{"abstract":"Reflection coefficients after the first step are mis-scaled and stability verdicts flip.","category":"Digital signal filters","checks":7,"contract":"Input the denominator [a0, a1, ..., an] as rational strings. Normalize by a0 (\"bad-a0\" if missing or 0), drop trailing zero coefficients, then step down: k = last coefficient, unstable if |k| >= 1, else a_i <- (a_i - k a_{p-i}) / (1 - k^2) for i < p. Return {\"stable\": bool, \"reflection\": [k strings so far]}.","evaluation_group":"w2-digital_signal_filters-schur-cohn-stability","failed_approach":"The attempted repair divides by 1 + k^2.","family":"w2-digital_signal_filters-schur-cohn-stability-step-down-normalizer","id":"FA-91581","implementations":{"attempt":{"sha256":"216d4fc2511669302344667e23400d23d738d348e9b2bb72faba4fa84258d311","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(x):\n    a = [Fraction(v) for v in x]\n    if not a or a[0] == 0:\n        return 'bad-a0'\n    a = [v / a[0] for v in a]\n    while len(a) > 1 and a[-1] == 0:\n        a.pop()\n    ks = []\n    while len(a) > 1:\n        p = len(a) - 1\n        k = a[p]\n        ks.append(str(k))\n        if abs(k) >= 1:\n            return {'stable': False, 'reflection': ks}\n        a = [(a[i] - k * a[p - i]) / (1 + k * k) for i in range(p)]\n    return {'stable': True, 'reflection': ks}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression: stable second order', ['1', '-1/2', '1/4'], {'stable': True, 'reflection': ['1/4', '-2/5']}], ['regression: negative leading coefficient', ['-2', '1', '-1/2'], {'stable': True, 'reflection': ['1/4', '-2/5']}], ['regression: third order', ['1', '-1/2', '1/3', '-1/5'], {'stable': True, 'reflection': ['-1/5', '35/144', '-65/179']}], ['control: marginal pole on unit circle', ['1', '0', '-1'], {'stable': False, 'reflection': ['-1']}], ['control: trailing zero coefficient', ['1', '1/2', '0'], {'stable': True, 'reflection': ['1/2']}], ['control: two trailing zeros', ['1', '-1/3', '0', '0'], {'stable': True, 'reflection': ['-1/3']}], ['control: pole at -1', ['1', '1'], {'stable': False, 'reflection': ['1']}]], [['regression: random denominator 1', ['1', '1/8', '1/8'], {'stable': True, 'reflection': ['1/8', '1/9']}], ['regression: random denominator 2', ['1', '1/3', '1/3'], {'stable': True, 'reflection': ['1/3', '1/4']}], ['regression: third order', ['1', '-1/2', '1/3', '-1/5'], {'stable': True, 'reflection': ['-1/5', '35/144', '-65/179']}], ['control: unstable first order', ['1', '-3/2'], {'stable': False, 'reflection': ['-3/2']}], ['control: bad a0', ['0', '1'], 'bad-a0'], ['control: random denominator 0', ['-1', '0'], {'stable': True, 'reflection': []}], ['control: random denominator 3', ['-1', '-1/2'], {'stable': True, 'reflection': ['1/2']}]], [['regression: random denominator 10', ['1', '-1/4', '1/8', '-1/2'], {'stable': True, 'reflection': ['-1/2', '0', '-1/4']}], ['regression: random denominator 13', ['1', '1/8', '1/8', '3/4'], {'stable': True, 'reflection': ['3/4', '1/14', '1/15']}], ['regression: random denominator 2', ['1', '1/3', '1/3'], {'stable': True, 'reflection': ['1/3', '1/4']}], ['control: random denominator 4', ['-1', '0', '5/4'], {'stable': False, 'reflection': ['-5/4']}], ['control: random denominator 6', ['1/2', '1/8'], {'stable': True, 'reflection': ['1/4']}], ['control: random denominator 7', ['1', '3/4', '-1'], {'stable': False, 'reflection': ['-1']}], ['control: random denominator 8', ['1', '-1/4'], {'stable': True, 'reflection': ['-1/4']}]], [['regression: random denominator 22', ['2', '1/8', '3/4'], {'stable': True, 'reflection': ['3/8', '1/22']}], ['regression: random denominator 26', ['1', '1/8', '3/4'], {'stable': True, 'reflection': ['3/4', '1/14']}], ['regression: random denominator 10', ['1', '-1/4', '1/8', '-1/2'], {'stable': True, 'reflection': ['-1/2', '0', '-1/4']}], ['control: random denominator 9', ['1', '-1', '-1'], {'stable': False, 'reflection': ['-1']}], ['control: random denominator 11', ['-1', '0', '-1/2'], {'stable': True, 'reflection': ['1/2', '0']}], ['control: random denominator 12', ['1', '5/4', '-1', '-1'], {'stable': False, 'reflection': ['-1']}], ['control: random denominator 14', ['1', '1/8', '5/4'], {'stable': False, 'reflection': ['5/4']}]], [['regression: random denominator 29', ['1', '-1/2', '3/4'], {'stable': True, 'reflection': ['3/4', '-2/7']}], ['regression: random denominator 30', ['1', '1/3', '1/2', '1/3'], {'stable': True, 'reflection': ['1/3', '7/16', '3/23']}], ['regression: random denominator 20', ['1', '1/2', '-1/4'], {'stable': True, 'reflection': ['-1/4', '2/3']}], ['control: random denominator 15', ['1', '-1/4'], {'stable': True, 'reflection': ['-1/4']}], ['control: random denominator 16', ['1/2', '-1', '3/4'], {'stable': False, 'reflection': ['3/2']}], ['control: random denominator 17', ['1', '1/8'], {'stable': True, 'reflection': ['1/8']}], ['control: random denominator 18', ['1', '1/2', '0'], {'stable': True, 'reflection': ['1/2']}]]]\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":"10ace9d78c593b52c48159e24c934752876ea95a42b83f19ae1f5fc391b556be","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(x):\n    a = [Fraction(v) for v in x]\n    if not a or a[0] == 0:\n        return 'bad-a0'\n    a = [v / a[0] for v in a]\n    while len(a) > 1 and a[-1] == 0:\n        a.pop()\n    ks = []\n    while len(a) > 1:\n        p = len(a) - 1\n        k = a[p]\n        ks.append(str(k))\n        if abs(k) >= 1:\n            return {'stable': False, 'reflection': ks}\n        a = [(a[i] - k * a[p - i]) / (1 - k) for i in range(p)]\n    return {'stable': True, 'reflection': ks}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression: stable second order', ['1', '-1/2', '1/4'], {'stable': True, 'reflection': ['1/4', '-2/5']}], ['regression: negative leading coefficient', ['-2', '1', '-1/2'], {'stable': True, 'reflection': ['1/4', '-2/5']}], ['regression: third order', ['1', '-1/2', '1/3', '-1/5'], {'stable': True, 'reflection': ['-1/5', '35/144', '-65/179']}], ['control: marginal pole on unit circle', ['1', '0', '-1'], {'stable': False, 'reflection': ['-1']}], ['control: trailing zero coefficient', ['1', '1/2', '0'], {'stable': True, 'reflection': ['1/2']}], ['control: two trailing zeros', ['1', '-1/3', '0', '0'], {'stable': True, 'reflection': ['-1/3']}], ['control: pole at -1', ['1', '1'], {'stable': False, 'reflection': ['1']}]], [['regression: random denominator 1', ['1', '1/8', '1/8'], {'stable': True, 'reflection': ['1/8', '1/9']}], ['regression: random denominator 2', ['1', '1/3', '1/3'], {'stable': True, 'reflection': ['1/3', '1/4']}], ['regression: third order', ['1', '-1/2', '1/3', '-1/5'], {'stable': True, 'reflection': ['-1/5', '35/144', '-65/179']}], ['control: unstable first order', ['1', '-3/2'], {'stable': False, 'reflection': ['-3/2']}], ['control: bad a0', ['0', '1'], 'bad-a0'], ['control: random denominator 0', ['-1', '0'], {'stable': True, 'reflection': []}], ['control: random denominator 