{"abstract":"Echoes arrive after one sample regardless of D.","category":"Digital signal filters","checks":7,"contract":"Input [D, g, samples]: y[n] = x[n] + g y[n-D] using a D-slot ring buffer with zero initial state; \"bad-delay\" if D < 1, \"unstable\" if |g| >= 1. Return exact fraction strings.","evaluation_group":"w2-digital_signal_filters-feedback-comb-ring-buffer","failed_approach":"The attempted repair reads buf[(pos + 1) % D], giving a delay of D - 1.","family":"w2-digital_signal_filters-feedback-comb-ring-buffer-ring-read-position","id":"FA-91746","implementations":{"attempt":{"sha256":"2e76a426a146ee847c08cb2e81a095e787403852287dd4abd25b73196be3e82b","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(x):\n    D, g, xs = x[0], Fraction(x[1]), x[2]\n    if D < 1:\n        return 'bad-delay'\n    if abs(g) >= 1:\n        return 'unstable'\n    buf = [Fraction(0)] * D\n    pos = 0\n    out = []\n    for v in xs:\n        delayed = buf[(pos + 1) % D]\n        y = v + g * delayed\n        buf[pos] = y\n        pos = (pos + 1) % D\n        out.append(str(y))\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression: impulse delay 2', [2, '1/2', [1, 0, 0, 0, 0, 0]], ['1', '0', '1/2', '0', '1/4', '0']], ['regression: random comb 0', [2, '1/2', [-1, 3, 3, 0, 3, 2, -3, -1, -2]], ['-1', '3', '5/2', '3/2', '17/4', '11/4', '-7/8', '3/8', '-39/16']], ['regression: random comb 1', [4, '1/2', [-3, -2, 2, -3, 2, -1, -3, -2, -3]], ['-3', '-2', '2', '-3', '1/2', '-2', '-2', '-7/2', '-11/4']], ['control: delay 1', [1, '-1/2', [1, 0, 0]], ['1', '-1/2', '1/4']], ['control: unit gain rejected', [3, '1', [1]], 'unstable'], ['control: negative unit gain', [3, '-1', [1]], 'unstable'], ['control: bad delay', [0, '1/2', [1]], 'bad-delay']], [['regression: random comb 2', [4, '-2/3', [2, 2, -1, 3, -1, 2, 1]], ['2', '2', '-1', '3', '-7/3', '2/3', '5/3']], ['regression: random comb 3', [2, '1/2', [2, -1, -3]], ['2', '-1', '-2']], ['regression: random comb 1', [4, '1/2', [-3, -2, 2, -3, 2, -1, -3, -2, -3]], ['-3', '-2', '2', '-3', '1/2', '-2', '-2', '-7/2', '-11/4']], ['control: random comb 11', [1, '3/4', [0, 1, 2, 0, -2, 1, 0]], ['0', '1', '11/4', '33/16', '-29/64', '169/256', '507/1024']], ['control: random comb 25', [1, '1/3', [0, -2, 2, 3, 0, 2, -2, -3]], ['0', '-2', '4/3', '31/9', '31/27', '193/81', '-293/243', '-2480/729']], ['control: random comb 29', [1, '1/2', [-3, 0, -3, -3, 2]], ['-3', '-3/2', '-15/4', '-39/8', '-7/16']], ['control: random comb 30', [1, '1/3', [1, 2, 1, -3, -1, 1, 2]], ['1', '7/3', '16/9', '-65/27', '-146/81', '97/243', '1555/729']]], [['regression: random comb 5', [2, '-2/3', [-3, -3, -1, -3, -1]], ['-3', '-3', '1', '-1', '-5/3']], ['regression: random comb 6', [4, '-2/3', [1, 0, -3, 3]], ['1', '0', '-3', '3']], ['regression: random comb 3', [2, '1/2', [2, -1, -3]], ['2', '-1', '-2']], ['control: random comb 33', [1, '3/4', [-3, -3, -1, 2, -2, 0, 2, 1, 3]], ['-3', '-21/4', '-79/16', '-109/64', '-839/256', '-2517/1024', '641/4096', '18307/16384', '251529/65536']], ['control: random comb 39', [1, '1/2', [3, 3, -2, 0, 2, -2, -3, 0, -3]], ['3', '9/2', '1/4', '1/8', '33/16', '-31/32', '-223/64', '-223/128', '-991/256']], ['control: delay 1', [1, '-1/2', [1, 0, 