{"abstract":"A constant input produces a decaying spike equal to the offset at start-up.","category":"Digital signal filters","checks":7,"contract":"Input [R, samples]: y[n] = x[n] - x[n-1] + R y[n-1] with 0 <= R < 1 (\"bad-pole\"), warm-started so x[-1] = x[0] and y[-1] = 0 (no start-up step). Return exact fraction strings.","contract_signature":"x","evaluation_group":"w2-digital_signal_filters-dc-blocker-warm-start","failed_approach":"The attempted repair warm-starts both x[-1] and y[-1] to x[0], injecting the offset through the feedback path.","family":"w2-digital_signal_filters-dc-blocker-warm-start-warm-start-input-history","id":"FA-91756","implementations":{"attempt":{"sha256":"6c0836148a2da4c59c904ece7c50194dd007bfcdaee1f6263a12bba830154bc6","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(x):\n    R, xs = Fraction(x[0]), x[1]\n    if not 0 <= R < 1:\n        return 'bad-pole'\n    if not xs:\n        return []\n    xp = xs[0]\n    yp = Fraction(xs[0])\n    out = []\n    for v in xs:\n        y = v - xp + R * yp\n        xp, yp = v, y\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: constant input warm start', ['9/10', [5, 5, 5]], ['0', '0', '0']], ['regression: pole zero', ['0', [1, 3, 2]], ['0', '2', '-1']], ['regression: random dc blocker 0', ['3/4', [-2, -1, 1, -3]], ['0', '1', '11/4', '-31/16']], ['control: step', ['1/2', [0, 4, 4, 4]], ['0', '4', '2', '1']], ['control: bad pole', ['1', [1]], 'bad-pole'], ['control: empty', ['1/2', []], []], ['control: random dc blocker 7', ['1/2', [0, 6, -2, -1, 2, 0]], ['0', '6', '-5', '-3/2', '9/4', '-7/8']]], [['regression: random dc blocker 1', ['3/4', [-2, 2]], ['0', '4']], ['regression: random dc blocker 2', ['1/4', [-3, 0, 1, -3]], ['0', '3', '7/4', '-57/16']], ['regression: random dc blocker 3', ['9/10', [1, 4, -3, -3, 5, -2]], ['0', '3', '-43/10', '-387/100', '4517/1000', '-29347/10000']], ['control: random dc blocker 18', ['3/4', [0, 5, 4]], ['0', '5', '11/4']], ['control: random dc blocker 25', ['3/4', [0, 4, 6, -2, 1, -3]], ['0', '4', '5', '-17/4', '-3/16', '-265/64']], ['control: random dc blocker 32', ['9/10', [0, 0]], ['0', '0']], ['control: step', ['1/2', [0, 4, 4, 4]], ['0', '4', '2', '1']]], [['regression: random dc blocker 4', ['3/4', [1, 2, 6, 0, -2]], ['0', '1', '19/4', '-39/16', '-245/64']], ['regression: random dc blocker 5', ['9/10', [2, 5]], ['0', '3']], ['regression: random dc blocker 3', ['9/10', [1, 4, -3, -3, 5, -2]], ['0', '3', '-43/10', '-387/100', '4517/1000', '-29347/10000']], ['control: bad pole', ['1', [1]], 'bad-pole'], ['control: empty', ['1/2', []], []], ['control: random dc blocker 7', ['1/2', [0, 6, -2, -1, 2, 0]], ['0', '6', '-5', '-3/2', '9/4', '-7/8']], ['control: random dc blocker 18', ['3/4', [0, 5, 4]], ['0', '5', '11/4']]], [['regression: random dc blocker 8', ['9/10', [-3, -3, 2, -2, 2, -2]], ['0', '0', '5', '1/2', '89/20', '1/200']], ['regression: random dc blocker 9', ['9/10', [3, 4, -2, 3]], ['0', '1', '-51/10', '41/100']], ['regression: random dc blocker 5', ['9/10', [2, 5]], ['0', '3']], ['control: random dc blocker 25', ['3/4', [0, 4, 6, -2, 1, -3]], ['0', '4', '5', '-17/4', '-3/16', '-265/64']], ['control: random dc blocker 32', ['9/10', [0, 0]], ['0', '0']], ['control: step', ['1/2', [0, 4, 4, 4]], ['0', '4', '2', '1']], ['control: bad pole', ['1', [1]], 'bad-pole']], [['regression: random dc blocker 11', ['1/2', [-1, 0, 6]], ['0', '1', '13/2']], ['regression: random dc blocker 12', ['3/4', [-3, 0, 6]], ['0', '3', '33/4']], ['regression: random dc blocker 8', ['9/10', [-3, -3, 2, -2, 2, -2]], ['0', '0', '5', '1/2', '89/20', '1/200']], ['control: empty', ['1/2', []], []], ['control: random dc blocker 7', ['1/2', [0, 6, -2, -1, 2, 0]], ['0', '6', '-5', '-3/2', '9/4', '-7/8']], ['control: random dc blocker 18', ['3/4', [0, 5, 