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FA-73796 / Rate limiter algorithms / Open access

Rolling window over a ring of sub-window counters: slot chosen from raw milliseconds · case 01

Requests in the same sub-window scatter across slots and reset each other.

Verified by executionVariant 1 · 6 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The slot index uses the millisecond timestamp instead of the epoch.

THE FAILURE

The slot index uses the millisecond timestamp instead of the epoch.

Unsuccessful approach: Using N - 1 slots makes consecutive epochs collide within one window.

Case contract

Input {slots N, slot_ms B, limit, requests [t]} with nondecreasing t. Epoch e = t div B maps to slot e mod N; each slot remembers the epoch it counts and is zeroed when reused for a newer epoch. The rolling total sums slots whose epoch lies in (e - N, e]. Admit while total < limit and count the request in the current slot. Return [decisions, slot counts, slot epochs].

Why this case matters

Rolling-window limiters in service meshes keep a ring of small buckets; forgetting to zero reused buckets or summing stale ones replays old traffic into current decisions.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    N = x['slots']
    B = x['slot_ms']
    lim = x['limit']
    cnt = [0] * N
    ep = [-1] * N
    out = []
    for t in x['requests']:
        e = t // B
        s = t % N
        if ep[s] != e:
            ep[s] = e
            cnt[s] = 0
        total = sum(cnt[i] for i in range(N) if e - N < ep[i] <= e)
        if total < lim:
            cnt[s] += 1
            out.append('allow')
        else:
            out.append('deny')
    return [out, cnt, ep]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[['slot reused after a lap',
   {'limit': 3, 'requests': [0, 10, 20, 401, 410, 420, 430], 'slot_ms': 100, 'slots': 4},
   [['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny'], [3, 0, 0, 0], [4, -1, -1, -1]]],
  ['old slots leave the window',
   {'limit': 4, 'requests': [0, 100, 200, 300, 501, 610, 620, 630], 'slot_ms': 100, 'slots': 5},
   [['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'deny'],
    [1, 1, 1, 1, 0],
    [5, 6, 2, 3, -1]]],
  ['long idle gap',
   {'limit': 2, 'requests': [0, 250, 5001, 5010, 5020], 'slot_ms': 200, 'slots': 3},
   [['allow', 'allow', 'allow', 'allow', 'deny'], [1, 2, 0], [0, 25, -1]]],
  ['slot index uses epoch',
   {'limit': 5, 'requests': [0, 1, 2, 3, 252, 252, 503, 999], 'slot_ms': 250, 'slots': 4},
   [['allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'deny', 'deny'],
    [4, 1, 0, 0],
    [0, 1, 2, 3]]],
  ['partial saturation reuse',
   {'limit': 5, 'requests': [0, 1, 150, 201, 201, 202, 203, 204], 'slot_ms': 100, 'slots': 2},
   [['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny'], [4, 1], [2, 1]]],
  ['random traffic',
   {'limit': 4,
    'requests': [46, 120, 415, 554, 645, 818, 865, 1373, 1525, 1554, 1664, 1801, 1833, 1867],
    'slot_ms': 100,
    'slots': 5},
   [['allow',
     'allow',
     'allow',
     'allow',
     'allow',
     'allow',
     'deny',
     'allow',
     'allow',
     'allow',
     'allow',
     'allow',
     'deny',
     'deny'],
    [2, 1, 0, 1, 1],
    [15, 16, -1, 18, 4]]]],
 [['slot reused after a lap',
