{"abstract":"Long call breakevens are reported below the strike.","category":"Options payoff and settlement","checks":8,"contract":"Inputs legs [kind C/P/S, strike (purchase price for stock S), signed qty, premium] and a multiplier. Expiry value V(S) = multiplier * sum(q*(intrinsic - premium)) for options and q*(S - price) for stock, in exact fractions. Breakpoints are 0 and every strike. Tail slope = V(top+1)-V(top). Max gain is None if the slope > 0 else the max over breakpoints; max loss is None if slope < 0 else the min. Breakevens are zeros at breakpoints and linear-interpolated sign changes between them and in the tail. Return [gain, loss, breakevens] rounded to 4.","evaluation_group":"w2-options_payoff_and_settlement-strategy-risk-profile","failed_approach":"Dropping the tail root entirely loses the only breakeven for long calls.","family":"w2-options_payoff_and_settlement-strategy-risk-profile-tail-breakeven","id":"FA-61506","implementations":{"attempt":{"sha256":"774184e814fe305f731d193445e9a519638b242299934e0da5e766dde49dbaf9","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(legs, multiplier):\n    def value(S):\n        t = Fraction(0)\n        for kind, k, q, prem in legs:\n            p = Fraction(str(prem))\n            if kind == 'C':\n                t += q * (max(S - k, 0) - p)\n            elif kind == 'P':\n                t += q * (max(k - S, 0) - p)\n            else:\n                t += q * (S - k)\n        return t * multiplier\n    pts = sorted(set([0] + [leg[1] for leg in legs]))\n    top = pts[-1]\n    slope = value(top + 1) - value(top)\n    vals = [value(p) for p in pts]\n    gain = None if slope > 0 else max(vals)\n    loss = None if slope < 0 else min(vals)\n    bes = []\n    for a, b in zip(pts, pts[1:]):\n        va, vb = value(a), value(b)\n        if va == 0:\n            bes.append(Fraction(a))\n        elif va * vb < 0:\n            bes.append(a - va * (b - a) / (vb - va))\n    vt = value(top)\n    if vt == 0:\n        bes.append(Fraction(top))\n    elif vt * slope < 0:\n        pass\n    def r4(x):\n        return None if x is None else float(round(x, 4))\n    return [r4(gain), r4(loss), [r4(x) for x in sorted(set(bes))]]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression tail breakeven 1', [[['C', 85, 2, 7.75]], 100], [None, -1550.0, [92.75]]], ['regression tail breakeven 2', [[['P', 90, -2, 0.5], ['C', 115, -1, 5.1]], 100], [610.0, None, [86.95, 121.1]]], ['partial repair probe 1', [[['C', 110, 1, 1.25], ['C', 115, -1, 3.4], ['C', 120, -1, 2.0]], 1], [9.15, None, [129.15]]], ['partial repair probe 2', [[['P', 105, -2, 2.0], ['P', 105, -1, 0.5], ['C', 100, -1, 3.4]], 1], [2.9, None, [103.55, 107.9]]], ['boundary control 1', [[['P', 100, 1, 2.0]], 1], [98.0, -2.0, [98.0]]], ['boundary control 2', [[['S', 100, 1, 0.0], ['C', 110, -1, 1.25]], 1], [11.25, -98.75, [98.75]]], ['normal control 1', [[['P', 105, 1, 2.0], ['P', 90, -2, 2.0]], 1], [17.0, -73.0, [73.0]]], ['normal control 2', [[['P', 90, 1, 3.4], ['S', 100, -1, 0.0]], 1], [186.6, None, [96.6]]]], [['regression tail breakeven 1', [[['P', 