4]], ['0', '5', '11/4']], ['control: random dc blocker 25', ['3/4', [0, 4, 6, -2, 1, -3]], ['0', '4', '5', '-17/4', '-3/16', '-265/64']]]]\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":"3183eeb04210b60ebaff82a881cdcfeebc5d5bb82d0aebe0ee9ac3e307e8931b","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(x):\n    R, xs = Fraction(x[0]), x[1]\n    if not 0 <= R < 1:\n        return 'bad-pole'\n    if not xs:\n        return []\n    xp = 0\n    yp = Fraction(0)\n    out = []\n    for v in xs:\n        y = v - xp + R * yp\n        xp, yp = v, y\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: constant input warm start', ['9/10', [5, 5, 5]], ['0', '0', '0']], ['regression: pole zero', ['0', [1, 3, 2]], ['0', '2', '-1']], ['regression: random dc blocker 0', ['3/4', [-2, -1, 1, -3]], ['0', '1', '11/4', '-31/16']], ['control: step', ['1/2', [0, 4, 4, 4]], ['0', '4', '2', '1']], ['control: bad pole', ['1', [1]], 'bad-pole'], ['control: empty', ['1/2', []], []], ['control: random dc blocker 7', ['1/2', [0, 6, -2, -1, 2, 0]], ['0', '6', '-5', '-3/2', '9/4', '-7/8']]], [['regression: random dc blocker 1', ['3/4', [-2, 2]], ['0', '4']], ['regression: random dc blocker 2', ['1/4', [-3, 0, 1, -3]], ['0', '3', '7/4', '-57/16']], ['regression: random dc blocker 3', ['9/10', [1, 4, -3, -3, 5, -2]], ['0', '3', '-43/10', '-387/100', '4517/1000', '-29347/10000']], ['control: random dc blocker 18', ['3/4', [0, 5, 4]], ['0', '5', '11/4']], ['control: random dc blocker 25', ['3/4', [0, 4, 6, -2, 1, -3]], ['0', '4', '5', '-17/4', '-3/16', '-265/64']], ['control: random dc blocker 32', ['9/10', [0, 0]], ['0', '0']], ['control: step', ['1/2', [0, 4, 4, 4]], ['0', '4', '2', '1']]], [['regression: random dc blocker 4', ['3/4', [1, 2, 6, 0, -2]], ['0', '1', '19/4', '-39/16', '-245/64']], ['regression: random dc blocker 5', ['9/10', [2, 5]], ['0', '3']], ['regression: random dc blocker 3', ['9/10', [1, 4, -3, -3, 5, -2]], ['0', '3', '-43/10', '-387/100', '4517/1000', '-29347/10000']], ['control: bad pole', ['1', [1]], 'bad-pole'], ['control: empty', ['1/2', []], []], ['control: random dc blocker 7', ['1/2', [0, 6, -2, -1, 2, 0]], ['0', '6', '-5', '-3/2', '9/4', '-7/8']], ['control: random dc blocker 18', ['3/4', [0, 5, 4]], ['0', '5', '11/4']]], [['regression: random dc blocker 8', ['9/10', [-3, -3, 2, -2, 2, -2]], ['0', '0', '5', '1/2', '89/20', '1/200']], ['regression: random dc blocker 9', ['9/10', [3, 4, -2, 3]], ['0', '1', '-51/10', '41/100']], ['regression: random dc blocker 5', ['9/10', [2, 5]], ['0', '3']], ['control: random dc blocker 25', ['3/4', [0, 4, 6, -2, 1, -3]], ['0', '4', '5', '-17/4', '-3/16', '-265/64']], ['control: random dc blocker 32', ['9/10', [0, 0]], ['0', '0']], ['control: step', ['1/2', [0, 4, 4, 4]], ['0', '4', '2', '1']], ['control: bad pole', ['1', [1]], 'bad-pole']], [['regression: random dc blocker 11', ['1/2', [-1, 0, 6]], ['0', '1', '13/2']], ['regression: random dc blocker 12', ['3/4', [-3, 0, 6]], ['0', '3', '33/4']], ['regression: random dc blocker 8', ['9/10', [-3, -3, 2, -2, 2, -2]], ['0', '0', '5', '1/2', '89/20', '1/200']], ['control: empty', ['1/2', []], []], ['control: random dc blocker 7', ['1/2', [0, 6, -2, -1, 2, 0]], ['0', '6', '-5', '-3/2', '9/4', '-7/8']], ['control: random dc blocker 18', ['3/4', [0, 5, 4]], ['0', '5', '11/4']], ['control: random dc blocker 25', ['3/4', [0, 4, 6, -2, 1, -3]], ['0', '4', '5', '-17/4', '-3/16', '-265/64']]]]\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-dc-blocker-warm-start-warm-start-input-history","generated_at":"2026-09-29T14:51:38.910503+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"DC blockers remove offsets before further processing; a cold start injects a large transient.","root_cause":"x[-1] is initialized to 0 instead of