{"abstract":"The superstable case r=1 is labelled damped oscillation.","category":"Ecological population dynamics","checks":7,"contract":"Regime by r: r<0 decline, r==0 neutral, 0<r<=1 monotone, 1<r<2 damped, 2<=r<2.526 cycle2, else complex; trajectory N[t+1]=N*exp(r*(1-N/K)) rounded 4; None for K<=0 or N0<0.","evaluation_group":"w2-ecopop-ricker-regime","failed_approach":"Making the regime depend on the initial state conflates transient and asymptotic behaviour.","family":"w2-ecopop-ricker-regime-superstable-boundary","id":"FA-65361","implementations":{"attempt":{"sha256":"f4ab09d668b7d8698b012362c7dfa0c88d59164aa10838f7045055e355bd8b50","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(r, k, n0, years):\n    if k <= 0 or n0 < 0:\n        return None\n    if r < 0:\n        regime = 'decline'\n    elif r == 0:\n        regime = 'neutral'\n    elif r <= 1 and n0 <= k:\n        regime = 'monotone'\n    elif r < 2:\n        regime = 'damped'\n    elif r < 2.526:\n        regime = 'cycle2'\n    else:\n        regime = 'complex'\n    n = float(n0)\n    traj = []\n    for _ in range(years):\n        n = n * math.exp(r * (1 - n / k))\n        traj.append(round(n, 4))\n    return [regime, traj]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('control: salmon stock damped',\n   (1.5, 1000, 200, 6),\n   ['damped', [664.0234, 1099.1389, 947.2604, 1025.2415, 987.1493, 1006.3622]]),\n  ('regression: superstable r one',\n   (1.0, 500, 100, 5),\n   ['monotone', [222.5541, 387.6342, 485.3128, 499.78, 500.0]]),\n  ('control: two cycle',\n   (2.2, 100, 30, 6),\n   ['cycle2', [139.9377, 58.1234, 146.0361, 53.0407, 149.0324, 50.6759]]),\n  ('control: period doubling onset exactly 2',\n   (2.0, 100, 40, 5),\n   ['cycle2', [132.8047, 68.9089, 128.3303, 72.8208, 125.4096]]),\n  ('control: near two', (1.96, 100, 40, 4), ['damped', [129.6553, 72.5035, 124.2836, 77.2161]]),\n  ('control: chaotic', (3.0, 100, 10, 5), ['complex', [148.7973, 34.421, 246.1736, 3.0674, 56.1939]]),\n  ('regression: weak growth above K',\n   (0.5, 200, 350, 5),\n   ['monotone', [240.5512, 217.36, 208.1284, 203.9417, 201.9419]])],\n [('regression: superstable r one',\n   (1.0, 500, 100, 5),\n   ['monotone', [222.5541, 387.6342, 485.3128, 499.78, 500.0]]),\n  ('control: period doubling onset exactly 2',\n   (2.0, 100, 40, 5),\n   ['cycle2', [132.8047, 68.9089, 128.3303, 72.8208, 125.4096]]),\n  ('control: near two', (1.96, 100, 40, 4), ['damped', [129.6553, 72.5035, 124.2836, 77.2161]]),\n  ('control: chaotic', (3.0, 100, 10, 5), ['complex', [148.7973, 34.421, 246.1736, 3.0674, 56.1939]]),\n  ('control: neutral', (0.0, 100, 60, 3), ['neutral', [60.0, 60.0, 60.0]]),\n  ('control: neutral empty patch', (0.0, 100, 0, 3), ['neutral', [0.0, 0.0, 0.0]]),\n  ('regression: weak growth above K',\n   (0.5, 200, 350, 5),\n   ['monotone', [240.5512, 217.36, 208.1284, 203.9417, 201.9419]])],\n [('regression: superstable r one',\n   (1.0, 500, 100, 5),\n   ['monotone', [222.5541, 387.6342, 485.3128, 499.78, 500.0]]),\n  ('control: neutral', (0.0, 100, 60, 3), ['neutral', [60.0, 60.0, 60.0]]),\n  ('control: neutral empty patch', (0.0, 100, 0, 3), ['neutral', [0.0, 0.0, 0.0]]),\n  ('control: declining', (-0.3, 100, 80, 4), ['decline', [75.3412, 69.9688, 63.9407, 57.3848]]),\n  ('control: invalid capacity', (1.0, 0, 10, 3), None),\n  ('regression: weak growth above K',\n   (0.5, 200, 350, 5),\n   ['monotone', [240.5512, 217.36, 208.1284, 203.9417, 201.9419]]),\n  ('control: weak growth below