115, 1, 1.25], ['C', 110, 2, 7.75], ['P', 80, -2, 0.5]], 1], [None, -60.75, [60.75, 99.25, 117.875]]], ['regression tail breakeven 2', [[['P', 100, 2, 7.75], ['S', 115, 2, 0.0]], 1], [None, -45.5, [122.75]]], ['partial repair probe 1', [[['C', 80, 1, 7.75]], 1], [None, -7.75, [87.75]]], ['partial repair probe 2', [[['P', 115, -1, 2.0], ['S', 115, 2, 0.0], ['C', 110, -1, 0.5]], 1], [None, -342.5, [117.5]]], ['boundary control 1', [[['P', 100, 1, 2.0]], 1], [98.0, -2.0, [98.0]]], ['boundary control 2', [[['S', 100, 1, 0.0], ['C', 110, -1, 1.25]], 1], [11.25, -98.75, [98.75]]], ['normal control 1', [[['S', 80, -2, 0.0], ['P', 95, -2, 2.0], ['S', 110, -1, 0.0], ['S', 100, 1, 0.0]], 1], [-16.0, None, []]], ['normal control 2', [[['P', 105, 1, 2.0], ['P', 100, -1, 7.75], ['S', 105, 1, 0.0], ['P', 80, -1, 3.4]], 100], [None, -17085.0, [90.85]]]], [['regression tail breakeven 1', [[['C', 85, -1, 7.75]], 1], [7.75, None, [92.75]]], ['regression tail breakeven 2', [[['C', 105, -2, 3.4], ['S', 100, 1, 0.0]], 100], [1180.0, None, [93.2, 116.8]]], ['partial repair probe 1', [[['P', 100, -1, 3.4], ['S', 100, -1, 0.0], ['P', 90, -2, 7.75]], 100], [1890.0, None, [80.55, 118.9]]], ['partial repair probe 2', [[['C', 115, -1, 2.0], ['C', 85, 1, 7.75], ['S', 105, -1, 0.0], ['C', 110, -1, 2.0]], 1], [101.25, None, [120.625]]], ['boundary control 1', [[['P', 100, 1, 2.0]], 1], [98.0, -2.0, [98.0]]], ['boundary control 2', [[['S', 100, 1, 0.0], ['C', 110, -1, 1.25]], 1], [11.25, -98.75, [98.75]]], ['normal control 1', [[['S', 120, 1, 0.0], ['P', 95, -1, 1.25], ['P', 95, -2, 0.5]], 100], [None, -40275.0, [117.75]]], ['normal control 2', [[['P', 100, -1, 1.25]], 100], [125.0, -9875.0, [98.75]]]], [['regression tail breakeven 1', [[['C', 80, -1, 5.1]], 100], [510.0, None, [85.1]]], ['regression tail breakeven 2', [[['C', 120, -2, 5.1]], 1], [10.2, None, [125.1]]], ['partial repair probe 1', [[['P', 115, -1, 1.25], ['P', 95, -2, 5.1], ['C', 120, -1, 2.0]], 1], [13.45, None, [101.55, 133.45]]], ['partial repair probe 2', [[['C', 110, 2, 1.25]], 100], [None, -250.0, [111.25]]], ['boundary control 1', [[['S', 100, 1, 0.0], ['C', 110, -1, 1.25]], 1], [11.25, -98.75, [98.75]]], ['boundary control 2', [[['P', 100, 1, 2.0]], 1], [98.0, -2.0, [98.0]]], ['normal control 1', [[['S', 90, -2, 0.0], ['P', 105, 1, 7.75], ['C', 95, -1, 5.1], ['C', 120, -1, 0.5]], 1], [282.85, None, [94.2833]]], ['normal control 2', [[['P', 85, 1, 2.0], ['P', 115, -1, 3.4]], 1], [1.4, -28.6, [113.6]]]], [['regression tail breakeven 1', [[['C', 85, -1, 5.1]], 1], [5.1, None, [90.1]]], ['regression tail breakeven 2', [[['C', 115, -1, 0.5], ['C', 115, -2, 1.25], ['P', 90, 2, 2.0], ['C', 90, 2, 1.25]], 1], [176.5, None, [88.25, 91.75, 161.5]]], ['partial repair probe 1', [[['C', 105, 2, 5.1]], 100], [None, -1020.0, [110.1]]], ['partial repair probe 2', [[['C', 90, -1, 5.1], ['P', 95, -1, 3.4]], 1], [3.5, None, [86.5, 98.5]]], ['boundary control 1', [[['P', 100, 1, 2.0]], 1], [98.0, -2.0, [98.0]]], ['boundary control 2', [[['S', 100, 1, 0.0], ['C', 110, -1, 1.25]], 1], [11.25, -98.75, [98.75]]], ['normal