3', ['-1', '-1/2'], {'stable': True, 'reflection': ['1/2']}]], [['regression: random denominator 10', ['1', '-1/4', '1/8', '-1/2'], {'stable': True, 'reflection': ['-1/2', '0', '-1/4']}], ['regression: random denominator 13', ['1', '1/8', '1/8', '3/4'], {'stable': True, 'reflection': ['3/4', '1/14', '1/15']}], ['regression: random denominator 2', ['1', '1/3', '1/3'], {'stable': True, 'reflection': ['1/3', '1/4']}], ['control: random denominator 4', ['-1', '0', '5/4'], {'stable': False, 'reflection': ['-5/4']}], ['control: random denominator 6', ['1/2', '1/8'], {'stable': True, 'reflection': ['1/4']}], ['control: random denominator 7', ['1', '3/4', '-1'], {'stable': False, 'reflection': ['-1']}], ['control: random denominator 8', ['1', '-1/4'], {'stable': True, 'reflection': ['-1/4']}]], [['regression: random denominator 22', ['2', '1/8', '3/4'], {'stable': True, 'reflection': ['3/8', '1/22']}], ['regression: random denominator 26', ['1', '1/8', '3/4'], {'stable': True, 'reflection': ['3/4', '1/14']}], ['regression: random denominator 10', ['1', '-1/4', '1/8', '-1/2'], {'stable': True, 'reflection': ['-1/2', '0', '-1/4']}], ['control: random denominator 9', ['1', '-1', '-1'], {'stable': False, 'reflection': ['-1']}], ['control: random denominator 11', ['-1', '0', '-1/2'], {'stable': True, 'reflection': ['1/2', '0']}], ['control: random denominator 12', ['1', '5/4', '-1', '-1'], {'stable': False, 'reflection': ['-1']}], ['control: random denominator 14', ['1', '1/8', '5/4'], {'stable': False, 'reflection': ['5/4']}]], [['regression: random denominator 29', ['1', '-1/2', '3/4'], {'stable': True, 'reflection': ['3/4', '-2/7']}], ['regression: random denominator 30', ['1', '1/3', '1/2', '1/3'], {'stable': True, 'reflection': ['1/3', '7/16', '3/23']}], ['regression: random denominator 20', ['1', '1/2', '-1/4'], {'stable': True, 'reflection': ['-1/4', '2/3']}], ['control: random denominator 15', ['1', '-1/4'], {'stable': True, 'reflection': ['-1/4']}], ['control: random denominator 16', ['1/2', '-1', '3/4'], {'stable': False, 'reflection': ['3/2']}], ['control: random denominator 17', ['1', '1/8'], {'stable': True, 'reflection': ['1/8']}], ['control: random denominator 18', ['1', '1/2', '0'], {'stable': True, 'reflection': ['1/2']}]]]\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":"da17a5c66fe9b9044dcd3926b1787c37e8ba588d039104d692f99c520cbea2d5","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(x):\n    a = [Fraction(v) for v in x]\n    if not a or a[0] == 0:\n        return 'bad-a0'\n    a = [v / a[0] for v in a]\n    while len(a) > 1 and a[-1] == 0:\n        a.pop()\n    ks = []\n    while len(a) > 1:\n        p = len(a) - 1\n        k = a[p]\n        ks.append(str(k))\n        if abs(k) >= 1:\n            return {'stable': False, 'reflection': ks}\n        a = [(a[i] - k * a[p - i]) / (1 - k * k) for i in range(p)]\n    return {'stable': True, 'reflection': ks}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression: stable second order', ['1', '-1/2', '1/4'], {'stable': True, 'reflection': ['1/4', '-2/5']}], ['regression: negative leading coefficient', ['-2', '1', '-1/2'], {'stable': True, 'reflection': ['1/4', '-2/5']}], ['regression: third order', ['1', '-1/2', '1/3', '-1/5'], {'stable': True, 'reflection': ['-1/5', '35/144', '-65/179']}], ['control: marginal pole on unit circle', ['1', '0', '-1'], {'stable': False, 'reflection': ['-1']}], ['control: trailing zero coefficient', ['1', '1/2', '0'], {'stable': True, 