{"abstract":"Sinc folds the denominator along with the periodic numerator.","category":"Floating-point arithmetic","checks":7,"contract":"Evaluate sin(x)/x on finite x with continuous value one at zero. Tiny values use the fourth-degree even series. Finite results are rendered to eleven significant decimal digits; modeled domain violations and arithmetic errors are explicit strings.","contract_signature":"x","evaluation_group":"s3-float-sinc","failed_approach":"The attempted local correction result=math.sin(x)/math.fmod(x,math.pi) still violates the explicit regression fixtures.","family":"s3-floating_point_arithmetic-sinc-phase-folding","id":"FA-16351","implementations":{"attempt":{"sha256":"98da7c086d02273d3a6b0090b116a032e786531a9caedaa752086b38ba324639","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport struct\ndef render(x):\n    if math.isnan(x): return 'nan'\n    if math.isinf(x): return '-infinity' if x<0 else '+infinity'\n    return format(x,'.11g')\n\nN = 1\nobservations = []\ndef solve(x):\n    try:\n        if x==0: return '1'\n        if abs(x)<1e-3:\n            t=x*x\n            result=1-t/6+t*t/120\n        else:\n            result=math.sin(x)/math.fmod(x,math.pi)\n        return render(result)\n    except (ValueError, OverflowError, ZeroDivisionError, TypeError):\n        return \"arithmetic-error\"\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('zero', solve(0.0), \"1\")\ncheck('negative zero', solve(-0.0), \"1\")\ncheck('small', solve(N*1e-4), render(math.sin(N*1e-4)/(N*1e-4)))\ncheck('negative small', solve(-N*1e-4), render(math.sin(-N*1e-4)/(-N*1e-4)))\ncheck('normal', solve(float(N)), render(math.sin(N)/N))\ncheck('negative normal', solve(-float(N)), render(math.sin(-N)/(-N)))\ncheck('phase crossing', solve(math.pi+0.125*N), render(math.sin(math.pi+0.125*N)/(math.pi+0.125*N)))\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":"cf6286e15e5dc341e4a3229023c84a1d7cb240c370620462f81befb4fca34a32","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport struct\ndef render(x):\n    if math.isnan(x): return 'nan'\n    if math.isinf(x): return '-infinity' if x<0 else '+infinity'\n    return format(x,'.11g')\n\nN = 1\nobservations = []\ndef solve(x):\n    try:\n        if x==0: return '1'\n        if abs(x)<1e-3:\n            t=x*x\n            result=1-t/6+t*t/120\n        else:\n            result=math.sin(x)/math.remainder(x,2*math.pi)\n        return render(result)\n    except (ValueError, OverflowError, ZeroDivisionError, TypeError):\n        return \"arithmetic-error\"\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('zero', solve(0.0), \"1\")\ncheck('negative zero', solve(-0.0), \"1\")\ncheck('small', solve(N*1e-4), render(math.sin(N*1e-4)/(N*1e-4)))\ncheck('negative small', solve(-N*1e-4), render(math.sin(-N*1e-4)/(-N*1e-4)))\ncheck('normal', solve(float(N)), render(math.sin(N)/N))\ncheck('negative normal', solve(-float(N)), render(math.sin(-N)/(-N)))\ncheck('phase crossing', solve(math.pi+0.125*N), render(math.sin(math.pi+0.125*N)/(math.pi+0.125*N)))\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":"Controlled binary64 or explicitly stipulated miniature format; no hardware exception flags or platform floating environment are 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":"s3-floating_point_arithmetic-sinc-phase-folding","generated_at":"2026-09-29T14:39:35.400742+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"An offline floating representation model isolates a reproducible arithmetic fault.","root_cause":"Sinc folds the denominator along with the periodic numerator. The faulty expression is result=math.sin(x)/math.remainder(x,2*math.pi).","sha256":"8d503e8621905a67b08346de9c6cf96a5a691c2455bf2aaec98e9a17bc6efe9c","title":"Sinc folds the denominator along with the periodic numerator · 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":44.153,"exit_code":1,"observations":[{"actual":"1","check":"zero","expected":"1","passed":true},{"actual":"1","check":"negative zero","expected":"1","passed":true},{"actual":"0.99999999833","check":"small","expected":"0.99999999833","passed":true},{"actual":"0.99999999833","check":"negative small","expected":"0.99999999833","passed":true},{"actual":"0.84147098481","check":"normal","expected":"0.84147098481","passed":true},{"actual":"0.84147098481","check":"negative normal","expected":"0.84147098481","passed":true},{"actual":"-0.99739786708","check":"phase crossing","expected":"-0.038166599453","passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"zero\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}, {\"check\": \"negative zero\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}, {\"check\": \"small\", \"actual\": \"0.99999999833\", \"expected\": \"0.99999999833\", \"passed\": true}, {\"check\": \"negative small\", \"actual\": \"0.99999999833\", \"expected\": \"0.99999999833\", \"passed\": true}, {\"check\": \"normal\", \"actual\": \"0.84147098481\", \"expected\": \"0.84147098481\", \"passed\": true}, {\"check\": \"negative normal\", \"actual\": \"0.84147098481\", \"expected\": \"0.84147098481\", \"passed\": true}, {\"check\": \"phase crossing\", \"actual\": \"-0.99739786708\", \"expected\": \"-0.038166599453\", \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":40.244,"exit_code":1,"observations":[{"actual":"1","check":"zero","expected":"1","passed":true},{"actual":"1","check":"negative zero","expected":"1","passed":true},{"actual":"0.99999999833","check":"small","expected":"0.99999999833","passed":true},{"actual":"0.99999999833","check":"negative small","expected":"0.99999999833","passed":true},{"actual":"0.84147098481","check":"normal","expected":"0.84147098481","passed":true},{"actual":"0.84147098481","check":"negative normal","expected":"0.84147098481","passed":true},{"actual":"0.041329654913","check":"phase crossing","expected":"-0.038166599453","passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"zero\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}, {\"check\": \"negative zero\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}, {\"check\": \"small\", \"actual\": \"0.99999999833\", \"expected\": \"0.99999999833\", \"passed\": true}, {\"check\": \"negative small\", \"actual\": \"0.99999999833\", \"expected\": \"0.99999999833\", \"passed\": true}, {\"check\": \"normal\", \"actual\": \"0.84147098481\", \"expected\": \"0.84147098481\", \"passed\": true}, {\"check\": \"negative normal\", \"actual\": \"0.84147098481\", \"expected\": \"0.84147098481\", \"passed\": true}, {\"check\": \"phase crossing\", \"actual\": \"0.041329654913\", \"expected\": \"-0.038166599453\", \"passed\": false}], \"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."}}