{"abstract":"The limiter admits too few or too many operations when fractional refills occur between requests.","category":"Runtime and resources","checks":7,"contract":"Capacity and initial balance are nonnegative integers with initial <= capacity; rate is nonnegative. Requests are [nondecreasing rational timestamp string,nonnegative integer cost]. Refill from time zero, cap at capacity, and accept iff sufficient credit exists. Return [acceptance flags,exact rational balance].","evaluation_group":"model-e062fcd76d0c39c4","failed_approach":"Rounding each refill upward prevents starvation by issuing tokens early, violating the rate contract.","family":"runtime-fractional-token-refill","id":"FA-236","implementations":{"attempt":{"sha256":"63ae5cb881652161ccf5284640cb5c9839a4d316e198552eedd361f088564dd0","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nfrom math import ceil\nN = 1\nobservations = []\ndef solve(capacity, initial, rate, requests):\n    tokens, last, accepted = Fraction(initial), Fraction(0), []\n    for timestamp, cost in requests:\n        now = Fraction(timestamp)\n        refill = ceil(Fraction(rate)*(now-last))\n        tokens = min(Fraction(capacity), tokens + refill)\n        last = now\n        allowed = tokens >= cost\n        if allowed:\n            tokens -= cost\n        accepted.append(allowed)\n    return [accepted, str(tokens)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nrate = 2*N+1\ncheck('fraction survives consumption', solve(rate, 0, rate, [['0.5', N], ['1', N+1]]), [[True, True], '0'])\ncheck('not yet enough for next token', solve(rate, 0, rate, [['0.5', N+1]]), [[False], str(Fraction(rate, 2))])\ncheck('capacity clips idle accrual', solve(N, 0, rate, [['10', 0]]), [[True], str(N)])\ncheck('same instant cannot refill twice', solve(N, N, rate, [['0', N], ['0', 1]]), [[True, False], '0'])\ncheck('oversized cost is rejected', solve(N, N, rate, [['1', N+1]]), [[False], str(N)])\ncheck('zero refill preserves balance', solve(N, N, 0, [['100', N]]), [[True], '0'])\ncheck('no requests preserve initial', solve(N, N, rate, []), [[], str(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":"4b0f5b0499597201ecc849b0820cbae7a313f597fbd7f2299a47682e554a883a","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nfrom math import ceil\nN = 1\nobservations = []\ndef solve(capacity, initial, rate, requests):\n    tokens, last, accepted = Fraction(initial), Fraction(0), []\n    for timestamp, cost in requests:\n        now = Fraction(timestamp)\n        refill = int(Fraction(rate)*(now-last))\n        tokens = min(Fraction(capacity), tokens + refill)\n        last = now\n        allowed = tokens >= cost\n        if allowed:\n            tokens -= cost\n        accepted.append(allowed)\n    return [accepted, str(tokens)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nrate = 2*N+1\ncheck('fraction survives consumption', solve(rate, 0, rate, [['0.5', N], ['1', N+1]]), [[True, True], '0'])\ncheck('not yet enough for next token', solve(rate, 0, rate, [['0.5', N+1]]), [[False], str(Fraction(rate, 2))])\ncheck('capacity clips idle accrual', solve(N, 0, rate, [['10', 0]]), [[True], str(N)])\ncheck('same instant cannot refill twice', solve(N, N, rate, [['0', N], ['0', 1]]), [[True, False], '0'])\ncheck('oversized cost is rejected', solve(N, N, rate, [['1', N+1]]), [[False], str(N)])\ncheck('zero refill preserves balance', solve(N, N, 0, [['100', N]]), [[True], '0'])\ncheck('no requests preserve initial', solve(N, N, rate, []), [[], str(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"},"fixed":{"sha256":"a45ea88a91ae13f57c8d351f7a6fcff244d78af54e3339817a04c24b6c97db23","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nfrom math import ceil\nN = 1\nobservations = []\ndef solve(capacity, initial, rate, requests):\n    tokens, last, accepted = Fraction(initial), Fraction(0), []\n    for timestamp, cost in requests:\n        now = Fraction(timestamp)\n        refill = Fraction(rate)*(now-last)\n        tokens = min(Fraction(capacity), tokens + refill)\n        last = now\n        allowed = tokens >= cost\n        if allowed:\n            tokens -= cost\n        accepted.append(allowed)\n    return [accepted, str(tokens)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nrate = 2*N+1\ncheck('fraction survives consumption', solve(rate, 0, rate, [['0.5', N], ['1', N+1]]), [[True, True], '0'])\ncheck('not yet enough for next token', solve(rate, 0, rate, [['0.5', N+1]]), [[False], str(Fraction(rate, 2))])\ncheck('capacity clips idle accrual', solve(N, 0, rate, [['10', 0]]), [[True], str(N)])\ncheck('same instant cannot refill twice', solve(N, N, rate, [['0', N], ['0', 1]]), [[True, False], '0'])\ncheck('oversized cost is rejected', solve(N, N, rate, [['1', N+1]]), [[False], str(N)])\ncheck('zero refill preserves balance', solve(N, N, 0, [['100', N]]), [[True], '0'])\ncheck('no requests preserve initial', solve(N, N, rate, []), [[], str(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":" 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":"runtime-fractional-token-refill","generated_at":"2026-09-29T14:36:51.531902+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Models token accounting under frequent polling without binary-float noise; timestamps are injected, so this experiment makes no claim about scheduler accuracy or concurrent atomic updates.","repair":"Carry exact fractional tokens between checks, cap the balance, and debit only accepted requests.","root_cause":"Rounding