K',\n   (0.7, 200, 20, 5),\n   ['monotone', [37.5522, 66.3073, 105.8713, 147.1827, 177.0682]])],\n [('control: salmon stock damped',\n   (1.5, 1000, 200, 6),\n   ['damped', [664.0234, 1099.1389, 947.2604, 1025.2415, 987.1493, 1006.3622]]),\n  ('regression: superstable r one',\n   (1.0, 500, 100, 5),\n   ['monotone', [222.5541, 387.6342, 485.3128, 499.78, 500.0]]),\n  ('control: two cycle',\n   (2.2, 100, 30, 6),\n   ['cycle2', [139.9377, 58.1234, 146.0361, 53.0407, 149.0324, 50.6759]]),\n  ('control: period doubling onset exactly 2',\n   (2.0, 100, 40, 5),\n   ['cycle2', [132.8047, 68.9089, 128.3303, 72.8208, 125.4096]]),\n  ('control: invalid capacity', (1.0, 0, 10, 3), None),\n  ('regression: weak growth above K',\n   (0.5, 200, 350, 5),\n   ['monotone', [240.5512, 217.36, 208.1284, 203.9417, 201.9419]]),\n  ('control: weak growth below K',\n   (0.7, 200, 20, 5),\n   ['monotone', [37.5522, 66.3073, 105.8713, 147.1827, 177.0682]])],\n [('control: salmon stock damped',\n   (1.5, 1000, 200, 6),\n   ['damped', [664.0234, 1099.1389, 947.2604, 1025.2415, 987.1493, 1006.3622]]),\n  ('regression: superstable r one',\n   (1.0, 500, 100, 5),\n   ['monotone', [222.5541, 387.6342, 485.3128, 499.78, 500.0]]),\n  ('control: two cycle',\n   (2.2, 100, 30, 6),\n   ['cycle2', [139.9377, 58.1234, 146.0361, 53.0407, 149.0324, 50.6759]]),\n  ('control: period doubling onset exactly 2',\n   (2.0, 100, 40, 5),\n   ['cycle2', [132.8047, 68.9089, 128.3303, 72.8208, 125.4096]]),\n  ('control: near two', (1.96, 100, 40, 4), ['damped', [129.6553, 72.5035, 124.2836, 77.2161]]),\n  ('control: chaotic', (3.0, 100, 10, 5), ['complex', [148.7973, 34.421, 246.1736, 3.0674, 56.1939]]),\n  ('regression: weak growth above K',\n   (0.5, 200, 350, 5),\n   ['monotone', [240.5512, 217.36, 208.1284, 203.9417, 201.9419]])]]\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":"4bb04352e049d32a6aa0f9ace0a3f15a9dd24dc593c43501883168d8d89be54a","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(r, k, n0, years):\n    if k <= 0 or n0 < 0:\n        return None\n    if r < 0:\n        regime = 'decline'\n    elif r == 0:\n        regime = 'neutral'\n    elif r < 1:\n        regime = 'monotone'\n    elif r < 2:\n        regime = 'damped'\n    elif r < 2.526:\n        regime = 'cycle2'\n    else:\n        regime = 'complex'\n    n = float(n0)\n    traj = []\n    for _ in range(years):\n        n = n * math.exp(r * (1 - n / k))\n        traj.append(round(n, 4))\n    return [regime, traj]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('control: salmon stock damped',\n   (1.5, 1000, 200, 6),\n   ['damped', [664.0234, 1099.1389, 947.2604, 1025.2415, 987.1493, 1006.3622]]),\n  ('regression: superstable r one',\n   (1.0, 500, 100, 5),\n   ['monotone', [222.5541, 387.6342, 485.3128, 499.78, 500.0]]),\n  ('control: two cycle',\n   (2.2, 100, 30, 6),\n   ['cycle2', [139.9377, 58.1234, 146.0361, 53.0407, 149.0324, 50.6759]]),\n  ('control: period doubling onset exactly 2',\n   (2.0, 100, 40, 5),\n   ['cycle2', [132.8047, 68.9089, 128.3303, 72.8208, 125.4096]]),\n  ('control: near two', (1.96, 100, 40, 4), ['damped', [129.6553, 72.5035, 124.2836, 77.2161]]),\n  ('control: chaotic', (3.0, 100, 10, 5), ['complex', [148.7973, 34.421, 246.1736, 3.0674, 56.1939]]),\n  ('regression: weak growth above K',\n   (0.5, 200, 350, 5),\n   ['monotone', [240.5512, 217.36, 208.1284, 203.9417, 201.9419]])],\n [('regression: superstable r one',\n   (1.0, 500, 100, 5),\n   ['monotone', [222.5541, 387.6342, 