0]], ['1', '-1/2', '1/4']], ['control: unit gain rejected', [3, '1', [1]], 'unstable']], [['regression: random comb 8', [4, '-2/3', [1, 3, -2, -1]], ['1', '3', '-2', '-1']], ['regression: random comb 9', [3, '1/2', [-2, 0, -3, 1, -3, 0, 3, 1]], ['-2', '0', '-3', '0', '-3', '-3/2', '3', '-1/2']], ['regression: random comb 5', [2, '-2/3', [-3, -3, -1, -3, -1]], ['-3', '-3', '1', '-1', '-5/3']], ['control: negative unit gain', [3, '-1', [1]], 'unstable'], ['control: bad delay', [0, '1/2', [1]], 'bad-delay'], ['control: random comb 11', [1, '3/4', [0, 1, 2, 0, -2, 1, 0]], ['0', '1', '11/4', '33/16', '-29/64', '169/256', '507/1024']], ['control: random comb 25', [1, '1/3', [0, -2, 2, 3, 0, 2, -2, -3]], ['0', '-2', '4/3', '31/9', '31/27', '193/81', '-293/243', '-2480/729']]], [['regression: random comb 12', [3, '1/2', [2, 3, 0, -2, 3, 1]], ['2', '3', '0', '-1', '9/2', '1']], ['regression: random comb 13', [4, '-2/3', [3, -1, -3, -2, 3]], ['3', '-1', '-3', '-2', '1']], ['regression: random comb 7', [4, '-2/3', [1, 3, 3, -1, -1, 2, 3, -2, 2]], ['1', '3', '3', '-1', '-5/3', '0', '1', '-4/3', '28/9']], ['control: random comb 29', [1, '1/2', [-3, 0, -3, -3, 2]], ['-3', '-3/2', '-15/4', '-39/8', '-7/16']], ['control: random comb 30', [1, '1/3', [1, 2, 1, -3, -1, 1, 2]], ['1', '7/3', '16/9', '-65/27', '-146/81', '97/243', '1555/729']], ['control: random comb 33', [1, '3/4', [-3, -3, -1, 2, -2, 0, 2, 1, 3]], ['-3', '-21/4', '-79/16', '-109/64', '-839/256', '-2517/1024', '641/4096', '18307/16384', '251529/65536']], ['control: random comb 39', [1, '1/2', [3, 3, -2, 0, 2, -2, -3, 0, -3]], ['3', '9/2', '1/4', '1/8', '33/16', '-31/32', '-223/64', '-223/128', '-991/256']]]]\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":"cc24ee6fbc456b05f1c0f675b7b3012c22fe2d7088c11b84dfa347555247db5a","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(x):\n    D, g, xs = x[0], Fraction(x[1]), x[2]\n    if D < 1:\n        return 'bad-delay'\n    if abs(g) >= 1:\n        return 'unstable'\n    buf = [Fraction(0)] * D\n    pos = 0\n    out = []\n    for v in xs:\n        delayed = buf[pos - 1]\n        y = v + g * delayed\n        buf[pos] = y\n        pos = (pos + 1) % D\n        out.append(str(y))\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression: impulse delay 2', [2, '1/2', [1, 0, 0, 0, 0, 0]], ['1', '0', '1/2', '0', '1/4', '0']], ['regression: random comb 0', [2, '1/2', [-1, 3, 3, 0, 3, 2, -3, -1, -2]], ['-1', '3', '5/2', '3/2', '17/4', '11/4', '-7/8', '3/8', '-39/16']], ['regression: random comb 1', [4, '1/2', [-3, -2, 2, -3, 2, -1, -3, -2, -3]], ['-3', '-2', '2', '-3', '1/2', '-2', '-2', '-7/2', '-11/4']], ['control: delay 1', [1, '-1/2', [1, 0, 0]], ['1', '-1/2', '1/4']], ['control: unit gain rejected', [3, '1', [1]], 'unstable'], ['control: negative unit gain', [3, '-1', [1]], 'unstable'], ['control: bad delay', [0, '1/2', [1]], 'bad-delay']], [['regression: random comb 2', [4, '-2/3', [2, 2, -1, 3, -1, 2, 1]], ['2', '2', '-1', '3', '-7/3', '2/3', '5/3']], ['regression: random comb 3', [2, '1/2', [2, -1, -3]], ['2', '-1', '-2']], ['regression: random comb 1', [4, '1/2', [-3, -2, 2, -3, 2, -1, -3, -2, -3]], ['-3', '-2', '2', '-3', '1/2', '-2', '-2', '-7/2', '-11/4']], ['control: random