control 1', [[['C', 100, 1, 3.4], ['C', 120, -2, 5.1], ['P', 100, -2, 2.0], ['C', 100, 2, 0.5]], 1], [None, -190.2, [95.1]]], ['normal control 2', [[['C', 95, 1, 1.25], ['C', 120, -1, 5.1], ['C', 85, -1, 3.4], ['P', 120, 1, 2.0]], 1], [125.25, None, [115.25]]]]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, solve(*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":"82b853184a27216a23e7c7dba2118a2af388237d501e57eddc42107cac1668f6","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(legs, multiplier):\n    def value(S):\n        t = Fraction(0)\n        for kind, k, q, prem in legs:\n            p = Fraction(str(prem))\n            if kind == 'C':\n                t += q * (max(S - k, 0) - p)\n            elif kind == 'P':\n                t += q * (max(k - S, 0) - p)\n            else:\n                t += q * (S - k)\n        return t * multiplier\n    pts = sorted(set([0] + [leg[1] for leg in legs]))\n    top = pts[-1]\n    slope = value(top + 1) - value(top)\n    vals = [value(p) for p in pts]\n    gain = None if slope > 0 else max(vals)\n    loss = None if slope < 0 else min(vals)\n    bes = []\n    for a, b in zip(pts, pts[1:]):\n        va, vb = value(a), value(b)\n        if va == 0:\n            bes.append(Fraction(a))\n        elif va * vb < 0:\n            bes.append(a - va * (b - a) / (vb - va))\n    vt = value(top)\n    if vt == 0:\n        bes.append(Fraction(top))\n    elif vt * slope < 0:\n        bes.append(top + vt / slope)\n    def r4(x):\n        return None if x is None else float(round(x, 4))\n    return [r4(gain), r4(loss), [r4(x) for x in sorted(set(bes))]]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression tail breakeven 1', [[['C', 85, 2, 7.75]], 100], [None, -1550.0, [92.75]]], ['regression tail breakeven 2', [[['P', 90, -2, 0.5], ['C', 115, -1, 5.1]], 100], [610.0, None, [86.95, 121.1]]], ['partial repair probe 1', [[['C', 110, 1, 1.25], ['C', 115, -1, 3.4], ['C', 120, -1, 2.0]], 1], [9.15, None, [129.15]]], ['partial repair probe 2', [[['P', 105, -2, 2.0], ['P', 105, -1, 0.5], ['C', 100, -1, 3.4]], 1], [2.9, None, [103.55, 107.9]]], ['boundary control 1', [[['P', 100, 1, 2.0]], 1], [98.0, -2.0, [98.0]]], ['boundary control 2', [[['S', 100, 1, 0.0], ['C', 110, -1, 1.25]], 1], [11.25, -98.75, [98.75]]], ['normal control 1', [[['P', 105, 1, 2.0], ['P', 90, -2, 2.0]], 1], [17.0, -73.0, [73.0]]], ['normal control 2', [[['P', 90, 1, 3.4], ['S', 100, -1, 0.0]], 1], [186.6, None, [96.6]]]], [['regression tail breakeven 1', [[['P', 115, 1, 1.25], ['C', 110, 2, 7.75], ['P', 80, -2, 0.5]], 1], [None, -60.75, [60.75, 99.25, 117.875]]], ['regression tail breakeven 2', [[['P', 100, 2, 7.75], ['S', 115, 2, 0.0]], 1], [None, -45.5, [122.75]]], ['partial repair probe 1', [[['C', 80, 1, 7.75]], 1], [None, -7.75, [87.75]]], ['partial repair probe 2', [[['P', 115, -1, 2.0], ['S', 115, 2, 0.0], ['C', 110, -1, 0.5]], 1], [None, -342.5, [117.5]]], ['boundary control 1', [[['P', 100, 1, 2.0]], 1], [98.0, -2.0, [98.0]]], ['boundary control 2', [[['S', 100, 1, 0.0], ['C', 110, -1, 1.25]], 1], [11.25, -98.75, [98.75]]], ['normal