   {'limit': 3, 'requests': [0, 10, 20, 402, 410, 420, 430], 'slot_ms': 100, 'slots': 4},
   [['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny'], [3, 0, 0, 0], [4, -1, -1, -1]]],
  ['old slots leave the window',
   {'limit': 4, 'requests': [0, 100, 200, 300, 502, 610, 620, 630], 'slot_ms': 100, 'slots': 5},
   [['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'deny'],
    [1, 1, 1, 1, 0],
    [5, 6, 2, 3, -1]]],
  ['long idle gap',
   {'limit': 2, 'requests': [0, 250, 5002, 5010, 5020], 'slot_ms': 200, 'slots': 3},
   [['allow', 'allow', 'allow', 'allow', 'deny'], [1, 2, 0], [0, 25, -1]]],
  ['slot index uses epoch',
   {'limit': 5, 'requests': [0, 1, 2, 3, 253, 252, 503, 999], 'slot_ms': 250, 'slots': 4},
   [['allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'deny', 'deny'],
    [4, 1, 0, 0],
    [0, 1, 2, 3]]],
  ['partial saturation reuse',
   {'limit': 5, 'requests': [0, 1, 150, 202, 201, 202, 203, 204], 'slot_ms': 100, 'slots': 2},
   [['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny'], [4, 1], [2, 1]]],
  ['random traffic',
   {'limit': 4,
    'requests': [98, 199, 284, 322, 376, 477, 477, 489, 1105, 1133, 1150, 1440, 1769, 1950],
    'slot_ms': 100,
    'slots': 5},
   [['allow',
     'allow',
     'allow',
     'allow',
     'deny',
     'deny',
     'deny',
     'deny',
     'allow',
     'allow',
     'allow',
     'allow',
     'allow',
     'allow'],
    [1, 3, 1, 1, 1],
    [0, 11, 17, 3, 19]]]],
 [['slot reused after a lap',
   {'limit': 3, 'requests': [0, 10, 20, 403, 410, 420, 430], 'slot_ms': 100, 'slots': 4},
   [['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny'], [3, 0, 0, 0], [4, -1, -1, -1]]],
  ['old slots leave the window',
   {'limit': 4, 'requests': [0, 100, 200, 300, 503, 610, 620, 630], 'slot_ms': 100, 'slots': 5},
   [['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'deny'],
    [1, 1, 1, 1, 0],
    [5, 6, 2, 3, -1]]],
  ['long idle gap',
   {'limit': 2, 'requests': [0, 250, 5003, 5010, 5020], 'slot_ms': 200, 'slots': 3},
   [['allow', 'allow', 'allow', 'allow', 'deny'], [1, 2, 0], [0, 25, -1]]],
  ['slot index uses epoch',
   {'limit': 5, 'requests': [0, 1, 2, 3, 254, 252, 503, 999], 'slot_ms': 250, 'slots': 4},
   [['allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'deny', 'deny'],
    [4, 1, 0, 0],
    [0, 1, 2, 3]]],
  ['partial saturation reuse',
   {'limit': 5, 'requests': [0, 1, 150, 203, 201, 202, 203, 204], 'slot_ms': 100, 'slots': 2},
   [['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny'], [4, 1], [2, 1]]],
  ['random traffic',
   {'limit': 4,
    'requests': [81, 356, 399, 715, 737, 761, 1248, 1286, 1450, 1484, 1518, 1539, 1635, 1691],
    'slot_ms': 100,
    'slots': 5},
   [['allow',
     'allow',
     'allow',
     'allow',
     'allow',
     'deny',
     'allow',
     'allow',
     'allow',
     'allow',
     'deny',
     'deny',
     'deny',
     'deny'],
    [0, 0, 2, 2, 2],
    [15, 16, 12, 3, 14]]]],
 [['slot reused after a lap',
   {'limit': 3, 'requests': [0, 10, 20, 404, 410, 420, 430], 'slot_ms': 100, 'slots': 4},
   [['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny'], [3, 0, 0, 0], [4, -1, -1, -1]]],
  ['old slots leave the window',
   {'limit': 4, 'requests': [0, 100, 200, 300, 504, 610, 620, 630], 'slot_ms': 100, 'slots': 5},
