{"abstract":"Long puts and long stock report the wrong extreme at a zero price.","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.","contract_signature":"legs, multiplier","evaluation_group":"w2-options_payoff_and_settlement-strategy-risk-profile","failed_approach":"Adding 0 only when a put is present still misses stock legs.","family":"w2-options_payoff_and_settlement-strategy-risk-profile-zero-price-breakpoint","id":"FA-61511","implementations":{"attempt":{"sha256":"54eb426c19e7682caea9fa703f31c73b285ea954458f3f15b757b5c0dff280b1","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] if any(l[0] == 'P' for l in legs) else []) + [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 zero price breakpoint 1', [[['S', 90, -1, 0.0], ['C', 95, -1, 1.25], ['P', 90, 2, 2.0], ['P', 115, -2, 1.25]], 1], [39.75, None, [39.75]]], ['regression zero price breakpoint 2', [[['P', 105, -2, 0.5]], 1], [1.0, -209.0, [104.5]]], ['partial repair probe 1', [[['S', 95, -1, 0.0]], 1], [95.0, None, [95.0]]], ['partial repair probe 2', [[['C', 105, 1, 2.0], ['C', 95, 2, 3.4], ['S', 105, 1, 0.0], ['C', 115, -2, 2.0]], 100], [None, -10980.0, [99.9333]]], ['boundary control 1', [[['C', 100, 1, 2.0]], 100], [None, -200.0, [102.0]]], ['normal control 1', [[['P', 95, -2, 0.5], ['S', 90, -1, 0.0]], 100], [-400.0, None, []]], ['normal control 2', [[['S', 115, 2, 0.0], ['C', 95, -2, 2.0], ['C', 85, -1, 1.25], ['C', 90, -1, 0.5]], 1], [-49.25, None, []]], ['normal control 3', [[['C', 90, -1, 2.0]], 100], [200.0, None, [92.0]]]], [['regression zero price breakpoint 1', [[['S', 115, -2, 0.0], ['P', 80, 1, 3.4]], 1], [306.6, None, [113.3]]], ['regression zero price breakpoint 2', [[['P', 100, -1, 1.25], ['C', 85, 1, 7.75], ['C', 100, 1, 0.5], ['C', 120, -1, 1.25]], 100], [None, -10575.0, [95.375]]], ['partial repair probe 1', [[['S', 120, -1, 0.0]], 1], [120.0, None, [120.0]]], ['partial repair probe 2', [[['S', 90, -1, 0.0]], 100], [9000.0, None, [90.0]]], ['boundary control 1', [[['C', 100, 1, 2.0]], 100], [None, -200.0, [102.0]]], ['normal control 1', [[['C', 85, -1, 3.4]], 100], [340.0, None, [88.4]]], ['normal control 2', [[['C', 85, -1, 5.1]], 1], [5.1, None, [90.1]]], ['normal control 3', [[['P', 95, 1, 2.0], ['C', 105, 2, 1.25], ['P', 105, -1, 5.1]], 100], [None, -940.0, [104.4]]]], [['regression zero price breakpoint 1', [[['P', 100, -2, 3.4], ['S', 115, 1, 0.0]], 1], [None, -308.2, [108.2]]], ['regression zero price breakpoint 2', [[['P', 100, -1, 2.0]], 100], [200.0, -9800.0, [98.0]]], ['partial repair probe 1', [[['S', 85, -2, 0.0], ['S', 85, 2, 0.0]], 1], [0.0, 0.0, [0.0, 85.0]]], ['partial repair probe 2', [[['C', 105, -1, 0.5], ['S', 115, -1, 0.0]], 100], [11550.0, None, [110.25]]], ['boundary control 1', [[['C', 100, 1, 2.0]], 100], [None, -200.0, [102.0]]], ['normal control 1', [[['C', 115, -1, 7.75]], 1], [7.75, None, [122.75]]], ['normal control 2', [[['S', 85, -1, 0.0], ['C', 80, -1, 2.0], ['P', 85, -1, 7.75]], 1], [9.75, None, [87.375]]], ['normal control 3', [[['C', 85, 1, 7.75], ['C', 95, -1, 5.1]], 1], [7.35, -2.65, [87.65]]]], [['regression zero price breakpoint 1', [[['C', 110, 1, 5.1], ['P', 115, -1, 5.1]], 1], [None, -115.0, [112.5]]], ['regression zero price breakpoint 2', [[['P', 80, 1, 0.5], ['C', 105, 1, 1.25], ['C', 105, 2, 5.1]], 1], [None, -11.95, [68.05, 108.9833]]], ['partial repair probe 1', [[['S', 105, 