485.3128, 499.78, 500.0]]),\n  ('control: period doubling onset exactly 2',\n   (2.0, 100, 40, 5),\n   ['cycle2', [132.8047, 68.9089, 128.3303, 72.8208, 125.4096]]),\n  ('control: near two', (1.96, 100, 40, 4), ['damped', [129.6553, 72.5035, 124.2836, 77.2161]]),\n  ('control: chaotic', (3.0, 100, 10, 5), ['complex', [148.7973, 34.421, 246.1736, 3.0674, 56.1939]]),\n  ('control: neutral', (0.0, 100, 60, 3), ['neutral', [60.0, 60.0, 60.0]]),\n  ('control: neutral empty patch', (0.0, 100, 0, 3), ['neutral', [0.0, 0.0, 0.0]]),\n  ('regression: weak growth above K',\n   (0.5, 200, 350, 5),\n   ['monotone', [240.5512, 217.36, 208.1284, 203.9417, 201.9419]])],\n [('regression: superstable r one',\n   (1.0, 500, 100, 5),\n   ['monotone', [222.5541, 387.6342, 485.3128, 499.78, 500.0]]),\n  ('control: neutral', (0.0, 100, 60, 3), ['neutral', [60.0, 60.0, 60.0]]),\n  ('control: neutral empty patch', (0.0, 100, 0, 3), ['neutral', [0.0, 0.0, 0.0]]),\n  ('control: declining', (-0.3, 100, 80, 4), ['decline', [75.3412, 69.9688, 63.9407, 57.3848]]),\n  ('control: invalid capacity', (1.0, 0, 10, 3), None),\n  ('regression: weak growth above K',\n   (0.5, 200, 350, 5),\n   ['monotone', [240.5512, 217.36, 208.1284, 203.9417, 201.9419]]),\n  ('control: weak growth below K',\n   (0.7, 200, 20, 5),\n   ['monotone', [37.5522, 66.3073, 105.8713, 147.1827, 177.0682]])],\n [('control: salmon stock damped',\n   (1.5, 1000, 200, 6),\n   ['damped', [664.0234, 1099.1389, 947.2604, 1025.2415, 987.1493, 1006.3622]]),\n  ('regression: superstable r one',\n   (1.0, 500, 100, 5),\n   ['monotone', [222.5541, 387.6342, 485.3128, 499.78, 500.0]]),\n  ('control: two cycle',\n   (2.2, 100, 30, 6),\n   ['cycle2', [139.9377, 58.1234, 146.0361, 53.0407, 149.0324, 50.6759]]),\n  ('control: period doubling onset exactly 2',\n   (2.0, 100, 40, 5),\n   ['cycle2', [132.8047, 68.9089, 128.3303, 72.8208, 125.4096]]),\n  ('control: invalid capacity', (1.0, 0, 10, 3), None),\n  ('regression: weak growth above K',\n   (0.5, 200, 350, 5),\n   ['monotone', [240.5512, 217.36, 208.1284, 203.9417, 201.9419]]),\n  ('control: weak growth below K',\n   (0.7, 200, 20, 5),\n   ['monotone', [37.5522, 66.3073, 105.8713, 147.1827, 177.0682]])],\n [('control: salmon stock damped',\n   (1.5, 1000, 200, 6),\n   ['damped', [664.0234, 1099.1389, 947.2604, 1025.2415, 987.1493, 1006.3622]]),\n  ('regression: superstable r one',\n   (1.0, 500, 100, 5),\n   ['monotone', [222.5541, 387.6342, 485.3128, 499.78, 500.0]]),\n  ('control: two cycle',\n   (2.2, 100, 30, 6),\n   ['cycle2', [139.9377, 58.1234, 146.0361, 53.0407, 149.0324, 50.6759]]),\n  ('control: period doubling onset exactly 2',\n   (2.0, 100, 40, 5),\n   ['cycle2', [132.8047, 68.9089, 128.3303, 72.8208, 125.4096]]),\n  ('control: near two', (1.96, 100, 40, 4), ['damped', [129.6553, 72.5035, 124.2836, 77.2161]]),\n  ('control: chaotic', (3.0, 100, 10, 5), ['complex', [148.7973, 34.421, 246.1736, 3.0674, 56.1939]]),\n  ('regression: weak growth above K',\n   (0.5, 200, 350, 5),\n   ['monotone', [240.5512, 217.36, 208.1284, 203.9417, 201.9419]])]]\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":"1bb49e3fb2e33152572493eb131ea538041034d99487b128bd353f2e20eff938","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(r, k, n0, years):\n    if k <= 0 or n0 < 0:\n        return None\n    if r < 0:\n        regime = 'decline'\n    elif r == 0:\n        regime = 'neutral'\n    elif r <= 1:\n        regime = 'monotone'\n    elif r < 2:\n        regime = 