comb 11', [1, '3/4', [0, 1, 2, 0, -2, 1, 0]], ['0', '1', '11/4', '33/16', '-29/64', '169/256', '507/1024']], ['control: random comb 25', [1, '1/3', [0, -2, 2, 3, 0, 2, -2, -3]], ['0', '-2', '4/3', '31/9', '31/27', '193/81', '-293/243', '-2480/729']], ['control: random comb 29', [1, '1/2', [-3, 0, -3, -3, 2]], ['-3', '-3/2', '-15/4', '-39/8', '-7/16']], ['control: random comb 30', [1, '1/3', [1, 2, 1, -3, -1, 1, 2]], ['1', '7/3', '16/9', '-65/27', '-146/81', '97/243', '1555/729']]], [['regression: random comb 5', [2, '-2/3', [-3, -3, -1, -3, -1]], ['-3', '-3', '1', '-1', '-5/3']], ['regression: random comb 6', [4, '-2/3', [1, 0, -3, 3]], ['1', '0', '-3', '3']], ['regression: random comb 3', [2, '1/2', [2, -1, -3]], ['2', '-1', '-2']], ['control: random comb 33', [1, '3/4', [-3, -3, -1, 2, -2, 0, 2, 1, 3]], ['-3', '-21/4', '-79/16', '-109/64', '-839/256', '-2517/1024', '641/4096', '18307/16384', '251529/65536']], ['control: random comb 39', [1, '1/2', [3, 3, -2, 0, 2, -2, -3, 0, -3]], ['3', '9/2', '1/4', '1/8', '33/16', '-31/32', '-223/64', '-223/128', '-991/256']], ['control: delay 1', [1, '-1/2', [1, 0, 0]], ['1', '-1/2', '1/4']], ['control: unit gain rejected', [3, '1', [1]], 'unstable']], [['regression: random comb 8', [4, '-2/3', [1, 3, -2, -1]], ['1', '3', '-2', '-1']], ['regression: random comb 9', [3, '1/2', [-2, 0, -3, 1, -3, 0, 3, 1]], ['-2', '0', '-3', '0', '-3', '-3/2', '3', '-1/2']], ['regression: random comb 5', [2, '-2/3', [-3, -3, -1, -3, -1]], ['-3', '-3', '1', '-1', '-5/3']], ['control: negative unit gain', [3, '-1', [1]], 'unstable'], ['control: bad delay', [0, '1/2', [1]], 'bad-delay'], ['control: random comb 11', [1, '3/4', [0, 1, 2, 0, -2, 1, 0]], ['0', '1', '11/4', '33/16', '-29/64', '169/256', '507/1024']], ['control: random comb 25', [1, '1/3', [0, -2, 2, 3, 0, 2, -2, -3]], ['0', '-2', '4/3', '31/9', '31/27', '193/81', '-293/243', '-2480/729']]], [['regression: random comb 12', [3, '1/2', [2, 3, 0, -2, 3, 1]], ['2', '3', '0', '-1', '9/2', '1']], ['regression: random comb 13', [4, '-2/3', [3, -1, -3, -2, 3]], ['3', '-1', '-3', '-2', '1']], ['regression: random comb 7', [4, '-2/3', [1, 3, 3, -1, -1, 2, 3, -2, 2]], ['1', '3', '3', '-1', '-5/3', '0', '1', '-4/3', '28/9']], ['control: random comb 29', [1, '1/2', [-3, 0, -3, -3, 2]], ['-3', '-3/2', '-15/4', '-39/8', '-7/16']], ['control: random comb 30', [1, '1/3', [1, 2, 1, -3, -1, 1, 2]], ['1', '7/3', '16/9', '-65/27', '-146/81', '97/243', '1555/729']], ['control: random comb 33', [1, '3/4', [-3, -3, -1, 2, -2, 0, 2, 1, 3]], ['-3', '-21/4', '-79/16', '-109/64', '-839/256', '-2517/1024', '641/4096', '18307/16384', '251529/65536']], ['control: random comb 39', [1, '1/2', [3, 3, -2, 0, 2, -2, -3, 0, -3]], ['3', '9/2', '1/4', '1/8', '33/16', '-31/32', '-223/64', '-223/128', '-991/256']]]]\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":"8f561a1402b1a6785acbafb787ea1ead1c981125377c5552c5c69b6ab92046be","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(x):\n    D, g, xs = x[0], Fraction(x[1]), x[2]\n    if D < 1:\n        return 'bad-delay'\n    if abs(g) >= 1:\n        return 'unstable'\n    buf = [Fraction(0)] * D\n    pos = 0\n    out = []\n    for v in xs:\n        delayed = buf[pos]\n        