control 1', [[['S', 80, -2, 0.0], ['P', 95, -2, 2.0], ['S', 110, -1, 0.0], ['S', 100, 1, 0.0]], 1], [-16.0, None, []]], ['normal control 2', [[['P', 105, 1, 2.0], ['P', 100, -1, 7.75], ['S', 105, 1, 0.0], ['P', 80, -1, 3.4]], 100], [None, -17085.0, [90.85]]]], [['regression tail breakeven 1', [[['C', 85, -1, 7.75]], 1], [7.75, None, [92.75]]], ['regression tail breakeven 2', [[['C', 105, -2, 3.4], ['S', 100, 1, 0.0]], 100], [1180.0, None, [93.2, 116.8]]], ['partial repair probe 1', [[['P', 100, -1, 3.4], ['S', 100, -1, 0.0], ['P', 90, -2, 7.75]], 100], [1890.0, None, [80.55, 118.9]]], ['partial repair probe 2', [[['C', 115, -1, 2.0], ['C', 85, 1, 7.75], ['S', 105, -1, 0.0], ['C', 110, -1, 2.0]], 1], [101.25, None, [120.625]]], ['boundary control 1', [[['P', 100, 1, 2.0]], 1], [98.0, -2.0, [98.0]]], ['boundary control 2', [[['S', 100, 1, 0.0], ['C', 110, -1, 1.25]], 1], [11.25, -98.75, [98.75]]], ['normal control 1', [[['S', 120, 1, 0.0], ['P', 95, -1, 1.25], ['P', 95, -2, 0.5]], 100], [None, -40275.0, [117.75]]], ['normal control 2', [[['P', 100, -1, 1.25]], 100], [125.0, -9875.0, [98.75]]]], [['regression tail breakeven 1', [[['C', 80, -1, 5.1]], 100], [510.0, None, [85.1]]], ['regression tail breakeven 2', [[['C', 120, -2, 5.1]], 1], [10.2, None, [125.1]]], ['partial repair probe 1', [[['P', 115, -1, 1.25], ['P', 95, -2, 5.1], ['C', 120, -1, 2.0]], 1], [13.45, None, [101.55, 133.45]]], ['partial repair probe 2', [[['C', 110, 2, 1.25]], 100], [None, -250.0, [111.25]]], ['boundary control 1', [[['S', 100, 1, 0.0], ['C', 110, -1, 1.25]], 1], [11.25, -98.75, [98.75]]], ['boundary control 2', [[['P', 100, 1, 2.0]], 1], [98.0, -2.0, [98.0]]], ['normal control 1', [[['S', 90, -2, 0.0], ['P', 105, 1, 7.75], ['C', 95, -1, 5.1], ['C', 120, -1, 0.5]], 1], [282.85, None, [94.2833]]], ['normal control 2', [[['P', 85, 1, 2.0], ['P', 115, -1, 3.4]], 1], [1.4, -28.6, [113.6]]]], [['regression tail breakeven 1', [[['C', 85, -1, 5.1]], 1], [5.1, None, [90.1]]], ['regression tail breakeven 2', [[['C', 115, -1, 0.5], ['C', 115, -2, 1.25], ['P', 90, 2, 2.0], ['C', 90, 2, 1.25]], 1], [176.5, None, [88.25, 91.75, 161.5]]], ['partial repair probe 1', [[['C', 105, 2, 5.1]], 100], [None, -1020.0, [110.1]]], ['partial repair probe 2', [[['C', 90, -1, 5.1], ['P', 95, -1, 3.4]], 1], [3.5, None, [86.5, 98.5]]], ['boundary control 1', [[['P', 100, 1, 2.0]], 1], [98.0, -2.0, [98.0]]], ['boundary control 2', [[['S', 100, 1, 0.0], ['C', 110, -1, 1.25]], 1], [11.25, -98.75, [98.75]]], ['normal control 1', [[['C', 100, 1, 3.4], ['C', 120, -2, 5.1], ['P', 100, -2, 2.0], ['C', 100, 2, 0.5]], 1], [None, -190.2, [95.1]]], ['normal control 2', [[['C', 95, 1, 1.25], ['C', 120, -1, 5.1], ['C', 85, -1, 3.4], ['P', 120, 1, 2.0]], 1], [125.25, None, [115.25]]]]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, solve(*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":"3b5a53ff2d3041350650edd3ec02015e3c5cd489d9064cbf04d3a3bbe2f33e0f","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(legs, multiplier):\n    def value(S):\n        t = Fraction(0)\n        for kind, k, q, prem