', '0.4737']),\n  ('control additive', (['1.80', '2.00'], 'additive'), ['0.5278', '0.4722']),\n  ('control power', (['1.80', '2.00'], 'power'), ['0.5285', '0.4715']),\n  ('boundary additive longshot',\n   (['1.01', '15.00', '100.00', '100.00'], 'additive'),\n   'additive infeasible'),\n  ('boundary unknown method', (['1.80', '2.00'], 'shin'), 'invalid method'),\n  ('regression: power bracket update',\n   (['5.55', '2.14', '2.00'], 'power'),\n   ['0.1375', '0.4144', '0.4482']),\n  ('variant scenario 1',\n   (['2.01', '2.51', '6.12', '10.10'], 'additive'),\n   ['0.4579', '0.3588', '0.1238', '0.0594']),\n  ('variant scenario 2', (['1.57', '1.97'], 'shin'), 'invalid method')],\n [('control multiplicative', (['1.80', '2.00'], 'multiplicative'), ['0.5263', '0.4737']),\n  ('control additive', (['1.80', '2.00'], 'additive'), ['0.5278', '0.4722']),\n  ('control power', (['1.80', '2.00'], 'power'), ['0.5285', '0.4715']),\n  ('boundary additive longshot',\n   (['1.01', '15.00', '100.00', '100.00'], 'additive'),\n   'additive infeasible'),\n  ('boundary unknown method', (['1.80', '2.00'], 'shin'), 'invalid method'),\n  ('regression: power bracket update',\n   (['6.44', '3.05', '2.57', '6.36'], 'power'),\n   ['0.1488', '0.3196', '0.3808', '0.1507']),\n  ('variant scenario 1',\n   (['2.82', '5.29', '5.54', '2.56'], 'additive'),\n   ['0.3259', '0.1603', '0.1518', '0.3619']),\n  ('variant scenario 2', (['1.27', '11.62', '4.64'], 'shin'), 'invalid method')],\n [('control multiplicative', (['1.80', '2.00'], 'multiplicative'), ['0.5263', '0.4737']),\n  ('control additive', (['1.80', '2.00'], 'additive'), ['0.5278', '0.4722']),\n  ('control power', (['1.80', '2.00'], 'power'), ['0.5285', '0.4715']),\n  ('boundary additive longshot',\n   (['1.01', '15.00', '100.00', '100.00'], 'additive'),\n   'additive infeasible'),\n  ('boundary unknown method', (['1.80', '2.00'], 'shin'), 'invalid method'),\n  ('regression: power bracket update',\n   (['2.85', '3.58', '3.18', '8.34'], 'power'),\n   ['0.3331', '0.2622', '0.2969', '0.1079']),\n  ('variant scenario 1', (['1.68', '4.49', '3.51'], 'additive'), ['0.5610', '0.1884', '0.2506']),\n  ('variant scenario 2', (['2.30', '1.48'], 'additive'), ['0.3796', '0.6204'])],\n [('control multiplicative', (['1.80', '2.00'], 'multiplicative'), ['0.5263', '0.4737']),\n  ('control additive', (['1.80', '2.00'], 'additive'), ['0.5278', '0.4722']),\n  ('control power', (['1.80', '2.00'], 'power'), ['0.5285', '0.4715']),\n  ('boundary additive longshot',\n   (['1.01', '15.00', '100.00', '100.00'], 'additive'),\n   'additive infeasible'),\n  ('boundary unknown method', (['1.80', '2.00'], 'shin'), 'invalid method'),\n  ('regression: power bracket update',\n   (['3.00', '5.62', '3.12', '2.96'], 'power'),\n   ['0.2887', '0.1420', '0.2762', '0.2931']),\n  ('variant scenario 1',\n   (['2.72', '54.78', '4.16', '2.80', '6.54'], 'multiplicative'),\n   ['0.3235', '0.0161', '0.2115', '0.3143', '0.1346']),\n  ('variant scenario 2',\n   (['4.03', '4.17', '5.00', '12.68', '4.10'], 'power'),\n   ['0.2458', '0.2374', '0.1978', '0.0775', '0.2415'])]]\nfor label, args, expected in cases[N - 1]:\n    check(label, run(args), expected)\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"},"fixed":{"sha256":"3e95fa1b777c4741f951f64429bf4a9540867ec22e5046e9c2a1269366e90cbe","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(prices, method):\n    ps = [1 / float(d) for d in prices]\n    book = sum(ps)\n    n = len(ps)\n    if method == 'multiplicative':\n        fair = [p / book for p in ps]\n    elif method == 'additive':\n        fair = [p - (book - 1) / n for p in ps]\n        if any(x < 0 for x in fair):\n            return 'additive infeasible'\n    elif method == 'power':\n        lo, hi = 1.0, 10.0\n        for _ in range(60):\n            mid = (lo + hi) / 2\n            if sum(p ** mid for p in ps) > 1:\n                lo = mid\n            else:\n                hi = mid\n        k = (lo + hi) / 2\n        fair = [p ** k for p in ps]\n    else:\n        return 'invalid method'\n    return ['%.4f' % x for x in fair]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ndef run(args):\n    try:\n        return solve(*args)\n    except Exception as exc:\n        return 'raised ' + type(exc).