x[0].","sha256":"d40c97af13cb3d54641736e0ebac0ba684ac82c12160d1a9f7e22a9013a67a2f","title":"DC blocker starts from a zero previous input · 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":41.845,"exit_code":1,"observations":[{"actual":["9/2","81/20","729/200"],"check":"regression: constant input warm start","expected":["0","0","0"],"passed":false},{"actual":["0","2","-1"],"check":"regression: pole zero","expected":["0","2","-1"],"passed":true},{"actual":["-3/2","-1/8","61/32","-329/128"],"check":"regression: random dc blocker 0","expected":["0","1","11/4","-31/16"],"passed":false},{"actual":["0","4","2","1"],"check":"control: step","expected":["0","4","2","1"],"passed":true},{"actual":"bad-pole","check":"control: bad pole","expected":"bad-pole","passed":true},{"actual":[],"check":"control: empty","expected":[],"passed":true},{"actual":["0","6","-5","-3/2","9/4","-7/8"],"check":"control: random dc blocker 7","expected":["0","6","-5","-3/2","9/4","-7/8"],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: constant input warm start\", \"actual\": [\"9/2\", \"81/20\", \"729/200\"], \"expected\": [\"0\", \"0\", \"0\"], \"passed\": false}, {\"check\": \"regression: pole zero\", \"actual\": [\"0\", \"2\", \"-1\"], \"expected\": [\"0\", \"2\", \"-1\"], \"passed\": true}, {\"check\": \"regression: random dc blocker 0\", \"actual\": [\"-3/2\", \"-1/8\", \"61/32\", \"-329/128\"], \"expected\": [\"0\", \"1\", \"11/4\", \"-31/16\"], \"passed\": false}, {\"check\": \"control: step\", \"actual\": [\"0\", \"4\", \"2\", \"1\"], \"expected\": [\"0\", \"4\", \"2\", \"1\"], \"passed\": true}, {\"check\": \"control: bad pole\", \"actual\": \"bad-pole\", \"expected\": \"bad-pole\", \"passed\": true}, {\"check\": \"control: empty\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"control: random dc blocker 7\", \"actual\": [\"0\", \"6\", \"-5\", \"-3/2\", \"9/4\", \"-7/8\"], \"expected\": [\"0\", \"6\", \"-5\", \"-3/2\", \"9/4\", \"-7/8\"], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":43.251,"exit_code":1,"observations":[{"actual":["5","9/2","81/20"],"check":"regression: constant input warm start","expected":["0","0","0"],"passed":false},{"actual":["1","2","-1"],"check":"regression: pole zero","expected":["0","2","-1"],"passed":false},{"actual":["-2","-1/2","13/8","-89/32"],"check":"regression: random dc blocker 0","expected":["0","1","11/4","-31/16"],"passed":false},{"actual":["0","4","2","1"],"check":"control: step","expected":["0","4","2","1"],"passed":true},{"actual":"bad-pole","check":"control: bad pole","expected":"bad-pole","passed":true},{"actual":[],"check":"control: empty","expected":[],"passed":true},{"actual":["0","6","-5","-3/2","9/4","-7/8"],"check":"control: random dc blocker 7","expected":["0","6","-5","-3/2","9/4","-7/8"],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: constant input warm start\", \"actual\": [\"5\", \"9/2\", \"81/20\"], \"expected\": [\"0\", \"0\", \"0\"], \"passed\": false}, {\"check\": \"regression: pole zero\", \"actual\": [\"1\", \"2\", \"-1\"], \"expected\": [\"0\", \"2\", \"-1\"], \"passed\": false}, {\"check\": \"regression: random dc blocker 0\", \"actual\": [\"-2\", \"-1/2\", \"13/8\", \"-89/32\"], \"expected\": [\"0\", \"1\", \"11/4\", \"-31/16\"], \"passed\": false}, {\"check\": \"control: step\", \"actual\": [\"0\", \"4\", \"2\", \"1\"], \"expected\": [\"0\", \"4\", \"2\", \"1\"], \"passed\": true}, {\"check\": \"control: bad pole\", \"actual\": \"bad-pole\", \"expected\": \"bad-pole\", \"passed\": true}, {\"check\": \"control: empty\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"control: random dc blocker 7\", \"actual\": [\"0\", \"6\", \"-5\", \"-3/2\", \"9/4\", \"-7/8\"], \"expected\": [\"0\", \"6\", \"-5\", \"-3/2\", \"9/4\", \"-7/8\"], \"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."}}