in legs:\n            p = Fraction(str(prem))\n            if kind == 'C':\n                t += q * (max(S - k, 0) - p)\n            elif kind == 'P':\n                t += q * (max(k - S, 0) - p)\n            else:\n                t += q * (S - k)\n        return t * multiplier\n    pts = sorted(set([0] + [leg[1] for leg in legs]))\n    top = pts[-1]\n    slope = value(top + 1) - value(top)\n    vals = [value(p) for p in pts]\n    gain = None if slope > 0 else max(vals)\n    loss = None if slope < 0 else min(vals)\n    bes = []\n    for a, b in zip(pts, pts[1:]):\n        va, vb = value(a), value(b)\n        if va == 0:\n            bes.append(Fraction(a))\n        elif va * vb < 0:\n            bes.append(a - va * (b - a) / (vb - va))\n    vt = value(top)\n    if vt == 0:\n        bes.append(Fraction(top))\n    elif vt * slope < 0:\n        bes.append(top - vt / slope)\n    def r4(x):\n        return None if x is None else float(round(x, 4))\n    return [r4(gain), r4(loss), [r4(x) for x in sorted(set(bes))]]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression tail breakeven 1', [[['C', 85, 2, 7.75]], 100], [None, -1550.0, [92.75]]], ['regression tail breakeven 2', [[['P', 90, -2, 0.5], ['C', 115, -1, 5.1]], 100], [610.0, None, [86.95, 121.1]]], ['partial repair probe 1', [[['C', 110, 1, 1.25], ['C', 115, -1, 3.4], ['C', 120, -1, 2.0]], 1], [9.15, None, [129.15]]], ['partial repair probe 2', [[['P', 105, -2, 2.0], ['P', 105, -1, 0.5], ['C', 100, -1, 3.4]], 1], [2.9, None, [103.55, 107.9]]], ['boundary control 1', [[['P', 100, 1, 2.0]], 1], [98.0, -2.0, [98.0]]], ['boundary control 2', [[['S', 100, 1, 0.0], ['C', 110, -1, 1.25]], 1], [11.25, -98.75, [98.75]]], ['normal control 1', [[['P', 105, 1, 2.0], ['P', 90, -2, 2.0]], 1], [17.0, -73.0, [73.0]]], ['normal control 2', [[['P', 90, 1, 3.4], ['S', 100, -1, 0.0]], 1], [186.6, None, [96.6]]]], [['regression tail breakeven 1', [[['P', 115, 1, 1.25], ['C', 110, 2, 7.75], ['P', 80, -2, 0.5]], 1], [None, -60.75, [60.75, 99.25, 117.875]]], ['regression tail breakeven 2', [[['P', 100, 2, 7.75], ['S', 115, 2, 0.0]], 1], [None, -45.5, [122.75]]], ['partial repair probe 1', [[['C', 80, 1, 7.75]], 1], [None, -7.75, [87.75]]], ['partial repair probe 2', [[['P', 115, -1, 2.0], ['S', 115, 2, 0.0], ['C', 110, -1, 0.5]], 1], [None, -342.5, [117.5]]], ['boundary control 1', [[['P', 100, 1, 2.0]], 1], [98.0, -2.0, [98.0]]], ['boundary control 2', [[['S', 100, 1, 0.0], ['C', 110, -1, 1.25]], 1], [11.25, -98.75, [98.75]]], ['normal control 1', [[['S', 80, -2, 0.0], ['P', 95, -2, 2.0], ['S', 110, -1, 0.0], ['S', 100, 1, 0.0]], 1], [-16.0, None, []]], ['normal control 2', [[['P', 105, 1, 2.0], ['P', 100, -1, 7.75], ['S', 105, 1, 0.0], ['P', 80, -1, 3.4]], 100], [None, -17085.0, [90.85]]]], [['regression tail breakeven 1', [[['C', 85, -1, 7.75]], 1], [7.75, None, [92.75]]], ['regression tail breakeven 2', [[['C', 105, -2, 3.4], ['S', 100, 1, 0.0]], 100], [1180.0, None, [93.2, 116.8]]], ['partial repair probe 1', [[['P', 100, -1, 3.4], ['S', 100, -1, 0.0], ['P', 90, -2, 7.75]], 100], [1890.0, None, [80.55, 