each elapsed refill interval loses residual credit or creates tokens before they accrue.","sha256":"442347cdbd67478b857422aa2999e365d390022a3f6d675992365f050eb79ca9","title":"Frequent checks destroy a token bucket's fractional credit · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":34.127,"exit_code":1,"observations":[{"actual":[[true,true],"1"],"check":"fraction survives consumption","expected":[[true,true],"0"],"passed":false},{"actual":[[true],"0"],"check":"not yet enough for next token","expected":[[false],"3/2"],"passed":false},{"actual":[[true],"1"],"check":"capacity clips idle accrual","expected":[[true],"1"],"passed":true},{"actual":[[true,false],"0"],"check":"same instant cannot refill twice","expected":[[true,false],"0"],"passed":true},{"actual":[[false],"1"],"check":"oversized cost is rejected","expected":[[false],"1"],"passed":true},{"actual":[[true],"0"],"check":"zero refill preserves balance","expected":[[true],"0"],"passed":true},{"actual":[[],"1"],"check":"no requests preserve initial","expected":[[],"1"],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fraction survives consumption\", \"actual\": [[true, true], \"1\"], \"expected\": [[true, true], \"0\"], \"passed\": false}, {\"check\": \"not yet enough for next token\", \"actual\": [[true], \"0\"], \"expected\": [[false], \"3/2\"], \"passed\": false}, {\"check\": \"capacity clips idle accrual\", \"actual\": [[true], \"1\"], \"expected\": [[true], \"1\"], \"passed\": true}, {\"check\": \"same instant cannot refill twice\", \"actual\": [[true, false], \"0\"], \"expected\": [[true, false], \"0\"], \"passed\": true}, {\"check\": \"oversized cost is rejected\", \"actual\": [[false], \"1\"], \"expected\": [[false], \"1\"], \"passed\": true}, {\"check\": \"zero refill preserves balance\", \"actual\": [[true], \"0\"], \"expected\": [[true], \"0\"], \"passed\": true}, {\"check\": \"no requests preserve initial\", \"actual\": [[], \"1\"], \"expected\": [[], \"1\"], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":35.325,"exit_code":1,"observations":[{"actual":[[true,false],"1"],"check":"fraction survives consumption","expected":[[true,true],"0"],"passed":false},{"actual":[[false],"1"],"check":"not yet enough for next token","expected":[[false],"3/2"],"passed":false},{"actual":[[true],"1"],"check":"capacity clips idle accrual","expected":[[true],"1"],"passed":true},{"actual":[[true,false],"0"],"check":"same instant cannot refill twice","expected":[[true,false],"0"],"passed":true},{"actual":[[false],"1"],"check":"oversized cost is rejected","expected":[[false],"1"],"passed":true},{"actual":[[true],"0"],"check":"zero refill preserves balance","expected":[[true],"0"],"passed":true},{"actual":[[],"1"],"check":"no requests preserve initial","expected":[[],"1"],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fraction survives consumption\", \"actual\": [[true, false], \"1\"], \"expected\": [[true, true], \"0\"], \"passed\": false}, {\"check\": \"not yet enough for next token\", \"actual\": [[false], \"1\"], \"expected\": [[false], \"3/2\"], \"passed\": false}, {\"check\": \"capacity clips idle accrual\", \"actual\": [[true], \"1\"], \"expected\": [[true], \"1\"], \"passed\": true}, {\"check\": \"same instant cannot refill twice\", \"actual\": [[true, false], \"0\"], \"expected\": [[true, false], \"0\"], \"passed\": true}, {\"check\": \"oversized cost is rejected\", \"actual\": [[false], \"1\"], \"expected\": [[false], \"1\"], \"passed\": true}, {\"check\": \"zero refill preserves balance\", \"actual\": [[true], \"0\"], \"expected\": [[true], \"0\"], \"passed\": true}, {\"check\": \"no requests preserve initial\", \"actual\": [[], \"1\"], \"expected\": [[], \"1\"], \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":36.838,"exit_code":0,"observations":[{"actual":[[true,true],"0"],"check":"fraction survives consumption","expected":[[true,true],"0"],"passed":true},{"actual":[[false],"3/2"],"check":"not yet enough for next token","expected":[[false],"3/2"],"passed":true},{"actual":[[true],"1"],"check":"capacity clips idle accrual","expected":[[true],"1"],"passed":true},{"actual":[[true,false],"0"],"check":"same instant cannot refill twice","expected":[[true,false],"0"],"passed":true},{"actual":[[false],"1"],"check":"oversized cost is rejected","expected":[[false],"1"],"passed":true},{"actual":[[true],"0"],"check":"zero refill preserves balance","expected":[[true],"0"],"passed":true},{"actual":[[],"1"],"check":"no requests preserve initial","expected":[[],"1"],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fraction survives consumption\", \"actual\": [[true, true], \"0\"], \"expected\": [[true, true], \"0\"], \"passed\": true}, {\"check\": \"not yet enough for next token\", \"actual\": [[false], \"3/2\"], \"expected\": [[false], \"3/2\"], \"passed\": true}, {\"check\": \"capacity clips idle accrual\", \"actual\": [[true], \"1\"], \"expected\": [[true], \"1\"], \"passed\": true}, {\"check\": \"same instant cannot refill twice\", \"actual\": [[true, false], \"0\"], \"expected\": [[true, false], \"0\"], \"passed\": true}, {\"check\": \"oversized cost is rejected\", \"actual\": [[false], \"1\"], \"expected\": [[false], \"1\"], \"passed\": true}, {\"check\": \"zero refill preserves balance\", \"actual\": [[true], \"0\"], \"expected\": [[true], \"0\"], \"passed\": true}, {\"check\": \"no requests preserve initial\", \"actual\": [[], \"1\"], \"expected\": [[], \"1\"], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}