1, 0.0]], 100], [None, -10500.0, [105.0]]], ['partial repair probe 2', [[['C', 80, 1, 2.0], ['S', 90, 2, 0.0]], 1], [None, -182.0, [87.3333]]], ['boundary control 1', [[['C', 100, 1, 2.0]], 100], [None, -200.0, [102.0]]], ['normal control 1', [[['C', 80, 1, 2.0], ['C', 80, 2, 5.1], ['C', 110, -2, 0.5]], 100], [None, -1120.0, [83.7333]]], ['normal control 2', [[['P', 115, 1, 7.75], ['C', 85, 2, 7.75]], 100], [None, 675.0, []]], ['normal control 3', [[['C', 80, 1, 5.1], ['P', 90, 2, 1.25], ['P', 90, -1, 2.0]], 1], [None, 4.4, []]]], [['regression zero price breakpoint 1', [[['S', 80, 1, 0.0], ['C', 105, -1, 1.25]], 1], [26.25, -78.75, [78.75]]], ['regression zero price breakpoint 2', [[['P', 110, -1, 5.1], ['P', 100, -1, 0.5], ['P', 85, -2, 5.1]], 100], [1580.0, -36420.0, [97.1]]], ['partial repair probe 1', [[['C', 120, 1, 2.0], ['S', 90, 1, 0.0], ['S', 120, 2, 0.0], ['S', 100, 1, 0.0]], 100], [None, -43200.0, [108.0]]], ['partial repair probe 2', [[['S', 95, 1, 0.0], ['S', 115, 2, 0.0]], 1], [None, -325.0, [108.3333]]], ['boundary control 1', [[['C', 100, 1, 2.0]], 100], [None, -200.0, [102.0]]], ['normal control 1', [[['C', 100, 2, 2.0], ['C', 85, 1, 3.4]], 1], [None, -7.4, [92.4]]], ['normal control 2', [[['C', 110, -1, 7.75]], 1], [7.75, None, [117.75]]], ['normal control 3', [[['C', 110, 1, 1.25]], 100], [None, -125.0, [111.25]]]]]\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":"30a9d72e16aa3fb5c979baf0cc4ebb5744cb4091471c3e93b740a3b4f7324c1a","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(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 zero price breakpoint 1', [[['S', 90, -1, 0.0], ['C', 95, -1, 1.25], ['P', 90, 2, 2.0], ['P', 115, -2, 1.25]], 1], [39.75, None, [39.75]]], ['regression zero price breakpoint 2', [[['P', 105, -2, 0.5]], 1], [1.0, -209.0, [104.5]]], ['partial repair probe 1', [[['S', 95, -1, 0.0]], 1], [95.0, None, [95.0]]], ['partial repair probe 2', [[['C', 105, 1, 2.0], ['C', 95, 2, 3.4], ['S', 105, 1, 0.0], ['C', 115, -2, 2.0]], 100], [None, -10980.0, [99.9333]]], ['boundary control 1', [[['C', 100, 1, 2.0]], 100], [None, -200.0, [102.0]]], ['normal control 1', [[['P', 95, -2, 0.5], ['S', 90, -1, 0.0]], 100], [-400.0, None, []]], ['normal control 2', [[['S', 115, 2, 0.0], ['C', 95, -2, 2.0], ['C', 85, -1, 1.25], ['C', 90, -1, 0.5]], 1], [-49.25, None, []]], ['normal control 3', [[['C', 90, -1, 2.0]], 100], [200.0, None, [92.0]]]], [['regression zero price breakpoint 1', [[['S', 115, -2, 0.0], ['P', 80, 1, 3.4]], 1], [306.6, None, [113.3]]], ['regression zero price breakpoint 2', [[['P', 100, -1, 1.25], ['C', 85, 1, 7.75], ['C', 100, 1, 0.5], ['C', 120, -1, 1.25]], 100], [None, -10575.0, [95.375]]], ['partial repair probe 1', [[['S', 120, -1, 0.0]], 1], [120.0, None, [120.0]]], ['partial repair probe 2', [[['S', 90, -1, 0.0]], 100], [9000.0, None, [90.0]]], ['boundary control 1', [[['C', 100, 1, 2.0]], 100], [None, -200.0, [102.0]]], ['normal control 1', [[['C', 85, -1, 3.4]], 100], [340.0, None, [88.4]]], ['normal control 2', [[['C', 85, -1, 5.1]], 1], [5.1, None, [90.1]]], ['normal control 3', [[['P', 95, 1, 2.0], ['C', 105, 2, 1.25], ['P', 105, -1, 5.1]], 100], [None, -940.0, [104.4]]]], [['regression zero price breakpoint 1', [[['P', 100, -2, 3.4], ['S', 115, 1, 0.0]], 1], [None, -308.2, [108.2]]], ['regression zero price breakpoint 2', [[['P', 100, -1, 2.0]], 