'reflection': ['1/2']}], ['control: two trailing zeros', ['1', '-1/3', '0', '0'], {'stable': True, 'reflection': ['-1/3']}], ['control: pole at -1', ['1', '1'], {'stable': False, 'reflection': ['1']}]], [['regression: random denominator 1', ['1', '1/8', '1/8'], {'stable': True, 'reflection': ['1/8', '1/9']}], ['regression: random denominator 2', ['1', '1/3', '1/3'], {'stable': True, 'reflection': ['1/3', '1/4']}], ['regression: third order', ['1', '-1/2', '1/3', '-1/5'], {'stable': True, 'reflection': ['-1/5', '35/144', '-65/179']}], ['control: unstable first order', ['1', '-3/2'], {'stable': False, 'reflection': ['-3/2']}], ['control: bad a0', ['0', '1'], 'bad-a0'], ['control: random denominator 0', ['-1', '0'], {'stable': True, 'reflection': []}], ['control: random denominator 3', ['-1', '-1/2'], {'stable': True, 'reflection': ['1/2']}]], [['regression: random denominator 10', ['1', '-1/4', '1/8', '-1/2'], {'stable': True, 'reflection': ['-1/2', '0', '-1/4']}], ['regression: random denominator 13', ['1', '1/8', '1/8', '3/4'], {'stable': True, 'reflection': ['3/4', '1/14', '1/15']}], ['regression: random denominator 2', ['1', '1/3', '1/3'], {'stable': True, 'reflection': ['1/3', '1/4']}], ['control: random denominator 4', ['-1', '0', '5/4'], {'stable': False, 'reflection': ['-5/4']}], ['control: random denominator 6', ['1/2', '1/8'], {'stable': True, 'reflection': ['1/4']}], ['control: random denominator 7', ['1', '3/4', '-1'], {'stable': False, 'reflection': ['-1']}], ['control: random denominator 8', ['1', '-1/4'], {'stable': True, 'reflection': ['-1/4']}]], [['regression: random denominator 22', ['2', '1/8', '3/4'], {'stable': True, 'reflection': ['3/8', '1/22']}], ['regression: random denominator 26', ['1', '1/8', '3/4'], {'stable': True, 'reflection': ['3/4', '1/14']}], ['regression: random denominator 10', ['1', '-1/4', '1/8', '-1/2'], {'stable': True, 'reflection': ['-1/2', '0', '-1/4']}], ['control: random denominator 9', ['1', '-1', '-1'], {'stable': False, 'reflection': ['-1']}], ['control: random denominator 11', ['-1', '0', '-1/2'], {'stable': True, 'reflection': ['1/2', '0']}], ['control: random denominator 12', ['1', '5/4', '-1', '-1'], {'stable': False, 'reflection': ['-1']}], ['control: random denominator 14', ['1', '1/8', '5/4'], {'stable': False, 'reflection': ['5/4']}]], [['regression: random denominator 29', ['1', '-1/2', '3/4'], {'stable': True, 'reflection': ['3/4', '-2/7']}], ['regression: random denominator 30', ['1', '1/3', '1/2', '1/3'], {'stable': True, 'reflection': ['1/3', '7/16', '3/23']}], ['regression: random denominator 20', ['1', '1/2', '-1/4'], {'stable': True, 'reflection': ['-1/4', '2/3']}], ['control: random denominator 15', ['1', '-1/4'], {'stable': True, 'reflection': ['-1/4']}], ['control: random denominator 16', ['1/2', '-1', '3/4'], {'stable': False, 'reflection': ['3/2']}], ['control: random denominator 17', ['1', '1/8'], {'stable': True, 'reflection': ['1/8']}], ['control: random denominator 18', ['1', '1/2', '0'], {'stable': True, 'reflection': ['1/2']}]]]\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 bounded teaching model with a stipulated toy contract; exact rational arithmetic or fixed-decimal rounding keeps outputs strict JSON. It is not a production DSP library and claims no standards conformance. 