y = v + g * delayed\n        buf[pos] = y\n        pos = (pos + 1) % D\n        out.append(str(y))\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression: impulse delay 2', [2, '1/2', [1, 0, 0, 0, 0, 0]], ['1', '0', '1/2', '0', '1/4', '0']], ['regression: random comb 0', [2, '1/2', [-1, 3, 3, 0, 3, 2, -3, -1, -2]], ['-1', '3', '5/2', '3/2', '17/4', '11/4', '-7/8', '3/8', '-39/16']], ['regression: random comb 1', [4, '1/2', [-3, -2, 2, -3, 2, -1, -3, -2, -3]], ['-3', '-2', '2', '-3', '1/2', '-2', '-2', '-7/2', '-11/4']], ['control: delay 1', [1, '-1/2', [1, 0, 0]], ['1', '-1/2', '1/4']], ['control: unit gain rejected', [3, '1', [1]], 'unstable'], ['control: negative unit gain', [3, '-1', [1]], 'unstable'], ['control: bad delay', [0, '1/2', [1]], 'bad-delay']], [['regression: random comb 2', [4, '-2/3', [2, 2, -1, 3, -1, 2, 1]], ['2', '2', '-1', '3', '-7/3', '2/3', '5/3']], ['regression: random comb 3', [2, '1/2', [2, -1, -3]], ['2', '-1', '-2']], ['regression: random comb 1', [4, '1/2', [-3, -2, 2, -3, 2, -1, -3, -2, -3]], ['-3', '-2', '2', '-3', '1/2', '-2', '-2', '-7/2', '-11/4']], ['control: random comb 11', [1, '3/4', [0, 1, 2, 0, -2, 1, 0]], ['0', '1', '11/4', '33/16', '-29/64', '169/256', '507/1024']], ['control: random comb 25', [1, '1/3', [0, -2, 2, 3, 0, 2, -2, -3]], ['0', '-2', '4/3', '31/9', '31/27', '193/81', '-293/243', '-2480/729']], ['control: random comb 29', [1, '1/2', [-3, 0, -3, -3, 2]], ['-3', '-3/2', '-15/4', '-39/8', '-7/16']], ['control: random comb 30', [1, '1/3', [1, 2, 1, -3, -1, 1, 2]], ['1', '7/3', '16/9', '-65/27', '-146/81', '97/243', '1555/729']]], [['regression: random comb 5', [2, '-2/3', [-3, -3, -1, -3, -1]], ['-3', '-3', '1', '-1', '-5/3']], ['regression: random comb 6', [4, '-2/3', [1, 0, -3, 3]], ['1', '0', '-3', '3']], ['regression: random comb 3', [2, '1/2', [2, -1, -3]], ['2', '-1', '-2']], ['control: random comb 33', [1, '3/4', [-3, -3, -1, 2, -2, 0, 2, 1, 3]], ['-3', '-21/4', '-79/16', '-109/64', '-839/256', '-2517/1024', '641/4096', '18307/16384', '251529/65536']], ['control: random comb 39', [1, '1/2', [3, 3, -2, 0, 2, -2, -3, 0, -3]], ['3', '9/2', '1/4', '1/8', '33/16', '-31/32', '-223/64', '-223/128', '-991/256']], ['control: delay 1', [1, '-1/2', [1, 0, 0]], ['1', '-1/2', '1/4']], ['control: unit gain rejected', [3, '1', [1]], 'unstable']], [['regression: random comb 8', [4, '-2/3', [1, 3, -2, -1]], ['1', '3', '-2', '-1']], ['regression: random comb 9', [3, '1/2', [-2, 0, -3, 1, -3, 0, 3, 1]], ['-2', '0', '-3', '0', '-3', '-3/2', '3', '-1/2']], ['regression: random comb 5', [2, '-2/3', [-3, -3, -1, -3, -1]], ['-3', '-3', '1', '-1', '-5/3']], ['control: negative unit gain', [3, '-1', [1]], 'unstable'], ['control: bad delay', [0, '1/2', [1]], 'bad-delay'], ['control: random comb 11', [1, '3/4', [0, 1, 2, 0, -2, 1, 0]], ['0', '1', '11/4', '33/16', '-29/64', '169/256', '507/1024']], ['control: random comb 25', [1, '1/3', [0, -2, 2, 3, 0, 2, -2, -3]], ['0', '-2', '4/3', '31/9', '31/27', '193/81', '-293/243', '-2480/729']]], [['regression: random comb 12', [3, '1/2', [2, 3, 0, -2, 3, 1]], ['2', '3', '0', '-1', '9/2', '1']], ['regression: random comb 13', [4, '-2/3', [3, -1, -3, -2, 3]], ['3', '-1', '-3', '-2', '1']], ['regression: random comb 7', [4, '-2/3', [1, 3, 3, -1, -1, 2, 3, -2, 2]], ['1', '3', '3', '-1', '-5/3', '0', '1', '-4/3', '28/9']], ['control: random comb 29', [1, '1/2', [-3, 0, -3, -3, 2]], ['-3', '-3/2', '-15/4', '-39/8', '-7/16']], ['control: random comb 30', [1, '1/3', [1, 2, 1, -3, -1, 1, 2]], ['1', '7/3', '16/9', '-65/27', '-146/81', '97/243', '1555/729']], ['control: random comb 33', [1, '3/4', [-3, -3, -1, 2, -2, 0, 2, 1, 3]], ['-3', '-21/4', '-79/16', '-109/64', '-839/256', '-2517/1024', '641/4096', '18307/16384', '251529/65536']], ['control: random comb 39', [1, '1/2', [3, 3, -2, 0, 2, -2, -3, 0, -3]], ['3', '9/2', '1/4', '1/8', '33/16', '-31/32', '-223/64', '-223/128', '-991/256']]]]\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-feedback-comb-ring-buffer-ring-read-position","generated_at":"2026-09-29T14:51:38.869840+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Feedback combs build resonators and reverberators; ring-buffer indexing slips change the delay and the pitch.","repair":"Read buf[pos] (the oldest slot) before overwriting it.","root_cause":"The delayed value is read from buf[pos - 1].","sha256":"5d324ae7534ce78d74df3dec7a47d4e5a6cc5d347d1e24b3ed95e2d37bcbfe42","title":"Feedback comb reads the most recently written slot · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":44.054,"exit_code":1,"observations":[{"actual":["1","1/2","1/4","1/8","1/16","1/32"],"check":"regression: impulse delay 2","expected":["1","0","1/2","0","1/4","0"],"passed":false},{"actual":["-1","5/2","17/4","17/8","65/16","129/32","-63/64","-191/128","-703/256"],"check":"regression: random comb 0","expected":["-1","3","5/2","3/2","17/4","11/4","-7/8","3/8","-39/16"],"passed":false},{"actual":["-3","-2","2","-9/2","1","0","-21/4","-3/2","-3"],"check":"regression: random comb 1","expected":["-3","-2","2","-3","1/2","-2","-2","-7/2","-11/4"],"passed":false},{"actual":["1","-1/2","1/4"],"check":"control: delay 1","expected":["1","-1/2","1/4"],"passed":true},{"actual":"unstable","check":"control: unit gain rejected","expected":"unstable","passed":true},{"actual":"unstable","check":"control: negative unit gain","expected":"unstable","passed":true},{"actual":"bad-delay","check":"control: bad delay","expected":"bad-delay","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: impulse delay 2\", \"actual\": [\"1\", \"1/2\", \"1/4\", \"1/8\", \"1/16\", \"1/32\"], \"expected\": [\"1\", \"0\", \"1/2\", \"0\", \"1/4\", \"0\"], \"passed\": false}, {\"check\": \"regression: random comb 0\", \"actual\": [\"-1\", \"5/2\", \"17/4\", \"17/8\", \"65/16\", \"129/32\", \"-63/64\", \"-191/128\", \"-703/256\"], \"expected\": [\"-1\", \"3\", \"5/2\", \"3/2\", \"17/4\", \"11/4\", \"-7/8\", \"3/8\", \"-39/16\"], \"passed\": false}, {\"check\": \"regression: random comb 1\", \"actual\": [\"-3\", \"-2\", \"2\", \"-9/2\", \"1\", \"0\", \"-21/4\", \"-3/2\", \"-3\"], \"expected\": [\"-3\", \"-2\", \"2\", \"-3\", \"1/2\", \"-2\", \"-2\", \"-7/2\", \"-11/4\"], \"passed\": false}, {\"check\": \"control: delay 1\", \"actual\": [\"1\", \"-1/2\", \"1/4\"], \"expected\": [\"1\", \"-1/2\", \"1/4\"], \"passed\": true}, {\"check\": \"control: unit gain rejected\", 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