100], [200.0, -9800.0, [98.0]]], ['partial repair probe 1', [[['S', 85, -2, 0.0], ['S', 85, 2, 0.0]], 1], [0.0, 0.0, [0.0, 85.0]]], ['partial repair probe 2', [[['C', 105, -1, 0.5], ['S', 115, -1, 0.0]], 100], [11550.0, None, [110.25]]], ['boundary control 1', [[['C', 100, 1, 2.0]], 100], [None, -200.0, [102.0]]], ['normal control 1', [[['C', 115, -1, 7.75]], 1], [7.75, None, [122.75]]], ['normal control 2', [[['S', 85, -1, 0.0], ['C', 80, -1, 2.0], ['P', 85, -1, 7.75]], 1], [9.75, None, [87.375]]], ['normal control 3', [[['C', 85, 1, 7.75], ['C', 95, -1, 5.1]], 1], [7.35, -2.65, [87.65]]]], [['regression zero price breakpoint 1', [[['C', 110, 1, 5.1], ['P', 115, -1, 5.1]], 1], [None, -115.0, [112.5]]], ['regression zero price breakpoint 2', [[['P', 80, 1, 0.5], ['C', 105, 1, 1.25], ['C', 105, 2, 5.1]], 1], [None, -11.95, [68.05, 108.9833]]], ['partial repair probe 1', [[['S', 105, 1, 0.0]], 100], [None, -10500.0, [105.0]]], ['partial repair probe 2', [[['C', 80, 1, 2.0], ['S', 90, 2, 0.0]], 1], [None, -182.0, [87.3333]]], ['boundary control 1', [[['C', 100, 1, 2.0]], 100], [None, -200.0, [102.0]]], ['normal control 1', [[['C', 80, 1, 2.0], ['C', 80, 2, 5.1], ['C', 110, -2, 0.5]], 100], [None, -1120.0, [83.7333]]], ['normal control 2', [[['P', 115, 1, 7.75], ['C', 85, 2, 7.75]], 100], [None, 675.0, []]], ['normal control 3', [[['C', 80, 1, 5.1], ['P', 90, 2, 1.25], ['P', 90, -1, 2.0]], 1], [None, 4.4, []]]], [['regression zero price breakpoint 1', [[['S', 80, 1, 0.0], ['C', 105, -1, 1.25]], 1], [26.25, -78.75, [78.75]]], ['regression zero price breakpoint 2', [[['P', 110, -1, 5.1], ['P', 100, -1, 0.5], ['P', 85, -2, 5.1]], 100], [1580.0, -36420.0, [97.1]]], ['partial repair probe 1', [[['C', 120, 1, 2.0], ['S', 90, 1, 0.0], ['S', 120, 2, 0.0], ['S', 100, 1, 0.0]], 100], [None, -43200.0, [108.0]]], ['partial repair probe 2', [[['S', 95, 1, 0.0], ['S', 115, 2, 0.0]], 1], [None, -325.0, [108.3333]]], ['boundary control 1', [[['C', 100, 1, 2.0]], 100], [None, -200.0, [102.0]]], ['normal control 1', [[['C', 100, 2, 2.0], ['C', 85, 1, 3.4]], 1], [None, -7.4, [92.4]]], ['normal control 2', [[['C', 110, -1, 7.75]], 1], [7.75, None, [117.75]]], ['normal control 3', [[['C', 110, 1, 1.25]], 100], [None, -125.0, [111.25]]]]]\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-zero-price-breakpoint","generated_at":"2026-09-29T14:46:55.871207+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.","root_cause":"Breakpoints are only the strikes.","sha256":"64099bd353a73831b4eb296ff530cc4a5281260fd76cb4e9a1b024ddbd18a5e4","title":"Option strategy max gain, max loss and breakevens: the zero underlying price is not evaluated · 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":41.804,"exit_code":1,"observations":[{"actual":[39.75,null,[39.75]],"check":"regression zero price breakpoint 1","expected":[39.75,null,[39.75]],"passed":true},{"actual":[1.0,-209.0,[104.5]],"check":"regression zero price breakpoint 2","expected":[1.0,-209.0,[104.5]],"passed":true},{"actual":[0.0,null,[95.0]],"check":"partial repair probe 1","expected":[95.0,null,[95.0]],"passed":false},{"actual":[null,-1480.0,[99.9333]],"check":"partial repair probe 2","expected":[null,-10980.0,[99.9333]],"passed":false},{"actual":[null,-200.0,[102.0]],"check":"boundary control 1","expected":[null,-200.0,[102.0]],"passed":true},{"actual":[-400.0,null,[]],"check":"normal control 