{"abstract":"Duty modulation discards fractional pulse credit.","category":"Discrete control systems","checks":6,"contract":"Given duty in [0,scale], positive scale and tick count, start credit zero; add duty each tick and emit 1 iff credit>=scale then subtract scale. Return the pulse list.","evaluation_group":"model-1507ba60f70a4d0c","failed_approach":"Resetting credit to zero on a pulse discards overshoot.","family":"z-control_systems-pulse-density-remainder","id":"FA-11966","implementations":{"attempt":{"sha256":"d3f981b184cd31b43a1f5e9f37583b4f0cc0c3ef6b85d39932b2f98a9ebac9f2","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(duty, scale, ticks):\n    credit=0\n    out=[]\n    for _ in range(ticks):\n        credit += duty\n        pulse=int(credit>=scale)\n        if pulse: credit=0\n        out.append(pulse)\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('two thirds', solve(2*N, 3*N, 6), [0,1,1,0,1,1])\ncheck('half duty', solve(N, 2*N, 6), [0,1,0,1,0,1])\ncheck('off', solve(0, N, 4), [0,0,0,0])\ncheck('full', solve(N, N, 4), [1,1,1,1])\ncheck('no ticks', solve(N, 2*N, 0), [])\ncheck('first credit', solve(N, 3*N, 2), [0,0])\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":"99d0edbd6821807bd4688c1c9125a59bd4c57cda0d261d9ef443948e630da366","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(duty, scale, ticks):\n    return [int(duty >= scale)]*ticks\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('two thirds', solve(2*N, 3*N, 6), [0,1,1,0,1,1])\ncheck('half duty', solve(N, 2*N, 6), [0,1,0,1,0,1])\ncheck('off', solve(0, N, 4), [0,0,0,0])\ncheck('full', solve(N, N, 4), [1,1,1,1])\ncheck('no ticks', solve(N, 2*N, 0), [])\ncheck('first credit', solve(N, 3*N, 2), [0,0])\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":"1b3bf18a963be06f25af9ad6d223adc56c7a9a41f1ac073f88bae9be5d0b0225","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(duty, scale, ticks):\n    credit=0\n    out=[]\n    for _ in range(ticks):\n        credit += duty\n        pulse=int(credit>=scale)\n        credit -= pulse*scale\n        out.append(pulse)\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('two thirds', solve(2*N, 3*N, 6), [0,1,1,0,1,1])\ncheck('half duty', solve(N, 2*N, 6), [0,1,0,1,0,1])\ncheck('off', solve(0, N, 4), [0,0,0,0])\ncheck('full', solve(N, N, 4), [1,1,1,1])\ncheck('no ticks', solve(N, 2*N, 0), [])\ncheck('first credit', solve(N, 3*N, 2), [0,0])\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":"Integer-valued controlled examples only; no physical plant, stability guarantee, timing jitter, or hardware behavior is modeled. 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":"z-control_systems-pulse-density-remainder","generated_at":"2026-09-29T14:38:52.616409+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"An offline discrete controller model isolates this state or arithmetic fault; it makes no physical plant or safety claim.","repair":"Carry integer pulse credit across ticks and subtract a full scale for each emitted pulse.","root_cause":"A fractional command is rounded independently each tick.","sha256":"67f9490a1a558d08320ad77e84e2c4d6c2f9837e5afd35272dee3d5c7f52a9c3","title":"Duty modulation discards fractional pulse credit · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":43.63,"exit_code":1,"observations":[{"actual":[0,1,0,1,0,1],"check":"two thirds","expected":[0,1,1,0,1,1],"passed":false},{"actual":[0,1,0,1,0,1],"check":"half duty","expected":[0,1,0,1,0,1],"passed":true},{"actual":[0,0,0,0],"check":"off","expected":[0,0,0,0],"passed":true},{"actual":[1,1,1,1],"check":"full","expected":[1,1,1,1],"passed":true},{"actual":[],"check":"no ticks","expected":[],"passed":true},{"actual":[0,0],"check":"first credit","expected":[0,0],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"two thirds\", \"actual\": [0, 1, 0, 1, 0, 1], \"expected\": [0, 1, 1, 0, 1, 1], \"passed\": false}, {\"check\": \"half duty\", \"actual\": [0, 1, 0, 1, 0, 1], \"expected\": [0, 1, 0, 1, 0, 1], \"passed\": true}, {\"check\": \"off\", \"actual\": [0, 0, 0, 0], \"expected\": [0, 0, 0, 0], \"passed\": true}, {\"check\": \"full\", \"actual\": [1, 1, 1, 1], \"expected\": [1, 1, 1, 1], \"passed\": true}, {\"check\": \"no ticks\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"first credit\", \"actual\": [0, 0], \"expected\": [0, 0], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":39.96,"exit_code":1,"observations":[{"actual":[0,0,0,0,0,0],"check":"two thirds","expected":[0,1,1,0,1,1],"passed":false},{"actual":[0,0,0,0,0,0],"check":"half duty","expected":[0,1,0,1,0,1],"passed":false},{"actual":[0,0,0,0],"check":"off","expected":[0,0,0,0],"passed":true},{"actual":[1,1,1,1],"check":"full","expected":[1,1,1,1],"passed":true},{"actual":[],"check":"no ticks","expected":[],"passed":true},{"actual":[0,0],"check":"first credit","expected":[0,0],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"two thirds\", \"actual\": [0, 0, 0, 0, 0, 0], \"expected\": [0, 1, 1, 0, 1, 1], \"passed\": false}, {\"check\": \"half duty\", \"actual\": [0, 0, 0, 0, 0, 0], \"expected\": [0, 1, 0, 1, 0, 1], \"passed\": false}, {\"check\": \"off\", \"actual\": [0, 0, 0, 0], \"expected\": [0, 0, 0, 0], \"passed\": true}, {\"check\": \"full\", \"actual\": [1, 1, 1, 1], \"expected\": [1, 1, 1, 1], \"passed\": true}, {\"check\": \"no ticks\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"first credit\", \"actual\": [0, 0], \"expected\": [0, 0], \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":41.367,"exit_code":0,"observations":[{"actual":[0,1,1,0,1,1],"check":"two thirds","expected":[0,1,1,0,1,1],"passed":true},{"actual":[0,1,0,1,0,1],"check":"half duty","expected":[0,1,0,1,0,1],"passed":true},{"actual":[0,0,0,0],"check":"off","expected":[0,0,0,0],"passed":true},{"actual":[1,1,1,1],"check":"full","expected":[1,1,1,1],"passed":true},{"actual":[],"check":"no ticks","expected":[],"passed":true},{"actual":[0,0],"check":"first credit","expected":[0,0],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"two thirds\", \"actual\": [0, 1, 1, 0, 1, 1], \"expected\": [0, 1, 1, 0, 1, 1], \"passed\": true}, {\"check\": \"half duty\", \"actual\": [0, 1, 0, 1, 0, 1], \"expected\": [0, 1, 0, 1, 0, 1], \"passed\": true}, {\"check\": \"off\", \"actual\": [0, 0, 0, 0], \"expected\": [0, 0, 0, 0], \"passed\": true}, {\"check\": \"full\", \"actual\": [1, 1, 1, 1], \"expected\": [1, 1, 1, 1], \"passed\": true}, {\"check\": \"no ticks\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"first credit\", \"actual\": [0, 0], \"expected\": [0, 0], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}