__name__\ncases = [[('control multiplicative', (['1.80', '2.00'], 'multiplicative'), ['0.5263', '0.4737']),\n  ('control additive', (['1.80', '2.00'], 'additive'), ['0.5278', '0.4722']),\n  ('control power', (['1.80', '2.00'], 'power'), ['0.5285', '0.4715']),\n  ('boundary additive longshot',\n   (['1.01', '15.00', '100.00', '100.00'], 'additive'),\n   'additive infeasible'),\n  ('boundary unknown method', (['1.80', '2.00'], 'shin'), 'invalid method'),\n  ('regression: power bracket update', (['3.67', '1.10'], 'power'), ['0.1360', '0.8640']),\n  ('variant scenario 1', (['1.16', '6.38'], 'power'), ['0.8562', '0.1438']),\n  ('variant scenario 2', (['2.05', '14.07', '2.09'], 'additive'), ['0.4754', '0.0586', '0.4660'])],\n [('control multiplicative', (['1.80', '2.00'], 'multiplicative'), ['0.5263', '0.4737']),\n  ('control additive', (['1.80', '2.00'], 'additive'), ['0.5278', '0.4722']),\n  ('control power', (['1.80', '2.00'], 'power'), ['0.5285', '0.4715']),\n  ('boundary additive longshot',\n   (['1.01', '15.00', '100.00', '100.00'], 'additive'),\n   'additive infeasible'),\n  ('boundary unknown method', (['1.80', '2.00'], 'shin'), 'invalid method'),\n  ('regression: power bracket update',\n   (['5.55', '2.14', '2.00'], 'power'),\n   ['0.1375', '0.4144', '0.4482']),\n  ('variant scenario 1',\n   (['2.01', '2.51', '6.12', '10.10'], 'additive'),\n   ['0.4579', '0.3588', '0.1238', '0.0594']),\n  ('variant scenario 2', (['1.57', '1.97'], 'shin'), 'invalid method')],\n [('control multiplicative', (['1.80', '2.00'], 'multiplicative'), ['0.5263', '0.4737']),\n  ('control additive', (['1.80', '2.00'], 'additive'), ['0.5278', '0.4722']),\n  ('control power', (['1.80', '2.00'], 'power'), ['0.5285', '0.4715']),\n  ('boundary additive longshot',\n   (['1.01', '15.00', '100.00', '100.00'], 'additive'),\n   'additive infeasible'),\n  ('boundary unknown method', (['1.80', '2.00'], 'shin'), 'invalid method'),\n  ('regression: power bracket update',\n   (['6.44', '3.05', '2.57', '6.36'], 'power'),\n   ['0.1488', '0.3196', '0.3808', '0.1507']),\n  ('variant scenario 1',\n   (['2.82', '5.29', '5.54', '2.56'], 'additive'),\n   ['0.3259', '0.1603', '0.1518', '0.3619']),\n  ('variant scenario 2', (['1.27', '11.62', '4.64'], 'shin'), 'invalid method')],\n [('control multiplicative', (['1.80', '2.00'], 'multiplicative'), ['0.5263', '0.4737']),\n  ('control additive', (['1.80', '2.00'], 'additive'), ['0.5278', '0.4722']),\n  ('control power', (['1.80', '2.00'], 'power'), ['0.5285', '0.4715']),\n  ('boundary additive longshot',\n   (['1.01', '15.00', '100.00', '100.00'], 'additive'),\n   'additive infeasible'),\n  ('boundary unknown method', (['1.80', '2.00'], 'shin'), 'invalid method'),\n  ('regression: power bracket update',\n   (['2.85', '3.58', '3.18', '8.34'], 'power'),\n   ['0.3331', '0.2622', '0.2969', '0.1079']),\n  ('variant scenario 1', (['1.68', '4.49', '3.51'], 'additive'), ['0.5610', '0.1884', '0.2506']),\n  ('variant scenario 2', (['2.30', '1.48'], 'additive'), ['0.3796', '0.6204'])],\n [('control multiplicative', (['1.80', '2.00'], 'multiplicative'), ['0.5263', '0.4737']),\n  ('control additive', (['1.80', '2.00'], 'additive'), ['0.5278', '0.4722']),\n  ('control power', (['1.80', '2.00'], 'power'), ['0.5285', '0.4715']),\n  ('boundary additive longshot',\n   (['1.01', '15.00', '100.00', '100.00'], 'additive'),\n   'additive infeasible'),\n  ('boundary unknown method', (['1.80', '2.00'], 'shin'), 'invalid method'),\n  ('regression: power bracket update',\n   (['3.00', '5.62', '3.12', '2.96'], 'power'),\n   ['0.2887', '0.1420', '0.2762', '0.2931']),\n  ('variant scenario 1',\n   (['2.72', '54.78', '4.16', '2.80', '6.54'], 'multiplicative'),\n   ['0.3235', '0.0161', '0.2115', '0.3143', '0.1346']),\n  ('variant scenario 2',\n   (['4.03', '4.17', '5.00', '12.68', '4.10'], 'power'),\n   ['0.2458', '0.2374', '0.1978', '0.0775', '0.2415'])]]\nfor label, args, expected in cases[N - 1]:\n    check(label, run(args), expected)\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":"Stipulated, bounded toy contract stated in the contract field; not a claim of conformance with any operator, exchange or regulator rule set. 