1","expected":[-400.0,null,[]],"passed":true},{"actual":[-49.25,null,[]],"check":"normal control 2","expected":[-49.25,null,[]],"passed":true},{"actual":[200.0,null,[92.0]],"check":"normal control 3","expected":[200.0,null,[92.0]],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression zero price breakpoint 1\", \"actual\": [39.75, null, [39.75]], \"expected\": [39.75, null, [39.75]], \"passed\": true}, {\"check\": \"regression zero price breakpoint 2\", \"actual\": [1.0, -209.0, [104.5]], \"expected\": [1.0, -209.0, [104.5]], \"passed\": true}, {\"check\": \"partial repair probe 1\", \"actual\": [0.0, null, [95.0]], \"expected\": [95.0, null, [95.0]], \"passed\": false}, {\"check\": \"partial repair probe 2\", \"actual\": [null, -1480.0, [99.9333]], \"expected\": [null, -10980.0, [99.9333]], \"passed\": false}, {\"check\": \"boundary control 1\", \"actual\": [null, -200.0, [102.0]], \"expected\": [null, -200.0, [102.0]], \"passed\": true}, {\"check\": \"normal control 1\", \"actual\": [-400.0, null, []], \"expected\": [-400.0, null, []], \"passed\": true}, {\"check\": \"normal control 2\", \"actual\": [-49.25, null, []], \"expected\": [-49.25, null, []], \"passed\": true}, {\"check\": \"normal control 3\", \"actual\": [200.0, null, [92.0]], \"expected\": [200.0, null, [92.0]], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":44.346,"exit_code":1,"observations":[{"actual":[-45.25,null,[]],"check":"regression zero price breakpoint 1","expected":[39.75,null,[39.75]],"passed":false},{"actual":[1.0,1.0,[]],"check":"regression zero price breakpoint 2","expected":[1.0,-209.0,[104.5]],"passed":false},{"actual":[0.0,null,[95.0]],"check":"partial repair probe 1","expected":[95.0,null,[95.0]],"passed":false},{"actual":[null,-1480.0,[99.9333]],"check":"partial repair probe 2","expected":[null,-10980.0,[99.9333]],"passed":false},{"actual":[null,-200.0,[102.0]],"check":"boundary control 1","expected":[null,-200.0,[102.0]],"passed":true},{"actual":[-400.0,null,[]],"check":"normal control 1","expected":[-400.0,null,[]],"passed":true},{"actual":[-49.25,null,[]],"check":"normal control 2","expected":[-49.25,null,[]],"passed":true},{"actual":[200.0,null,[92.0]],"check":"normal control 3","expected":[200.0,null,[92.0]],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression zero price breakpoint 1\", \"actual\": [-45.25, null, []], \"expected\": [39.75, null, [39.75]], \"passed\": false}, {\"check\": \"regression zero price breakpoint 2\", \"actual\": [1.0, 1.0, []], \"expected\": [1.0, -209.0, [104.5]], \"passed\": false}, {\"check\": \"partial repair probe 1\", \"actual\": [0.0, null, [95.0]], \"expected\": [95.0, null, [95.0]], \"passed\": false}, {\"check\": \"partial repair probe 2\", \"actual\": [null, -1480.0, [99.9333]], \"expected\": [null, -10980.0, [99.9333]], \"passed\": false}, {\"check\": \"boundary control 1\", \"actual\": [null, -200.0, [102.0]], \"expected\": [null, -200.0, [102.0]], \"passed\": true}, {\"check\": \"normal control 1\", \"actual\": [-400.0, null, []], \"expected\": [-400.0, null, []], \"passed\": true}, {\"check\": \"normal control 2\", \"actual\": [-49.25, null, []], \"expected\": [-49.25, null, []], \"passed\": true}, {\"check\": \"normal control 3\", \"actual\": [200.0, null, [92.0]], \"expected\": [200.0, null, [92.0]], \"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."}}