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-digital_signal_filters-schur-cohn-stability-step-down-normalizer","generated_at":"2026-09-29T14:51:37.433177+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Checking IIR denominators for stability before deployment prevents runaway filters; step-down slips accept unstable designs.","repair":"Divide by 1 - k^2.","root_cause":"The Levinson step-down divides by (1 - k) instead of (1 - k^2).","sha256":"b753d77f38b080f31ae52cc4459bcfc0941124b427987d521021cc84ac88cfdd","title":"Stability step-down divides by 1 - k · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":40.135,"exit_code":1,"observations":[{"actual":{"reflection":["1/4","-6/17"],"stable":true},"check":"regression: stable second order","expected":{"reflection":["1/4","-2/5"],"stable":true},"passed":false},{"actual":{"reflection":["1/4","-6/17"],"stable":true},"check":"regression: negative leading coefficient","expected":{"reflection":["1/4","-2/5"],"stable":true},"passed":false},{"actual":{"reflection":["-1/5","35/156","-7865/25561"],"stable":true},"check":"regression: third order","expected":{"reflection":["-1/5","35/144","-65/179"],"stable":true},"passed":false},{"actual":{"reflection":["-1"],"stable":false},"check":"control: marginal pole on unit circle","expected":{"reflection":["-1"],"stable":false},"passed":true},{"actual":{"reflection":["1/2"],"stable":true},"check":"control: trailing zero coefficient","expected":{"reflection":["1/2"],"stable":true},"passed":true},{"actual":{"reflection":["-1/3"],"stable":true},"check":"control: two trailing zeros","expected":{"reflection":["-1/3"],"stable":true},"passed":true},{"actual":{"reflection":["1"],"stable":false},"check":"control: pole at -1","expected":{"reflection":["1"],"stable":false},"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: stable second order\", \"actual\": {\"stable\": true, \"reflection\": [\"1/4\", \"-6/17\"]}, \"expected\": {\"stable\": true, \"reflection\": [\"1/4\", \"-2/5\"]}, \"passed\": false}, {\"check\": \"regression: negative leading coefficient\", \"actual\": {\"stable\": true, \"reflection\": [\"1/4\", \"-6/17\"]}, \"expected\": {\"stable\": true, \"reflection\": [\"1/4\", \"-2/5\"]}, \"passed\": false}, {\"check\": \"regression: third order\", \"actual\": {\"stable\": true, \"reflection\": [\"-1/5\", \"35/156\", \"-7865/25561\"]}, \"expected\": {\"stable\": true, \"reflection\": [\"-1/5\", \"35/144\", \"-65/179\"]}, \"passed\": false}, {\"check\": \"control: marginal pole on unit circle\", \"actual\": {\"stable\": false, \"reflection\": [\"-1\"]}, \"expected\": {\"stable\": false, \"reflection\": [\"-1\"]}, \"passed\": true}, {\"check\": \"control: trailing zero coefficient\", \"actual\": {\"stable\": true, \"reflection\": [\"1/2\"]}, \"expected\": {\"stable\": true, \"reflection\": [\"1/2\"]}, \"passed\": true}, {\"check\": \"control: two trailing zeros\", \"actual\": {\"stable\": true, \"reflection\": [\"-1/3\"]}, \"expected\": {\"stable\": true, \"reflection\": [\"-1/3\"]}, \"passed\": true}, {\"check\": \"control: pole at -1\", \"actual\": {\"stable\": false, \"reflection\": [\"1\"]}, \"expected\": {\"stable\": false, \"reflection\": [\"1\"]}, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":42.246,"exit_code":1,"observations":[{"actual":{"reflection":["1/4","-1/2"],"stable":true},"check":"regression: stable second order","expected":{"reflection":["1/4","-2/5"],"stable":true},"passed":false},{"actual":{"reflection":["1/4","-1/2"],"stable":true},"check":"regression: negative leading coefficient","expected":{"reflection":["1/4","-2/5"],"stable":true},"passed":false},{"actual":{"reflection":["-1/5","7/36","-13/36"],"stable":true},"check":"regression: third order","expected":{"reflection":["-1/5","35/144","-65/179"],"stable":true},"passed":false},{"actual":{"reflection":["-1"],"stable":false},"check":"control: marginal pole on unit circle","expected":{"reflection":["-1"],"stable":false},"passed":true},{"actual":{"reflection":["1/2"],"stable":true},"check":"control: trailing zero coefficient","expected":{"reflection":["1/2"],"stable":true},"passed":true},{"actual":{"reflection":["-1/3"],"stable":true},"check":"control: two trailing zeros","expected":{"reflection":["-1/3"],"stable":true},"passed":true},{"actual":{"reflection":["1"],"stable":false},"check":"control: pole at -1","expected":{"reflection":["1"],"stable":false},"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: stable second order\", \"actual\": {\"stable\": true, \"reflection\": [\"1/4\", \"-1/2\"]}, \"expected\": {\"stable\": true, \"reflection\": [\"1/4\", \"-2/5\"]}, \"passed\": false}, {\"check\": \"regression: negative leading coefficient\", \"actual\": {\"stable\": true, \"reflection\": [\"1/4\", \"-1/2\"]}, \"expected\": {\"stable\": true, \"reflection\": [\"1/4\", \"-2/5\"]}, \"passed\": false}, {\"check\": \"regression: third order\", \"actual\": {\"stable\": true, \"reflection\": [\"-1/5\", \"7/36\", \"-13/36\"]}, \"expected\": {\"stable\": true, \"reflection\": [\"-1/5\", \"35/144\", \"-65/179\"]}, \"passed\": false}, {\"check\": \"control: marginal pole on unit circle\", \"actual\": {\"stable\": false, \"reflection\": [\"-1\"]}, \"expected\": {\"stable\": false, \"reflection\": [\"-1\"]}, \"passed\": true}, {\"check\": \"control: trailing zero coefficient\", \"actual\": {\"stable\": true, \"reflection\": [\"1/2\"]}, \"expected\": {\"stable\": true, \"reflection\": [\"1/2\"]}, \"passed\": true}, {\"check\": \"control: two trailing zeros\", \"actual\": {\"stable\": true, \"reflection\": [\"-1/3\"]}, \"expected\": {\"stable\": true, \"reflection\": [\"-1/3\"]}, \"passed\": true}, {\"check\": \"control: pole at -1\", \"actual\": {\"stable\": false, \"reflection\": [\"1\"]}, \"expected\": {\"stable\": false, \"reflection\": [\"1\"]}, \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":40.737,"exit_code":0,"observations":[{"actual":{"reflection":["1/4","-2/5"],"stable":true},"check":"regression: stable second order","expected":{"reflection":["1/4","-2/5"],"stable":true},"passed":true},{"actual":{"reflection":["1/4","-2/5"],"stable":true},"check":"regression: negative leading coefficient","expected":{"reflection":["1/4","-2/5"],"stable":true},"passed":true},{"actual":{"reflection":["-1/5","35/144","-65/179"],"stable":true},"check":"regression: third order","expected":{"reflection":["-1/5","35/144","-65/179"],"stable":true},"passed":true},{"actual":{"reflection":["-1"],"stable":false},"check":"control: marginal pole on unit circle","expected":{"reflection":["-1"],"stable":false},"passed":true},{"actual":{"reflection":["1/2"],"stable":true},"check":"control: trailing zero coefficient","expected":{"reflection":["1/2"],"stable":true},"passed":true},{"actual":{"reflection":["-1/3"],"stable":true},"check":"control: two trailing zeros","expected":{"reflection":["-1/3"],"stable":true},"passed":true},{"actual":{"reflection":["1"],"stable":false},"check":"control: pole at -1","expected":{"reflection":["1"],"stable":false},"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: stable second order\", \"actual\": {\"stable\": 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