'damped'\n    elif r < 2.526:\n        regime = 'cycle2'\n    else:\n        regime = 'complex'\n    n = float(n0)\n    traj = []\n    for _ in range(years):\n        n = n * math.exp(r * (1 - n / k))\n        traj.append(round(n, 4))\n    return [regime, traj]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('control: salmon stock damped',\n   (1.5, 1000, 200, 6),\n   ['damped', [664.0234, 1099.1389, 947.2604, 1025.2415, 987.1493, 1006.3622]]),\n  ('regression: superstable r one',\n   (1.0, 500, 100, 5),\n   ['monotone', [222.5541, 387.6342, 485.3128, 499.78, 500.0]]),\n  ('control: two cycle',\n   (2.2, 100, 30, 6),\n   ['cycle2', [139.9377, 58.1234, 146.0361, 53.0407, 149.0324, 50.6759]]),\n  ('control: period doubling onset exactly 2',\n   (2.0, 100, 40, 5),\n   ['cycle2', [132.8047, 68.9089, 128.3303, 72.8208, 125.4096]]),\n  ('control: near two', (1.96, 100, 40, 4), ['damped', [129.6553, 72.5035, 124.2836, 77.2161]]),\n  ('control: chaotic', (3.0, 100, 10, 5), ['complex', [148.7973, 34.421, 246.1736, 3.0674, 56.1939]]),\n  ('regression: weak growth above K',\n   (0.5, 200, 350, 5),\n   ['monotone', [240.5512, 217.36, 208.1284, 203.9417, 201.9419]])],\n [('regression: superstable r one',\n   (1.0, 500, 100, 5),\n   ['monotone', [222.5541, 387.6342, 485.3128, 499.78, 500.0]]),\n  ('control: period doubling onset exactly 2',\n   (2.0, 100, 40, 5),\n   ['cycle2', [132.8047, 68.9089, 128.3303, 72.8208, 125.4096]]),\n  ('control: near two', (1.96, 100, 40, 4), ['damped', [129.6553, 72.5035, 124.2836, 77.2161]]),\n  ('control: chaotic', (3.0, 100, 10, 5), ['complex', [148.7973, 34.421, 246.1736, 3.0674, 56.1939]]),\n  ('control: neutral', (0.0, 100, 60, 3), ['neutral', [60.0, 60.0, 60.0]]),\n  ('control: neutral empty patch', (0.0, 100, 0, 3), ['neutral', [0.0, 0.0, 0.0]]),\n  ('regression: weak growth above K',\n   (0.5, 200, 350, 5),\n   ['monotone', [240.5512, 217.36, 208.1284, 203.9417, 201.9419]])],\n [('regression: superstable r one',\n   (1.0, 500, 100, 5),\n   ['monotone', [222.5541, 387.6342, 485.3128, 499.78, 500.0]]),\n  ('control: neutral', (0.0, 100, 60, 3), ['neutral', [60.0, 60.0, 60.0]]),\n  ('control: neutral empty patch', (0.0, 100, 0, 3), ['neutral', [0.0, 0.0, 0.0]]),\n  ('control: declining', (-0.3, 100, 80, 4), ['decline', [75.3412, 69.9688, 63.9407, 57.3848]]),\n  ('control: invalid capacity', (1.0, 0, 10, 3), None),\n  ('regression: weak growth above K',\n   (0.5, 200, 350, 5),\n   ['monotone', [240.5512, 217.36, 208.1284, 203.9417, 201.9419]]),\n  ('control: weak growth below K',\n   (0.7, 200, 20, 5),\n   ['monotone', [37.5522, 66.3073, 105.8713, 147.1827, 177.0682]])],\n [('control: salmon stock damped',\n   (1.5, 1000, 200, 6),\n   ['damped', [664.0234, 1099.1389, 947.2604, 1025.2415, 987.1493, 1006.3622]]),\n  ('regression: superstable r one',\n   (1.0, 500, 100, 5),\n   ['monotone', [222.5541, 387.6342, 485.3128, 499.78, 500.0]]),\n  ('control: two cycle',\n   (2.2, 100, 30, 6),\n   ['cycle2', [139.9377, 58.1234, 146.0361, 53.0407, 149.0324, 50.6759]]),\n  ('control: period doubling onset exactly 2',\n   (2.0, 100, 40, 5),\n   ['cycle2', [132.8047, 68.9089, 128.3303, 72.8208, 125.4096]]),\n  ('control: invalid capacity', (1.0, 0, 10, 3), None),\n  ('regression: weak growth above K',\n   (0.5, 200, 350, 5),\n   ['monotone', [240.5512, 217.36, 208.1284, 203.9417, 201.9419]]),\n  ('control: weak growth below K',\n   (0.7, 200, 20, 5),\n   ['monotone', [37.5522, 66.3073, 105.8713, 147.1827, 177.0682]])],\n [('control: salmon stock damped',\n   (1.5, 1000, 200, 6),\n   ['damped', [664.0234, 1099.1389, 947.2604, 1025.2415, 987.1493, 1006.3622]]),\n  ('regression: superstable r one',\n   (1.0, 500, 100, 5),\n   ['monotone', [222.5541, 387.6342, 485.3128, 499.78, 500.0]]),\n  ('control: two cycle',\n   (2.2, 100, 30, 6),\n   ['cycle2', [139.9377, 58.1234, 146.0361, 53.0407, 149.0324, 50.6759]]),\n  ('control: period doubling onset exactly 2',\n   (2.0, 100, 40, 5),\n   ['cycle2', [132.8047, 68.9089, 128.3303, 72.8208, 125.4096]]),\n  ('control: near two', (1.96, 100, 40, 4), ['damped', [129.6553, 72.5035, 124.2836, 77.2161]]),\n  ('control: chaotic', (3.0, 100, 10, 5), ['complex', [148.7973, 34.421, 246.1736, 3.0674, 56.1939]]),\n  ('regression: weak growth above K',\n   (0.5, 200, 350, 5),\n   ['monotone', [240.5512, 217.36, 208.1284, 203.9417, 201.9419]])]]\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":"Deterministic bounded teaching model with a stipulated contract; not a validated scientific or public-health modelling 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":"w2-ecopop-ricker-regime-superstable-boundary","generated_at":"2026-09-29T14:47:33.321973+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Population projections set harvest quotas, conservation status and pest-control timing; a wrong update order, boundary or rate conversion silently changes management advice.","repair":"Restore the superstable boundary rule: `elif r <= 1:`.","root_cause":"The monotone band excludes its upper boundary r=1.","sha256":"4ce777eb15e39f60d1abecfee947a5b79dcae8f09f49843de1431d9dd005cc48","title":"Ricker map trajectory and dynamic regime: superstable boundary · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":41.142,"exit_code":1,"observations":[{"actual":["damped",[664.0234,1099.1389,947.2604,1025.2415,987.1493,1006.3622]],"check":"control: salmon stock damped","expected":["damped",[664.0234,1099.1389,947.2604,1025.2415,987.1493,1006.3622]],"passed":true},{"actual":["monotone",[222.5541,387.6342,485.3128,499.78,500.0]],"check":"regression: superstable r one","expected":["monotone",[222.5541,387.6342,485.3128,499.78,500.0]],"passed":true},{"actual":["cycle2",[139.9377,58.1234,146.0361,53.0407,149.0324,50.6759]],"check":"control: two cycle","expected":["cycle2",[139.9377,58.1234,146.0361,53.0407,149.0324,50.6759]],"passed":true},{"actual":["cycle2",[132.8047,68.9089,128.3303,72.8208,125.4096]],"check":"control: period doubling onset exactly 2","expected":["cycle2",[132.8047,68.9089,128.3303,72.8208,125.4096]],"passed":true},{"actual":["damped",[129.6553,72.5035,124.2836,77.2161]],"check":"control: near two","expected":["damped",[129.6553,72.5035,124.2836,77.2161]],"passed":true},{"actual":["complex",[148.7973,34.421,246.1736,3.0674,56.1939]],"check":"control: chaotic","expected":["complex",[148.7973,34.421,246.1736,3.0674,56.1939]],"passed":true},{"actual":["damped",[240.5512,217.36,208.1284,203.9417,201.9419]],"check":"regression: weak growth above K","expected":["monotone",[240.5512,217.36,208.1284,203.9417,201.9419]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"control: salmon stock damped\", \"actual\": [\"damped\", [664.0234, 1099.1389, 947.2604, 1025.2415, 987.1493, 1006.3622]], \"expected\": [\"damped\", [664.0234, 1099.1389, 947.2604, 1025.2415, 987.1493, 1006.3622]], \"passed\": true}, {\"check\": \"regression: superstable r one\", \"actual\": [\"monotone\", [222.5541, 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