{"abstract":"Closeness excludes values exactly at tolerance.","category":"Floating-point arithmetic","checks":11,"contract":"Symmetric binary64 closeness: equal values including like-signed infinities are close; remaining nonfinite pairs are not. For finite a,b require abs(a-b)<=max(abs_tol,rel_tol*max(abs(a),abs(b))). Negative tolerances return invalid.","contract_signature":"a,b,rel_tol,abs_tol","evaluation_group":"s3-float-isclose","failed_approach":"The attempted local correction return difference<=min(abs_tol,relative) still violates the explicit regression fixtures.","family":"s3-floating_point_arithmetic-isclose-boundary-strict","id":"FA-17081","implementations":{"attempt":{"sha256":"acbae5b7fd30749737ce77bc05e71dd2d5e2b01946941f580573ec931bf829c9","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport struct\nN = 1\nobservations = []\ndef solve(a,b,rel_tol,abs_tol):\n    if rel_tol<0 or abs_tol<0: return 'invalid'\n    if a==b: return True\n    if not math.isfinite(a) or not math.isfinite(b): return False\n    difference=abs(a-b)\n    relative=rel_tol*max(abs(a),abs(b))\n    return difference<=min(abs_tol,relative)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('equal infinity', solve(math.inf,math.inf,1e-9,0.0), True)\ncheck('opposite infinity', solve(math.inf,-math.inf,1e-9,0.0), False)\ncheck('nan', solve(math.nan,math.nan,1.0,1.0), False)\ncheck('absolute zero', solve(0.0,N*1e-9,0.0,N*1e-9), True)\ncheck('relative boundary', solve(float(N),float(N*2),0.5,0.0), True)\ncheck('reverse relative', solve(float(N*2),float(N),0.5,0.0), True)\ncheck('negative values', solve(-float(N),-float(N*2),0.5,0.0), True)\ncheck('disjoint tolerances', solve(0.0,1.5,0.5,1.0), False)\ncheck('ordinary apart', solve(float(N),float(N+1),1e-6,0.0), False)\ncheck('bad relative', solve(1.0,1.0,-1.0,0.0), \"invalid\")\ncheck('bad absolute', solve(1.0,1.0,0.0,-1.0), \"invalid\")\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":"64b2babbcacf37d6290f720e22e028ac81195fed9d336969af69faaf769fd17b","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport struct\nN = 1\nobservations = []\ndef solve(a,b,rel_tol,abs_tol):\n    if rel_tol<0 or abs_tol<0: return 'invalid'\n    if a==b: return True\n    if not math.isfinite(a) or not math.isfinite(b): return False\n    difference=abs(a-b)\n    relative=rel_tol*max(abs(a),abs(b))\n    return difference<max(abs_tol,relative)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('equal infinity', solve(math.inf,math.inf,1e-9,0.0), True)\ncheck('opposite infinity', solve(math.inf,-math.inf,1e-9,0.0), False)\ncheck('nan', solve(math.nan,math.nan,1.0,1.0), False)\ncheck('absolute zero', solve(0.0,N*1e-9,0.0,N*1e-9), True)\ncheck('relative boundary', solve(float(N),float(N*2),0.5,0.0), True)\ncheck('reverse relative', solve(float(N*2),float(N),0.5,0.0), True)\ncheck('negative values', solve(-float(N),-float(N*2),0.5,0.0), True)\ncheck('disjoint tolerances', solve(0.0,1.5,0.5,1.0), False)\ncheck('ordinary apart', solve(float(N),float(N+1),1e-6,0.0), False)\ncheck('bad relative', solve(1.0,1.0,-1.0,0.0), \"invalid\")\ncheck('bad absolute', solve(1.0,1.0,0.0,-1.0), \"invalid\")\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-isclose-boundary-strict","generated_at":"2026-09-29T14:39:42.977273+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":"Closeness excludes values exactly at tolerance. The faulty expression is return difference<max(abs_tol,relative).","sha256":"668c1f2b6a42a6e5fea0d7acd5fbef178dc76a1c3f52a47aa84c11a6b2fccb4f","title":"Closeness excludes values exactly at tolerance · 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":44.964,"exit_code":1,"observations":[{"actual":true,"check":"equal