118.9]]], ['partial repair probe 2', [[['C', 115, -1, 2.0], ['C', 85, 1, 7.75], ['S', 105, -1, 0.0], ['C', 110, -1, 2.0]], 1], [101.25, None, [120.625]]], ['boundary control 1', [[['P', 100, 1, 2.0]], 1], [98.0, -2.0, [98.0]]], ['boundary control 2', [[['S', 100, 1, 0.0], ['C', 110, -1, 1.25]], 1], [11.25, -98.75, [98.75]]], ['normal control 1', [[['S', 120, 1, 0.0], ['P', 95, -1, 1.25], ['P', 95, -2, 0.5]], 100], [None, -40275.0, [117.75]]], ['normal control 2', [[['P', 100, -1, 1.25]], 100], [125.0, -9875.0, [98.75]]]], [['regression tail breakeven 1', [[['C', 80, -1, 5.1]], 100], [510.0, None, [85.1]]], ['regression tail breakeven 2', [[['C', 120, -2, 5.1]], 1], [10.2, None, [125.1]]], ['partial repair probe 1', [[['P', 115, -1, 1.25], ['P', 95, -2, 5.1], ['C', 120, -1, 2.0]], 1], [13.45, None, [101.55, 133.45]]], ['partial repair probe 2', [[['C', 110, 2, 1.25]], 100], [None, -250.0, [111.25]]], ['boundary control 1', [[['S', 100, 1, 0.0], ['C', 110, -1, 1.25]], 1], [11.25, -98.75, [98.75]]], ['boundary control 2', [[['P', 100, 1, 2.0]], 1], [98.0, -2.0, [98.0]]], ['normal control 1', [[['S', 90, -2, 0.0], ['P', 105, 1, 7.75], ['C', 95, -1, 5.1], ['C', 120, -1, 0.5]], 1], [282.85, None, [94.2833]]], ['normal control 2', [[['P', 85, 1, 2.0], ['P', 115, -1, 3.4]], 1], [1.4, -28.6, [113.6]]]], [['regression tail breakeven 1', [[['C', 85, -1, 5.1]], 1], [5.1, None, [90.1]]], ['regression tail breakeven 2', [[['C', 115, -1, 0.5], ['C', 115, -2, 1.25], ['P', 90, 2, 2.0], ['C', 90, 2, 1.25]], 1], [176.5, None, [88.25, 91.75, 161.5]]], ['partial repair probe 1', [[['C', 105, 2, 5.1]], 100], [None, -1020.0, [110.1]]], ['partial repair probe 2', [[['C', 90, -1, 5.1], ['P', 95, -1, 3.4]], 1], [3.5, None, [86.5, 98.5]]], ['boundary control 1', [[['P', 100, 1, 2.0]], 1], [98.0, -2.0, [98.0]]], ['boundary control 2', [[['S', 100, 1, 0.0], ['C', 110, -1, 1.25]], 1], [11.25, -98.75, [98.75]]], ['normal control 1', [[['C', 100, 1, 3.4], ['C', 120, -2, 5.1], ['P', 100, -2, 2.0], ['C', 100, 2, 0.5]], 1], [None, -190.2, [95.1]]], ['normal control 2', [[['C', 95, 1, 1.25], ['C', 120, -1, 5.1], ['C', 85, -1, 3.4], ['P', 120, 1, 2.0]], 1], [125.25, None, [115.25]]]]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, solve(*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":"A deterministic toy contract stated explicitly in the contract field; no claim of conformance to any exchange or clearing rulebook. 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-options_payoff_and_settlement-strategy-risk-profile-tail-breakeven","generated_at":"2026-09-29T14:46:55.829977+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Option expiry, exercise and settlement engines move cash and shares; a wrong branch misstates obligations.","repair":"The tail breakeven is top - V(top)/slope.","root_cause":"The tail root adds vt/slope instead of subtracting it.","sha256":"2b72f8ce75786d56982b9d71a21437ed2279eeb69cd77a2d487664fd8e821fe6","title":"Option strategy max gain, max loss and breakevens: the upside tail root has the wrong sign · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":44.65,"exit_code":1,"observations":[{"actual":[null,-1550.0,[]],"check":"regression tail breakeven 1","expected":[null,-1550.0,[92.75]],"passed":false},{"actual":[610.0,null,[86.95]],"check":"regression tail breakeven 2","expected":[610.0,null,[86.95,121.1]],"passed":false},{"actual":[9.15,null,[]],"check":"partial repair probe 1","expected":[9.15,null,[129.15]],"passed":false},{"actual":[2.9,null,[103.55]],"check":"partial repair probe 2","expected":[2.9,null,[103.55,107.9]],"passed":false},{"actual":[98.0,-2.0,[98.0]],"check":"boundary control 1","expected":[98.0,-2.0,[98.0]],"passed":true},{"actual":[11.25,-98.75,[98.75]],"check":"boundary control 2","expected":[11.25,-98.75,[98.75]],"passed":true},{"actual":[17.0,-73.0,[73.0]],"check":"normal control 1","expected":[17.0,-73.0,[73.0]],"passed":true},{"actual":[186.6,null,[96.6]],"check":"normal control 2","expected":[186.6,null,[96.6]],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression tail breakeven 1\", \"actual\": [null, -1550.0, []], \"expected\": [null, -1550.0, [92.75]], \"passed\": false}, {\"check\": \"regression tail breakeven 2\", \"actual\": [610.0, null, [86.95]], \"expected\": [610.0, null, [86.95, 121.1]], \"passed\": false}, {\"check\": \"partial repair probe 1\", \"actual\": [9.15, null, []], \"expected\": [9.15, null, [129.15]], \"passed\": false}, {\"check\": \"partial repair probe 2\", \"actual\": [2.9, null, [103.55]], \"expected\": [2.9, null, [103.55, 107.9]], \"passed\": false}, {\"check\": \"boundary control 1\", \"actual\": [98.0, -2.0, [98.0]], \"expected\": [98.0, -2.0, [98.0]], \"passed\": true}, {\"check\": \"boundary control 2\", \"actual\": [11.25, -98.75, [98.75]], \"expected\": [11.25, -98.75, [98.75]], \"passed\": true}, {\"check\": \"normal control 1\", \"actual\": [17.0, -73.0, [73.0]], \"expected\": [17.0, -73.0, [73.0]], \"passed\": true}, {\"check\": \"normal control 2\", \"actual\": [186.6, null, [96.6]], \"expected\": [186.6, null, [96.6]], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":44.007,"exit_code":1,"observations":[{"actual":[null,-1550.0,[77.25]],"check":"regression tail breakeven 1","expected":[null,-1550.0,[92.75]],"passed":false},{"actual":[610.0,null,[86.95,108.9]],"check":"regression tail breakeven 2","expected":[610.0,null,[86.95,121.1]],"passed":false},{"actual":[9.15,null,[110.85]],"check":"partial repair probe 1","expected":[9.15,null,[129.15]],"passed":false},{"actual":[2.9,null,[102.1,103.55]],"check":"partial repair probe 2","expected":[2.9,null,[103.55,107.9]],"passed":false},{"actual":[98.0,-2.0,[98.0]],"check":"boundary control 1","expected":[98.0,-2.0,[98.0]],"passed":true},{"actual":[11.25,-98.75,[98.75]],"check":"boundary control 2","expected":[11.25,-98.75,[98.75]],"passed":true},{"actual":[17.0,-73.0,[73.0]],"check":"normal control 1","expected":[17.0,-73.0,[73.0]],"passed":true},{"actual":[186.6,null,[96.6]],"check":"normal control 2","expected":[186.6,null,[96.6]],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression tail breakeven 