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":"w2-odds-conversion-margin-removal-methods-power-bracket-update","generated_at":"2026-09-29T14:50:30.941542+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Pricing models strip margins differently; favourite-longshot bias makes the method matter.","repair":"Raise lo while the powered sum exceeds one.","root_cause":"The bisection sets hi when the powered sum is still above one.","sha256":"a27665ca27b2a1ee24f3eeb578d4035481bbe73f0a82e0ce6c2d3ce9fad09c96","title":"Power-method bisection moves the wrong bracket end · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":38.505,"exit_code":1,"observations":[{"actual":["0.5263","0.4737"],"check":"control multiplicative","expected":["0.5263","0.4737"],"passed":true},{"actual":["0.5278","0.4722"],"check":"control additive","expected":["0.5278","0.4722"],"passed":true},{"actual":["0.5556","0.5000"],"check":"control power","expected":["0.5285","0.4715"],"passed":false},{"actual":"additive infeasible","check":"boundary additive longshot","expected":"additive infeasible","passed":true},{"actual":"invalid method","check":"boundary unknown method","expected":"invalid method","passed":true},{"actual":["0.2725","0.9091"],"check":"regression: power bracket update","expected":["0.1360","0.8640"],"passed":false},{"actual":["0.8621","0.1567"],"check":"variant scenario 1","expected":["0.8562","0.1438"],"passed":false},{"actual":["0.4754","0.0586","0.4660"],"check":"variant scenario 2","expected":["0.4754","0.0586","0.4660"],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"control multiplicative\", \"actual\": [\"0.5263\", \"0.4737\"], \"expected\": [\"0.5263\", \"0.4737\"], \"passed\": true}, {\"check\": \"control additive\", \"actual\": [\"0.5278\", \"0.4722\"], \"expected\": [\"0.5278\", \"0.4722\"], \"passed\": true}, {\"check\": \"control power\", \"actual\": [\"0.5556\", \"0.5000\"], \"expected\": [\"0.5285\", \"0.4715\"], \"passed\": false}, {\"check\": \"boundary additive longshot\", \"actual\": \"additive infeasible\", \"expected\": \"additive infeasible\", \"passed\": true}, {\"check\": \"boundary unknown method\", \"actual\": \"invalid method\", \"expected\": \"invalid method\", \"passed\": true}, {\"check\": \"regression: power bracket update\", \"actual\": [\"0.2725\", \"0.9091\"], \"expected\": [\"0.1360\", \"0.8640\"], \"passed\": false}, {\"check\": \"variant scenario 1\", \"actual\": [\"0.8621\", \"0.1567\"], \"expected\": [\"0.8562\", \"0.1438\"], \"passed\": false}, {\"check\": \"variant scenario 2\", \"actual\": [\"0.4754\", \"0.0586\", \"0.4660\"], \"expected\": [\"0.4754\", \"0.0586\", \"0.4660\"], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":39.159,"exit_code":1,"observations":[{"actual":["0.5263","0.4737"],"check":"control multiplicative","expected":["0.5263","0.4737"],"passed":true},{"actual":["0.5278","0.4722"],"check":"control additive","expected":["0.5278","0.4722"],"passed":true},{"actual":["0.0028","0.0010"],"check":"control power","expected":["0.5285","0.4715"],"passed":false},{"actual":"additive infeasible","check":"boundary additive longshot","expected":"additive infeasible","passed":true},{"actual":"invalid method","check":"boundary unknown method","expected":"invalid method","passed":true},{"actual":["0.0000","0.3855"],"check":"regression: power bracket 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