infinity","expected":true,"passed":true},{"actual":false,"check":"opposite infinity","expected":false,"passed":true},{"actual":false,"check":"nan","expected":false,"passed":true},{"actual":false,"check":"absolute zero","expected":true,"passed":false},{"actual":false,"check":"relative boundary","expected":true,"passed":false},{"actual":false,"check":"reverse relative","expected":true,"passed":false},{"actual":false,"check":"negative values","expected":true,"passed":false},{"actual":false,"check":"disjoint tolerances","expected":false,"passed":true},{"actual":false,"check":"ordinary apart","expected":false,"passed":true},{"actual":"invalid","check":"bad relative","expected":"invalid","passed":true},{"actual":"invalid","check":"bad absolute","expected":"invalid","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"equal infinity\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"opposite infinity\", \"actual\": false, \"expected\": false, \"passed\": true}, {\"check\": \"nan\", \"actual\": false, \"expected\": false, \"passed\": true}, {\"check\": \"absolute zero\", \"actual\": false, \"expected\": true, \"passed\": false}, {\"check\": \"relative boundary\", \"actual\": false, \"expected\": true, \"passed\": false}, {\"check\": \"reverse relative\", \"actual\": false, \"expected\": true, \"passed\": false}, {\"check\": \"negative values\", \"actual\": false, \"expected\": true, \"passed\": false}, {\"check\": \"disjoint tolerances\", \"actual\": false, \"expected\": false, \"passed\": true}, {\"check\": \"ordinary apart\", \"actual\": false, \"expected\": false, \"passed\": true}, {\"check\": \"bad relative\", \"actual\": \"invalid\", \"expected\": \"invalid\", \"passed\": true}, {\"check\": \"bad absolute\", \"actual\": \"invalid\", \"expected\": \"invalid\", \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":44.151,"exit_code":1,"observations":[{"actual":true,"check":"equal infinity","expected":true,"passed":true},{"actual":false,"check":"opposite infinity","expected":false,"passed":true},{"actual":false,"check":"nan","expected":false,"passed":true},{"actual":false,"check":"absolute zero","expected":true,"passed":false},{"actual":false,"check":"relative boundary","expected":true,"passed":false},{"actual":false,"check":"reverse relative","expected":true,"passed":false},{"actual":false,"check":"negative values","expected":true,"passed":false},{"actual":false,"check":"disjoint tolerances","expected":false,"passed":true},{"actual":false,"check":"ordinary apart","expected":false,"passed":true},{"actual":"invalid","check":"bad relative","expected":"invalid","passed":true},{"actual":"invalid","check":"bad absolute","expected":"invalid","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"equal infinity\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"opposite infinity\", \"actual\": false, \"expected\": false, \"passed\": true}, {\"check\": \"nan\", \"actual\": false, \"expected\": false, \"passed\": true}, {\"check\": \"absolute zero\", \"actual\": false, \"expected\": true, \"passed\": false}, {\"check\": \"relative boundary\", \"actual\": false, \"expected\": true, \"passed\": false}, {\"check\": \"reverse relative\", \"actual\": false, \"expected\": true, \"passed\": false}, {\"check\": \"negative values\", \"actual\": false, \"expected\": true, \"passed\": false}, {\"check\": \"disjoint tolerances\", \"actual\": false, \"expected\": false, \"passed\": true}, {\"check\": \"ordinary apart\", \"actual\": false, \"expected\": false, \"passed\": true}, {\"check\": \"bad relative\", \"actual\": \"invalid\", \"expected\": \"invalid\", \"passed\": true}, {\"check\": \"bad absolute\", \"actual\": \"invalid\", \"expected\": \"invalid\", \"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."}}