1\", \"actual\": [null, -1550.0, [77.25]], \"expected\": [null, -1550.0, [92.75]], \"passed\": false}, {\"check\": \"regression tail breakeven 2\", \"actual\": [610.0, null, [86.95, 108.9]], \"expected\": [610.0, null, [86.95, 121.1]], \"passed\": false}, {\"check\": \"partial repair probe 1\", \"actual\": [9.15, null, [110.85]], \"expected\": [9.15, null, [129.15]], \"passed\": false}, {\"check\": \"partial repair probe 2\", \"actual\": [2.9, null, [102.1, 103.55]], \"expected\": [2.9, null, [103.55, 107.9]], \"passed\": false}, {\"check\": \"boundary control 1\", \"actual\": [98.0, -2.0, [98.0]], \"expected\": [98.0, -2.0, [98.0]], \"passed\": true}, {\"check\": \"boundary control 2\", \"actual\": [11.25, -98.75, [98.75]], \"expected\": [11.25, -98.75, [98.75]], \"passed\": true}, {\"check\": \"normal control 1\", \"actual\": [17.0, -73.0, [73.0]], \"expected\": [17.0, -73.0, [73.0]], \"passed\": true}, {\"check\": \"normal control 2\", \"actual\": [186.6, null, [96.6]], \"expected\": [186.6, null, [96.6]], \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":43.24,"exit_code":0,"observations":[{"actual":[null,-1550.0,[92.75]],"check":"regression tail breakeven 1","expected":[null,-1550.0,[92.75]],"passed":true},{"actual":[610.0,null,[86.95,121.1]],"check":"regression tail breakeven 2","expected":[610.0,null,[86.95,121.1]],"passed":true},{"actual":[9.15,null,[129.15]],"check":"partial repair probe 1","expected":[9.15,null,[129.15]],"passed":true},{"actual":[2.9,null,[103.55,107.9]],"check":"partial repair probe 2","expected":[2.9,null,[103.55,107.9]],"passed":true},{"actual":[98.0,-2.0,[98.0]],"check":"boundary control 1","expected":[98.0,-2.0,[98.0]],"passed":true},{"actual":[11.25,-98.75,[98.75]],"check":"boundary control 2","expected":[11.25,-98.75,[98.75]],"passed":true},{"actual":[17.0,-73.0,[73.0]],"check":"normal control 1","expected":[17.0,-73.0,[73.0]],"passed":true},{"actual":[186.6,null,[96.6]],"check":"normal control 2","expected":[186.6,null,[96.6]],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression tail breakeven 1\", \"actual\": [null, -1550.0, [92.75]], \"expected\": [null, -1550.0, [92.75]], \"passed\": true}, {\"check\": \"regression tail breakeven 2\", \"actual\": [610.0, null, [86.95, 121.1]], \"expected\": [610.0, null, [86.95, 121.1]], \"passed\": true}, {\"check\": \"partial repair probe 1\", \"actual\": [9.15, null, [129.15]], \"expected\": [9.15, null, [129.15]], \"passed\": true}, {\"check\": \"partial repair probe 2\", \"actual\": [2.9, null, [103.55, 107.9]], \"expected\": [2.9, null, [103.55, 107.9]], \"passed\": true}, {\"check\": \"boundary control 1\", \"actual\": [98.0, -2.0, [98.0]], \"expected\": [98.0, -2.0, [98.0]], \"passed\": true}, {\"check\": \"boundary control 2\", \"actual\": [11.25, -98.75, [98.75]], \"expected\": [11.25, -98.75, [98.75]], \"passed\": true}, {\"check\": \"normal control 1\", \"actual\": [17.0, -73.0, [73.0]], \"expected\": [17.0, -73.0, [73.0]], \"passed\": true}, {\"check\": \"normal control 2\", \"actual\": [186.6, null, [96.6]], \"expected\": [186.6, null, [96.6]], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}