   [['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'deny'],
    [1, 1, 1, 1, 0],
    [5, 6, 2, 3, -1]]],
  ['long idle gap',
   {'limit': 2, 'requests': [0, 250, 5004, 5010, 5020], 'slot_ms': 200, 'slots': 3},
   [['allow', 'allow', 'allow', 'allow', 'deny'], [1, 2, 0], [0, 25, -1]]],
  ['slot index uses epoch',
   {'limit': 5, 'requests': [0, 1, 2, 3, 255, 252, 503, 999], 'slot_ms': 250, 'slots': 4},
   [['allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'deny', 'deny'],
    [4, 1, 0, 0],
    [0, 1, 2, 3]]],
  ['partial saturation reuse',
   {'limit': 5, 'requests': [0, 1, 150, 204, 201, 202, 203, 204], 'slot_ms': 100, 'slots': 2},
   [['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny'], [4, 1], [2, 1]]],
  ['random traffic',
   {'limit': 4,
    'requests': [39, 260, 414, 610, 686, 731, 892, 1075, 1107, 1491, 1496, 1594, 1832, 1860],
    'slot_ms': 100,
    'slots': 5},
   [['allow',
     'allow',
     'allow',
     'allow',
     'allow',
     'allow',
     'deny',
     'allow',
     'allow',
     'allow',
     'allow',
     'allow',
     'allow',
     'deny'],
    [1, 1, 1, 1, 2],
    [15, 11, 7, 18, 14]]]],
 [['slot reused after a lap',
   {'limit': 3, 'requests': [0, 10, 20, 405, 410, 420, 430], 'slot_ms': 100, 'slots': 4},
   [['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny'], [3, 0, 0, 0], [4, -1, -1, -1]]],
  ['old slots leave the window',
   {'limit': 4, 'requests': [0, 100, 200, 300, 505, 610, 620, 630], 'slot_ms': 100, 'slots': 5},
   [['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'deny'],
    [1, 1, 1, 1, 0],
    [5, 6, 2, 3, -1]]],
  ['long idle gap',
   {'limit': 2, 'requests': [0, 250, 5005, 5010, 5020], 'slot_ms': 200, 'slots': 3},
   [['allow', 'allow', 'allow', 'allow', 'deny'], [1, 2, 0], [0, 25, -1]]],
  ['slot index uses epoch',
   {'limit': 5, 'requests': [0, 1, 2, 3, 256, 252, 503, 999], 'slot_ms': 250, 'slots': 4},
   [['allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'deny', 'deny'],
    [4, 1, 0, 0],
    [0, 1, 2, 3]]],
  ['partial saturation reuse',
   {'limit': 5, 'requests': [0, 1, 150, 205, 201, 202, 203, 204], 'slot_ms': 100, 'slots': 2},
   [['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny'], [4, 1], [2, 1]]],
  ['random traffic',
   {'limit': 4,
    'requests': [2, 79, 224, 260, 340, 480, 497, 648, 755, 916, 1103, 1554, 1762, 1944],
    'slot_ms': 100,
    'slots': 5},
   [['allow',
     'allow',
     'allow',
     'allow',
     'deny',
     'deny',
     'deny',
     'allow',
     'allow',
     'allow',
     'allow',
     'allow',
     'allow',
     'allow'],
    [1, 1, 1, 0, 1],
    [15, 11, 17, 3, 19]]]]]
for label, args, expected in cases[N - 1]:
    check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
slot reused after a lap[['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny'], [1, 1, 1, 0], [4, 4, 4, -1]][['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny'], [3, 0, 0, 0], [4, -1, -1, -1]]Failed
old slots leave the window[['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'allow'], [3, 1, 0, 0, 0], [6, 5, -1, -1, -1]][['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'deny'], [1, 1, 1, 1, 0], [5, 6, 2, 3, -1]]Failed
long idle gap[['allow', 'allow', 'allow', 'allow', 'deny'], [2, 0, 0], [25, 25, -1]][['allow', 'allow', 'allow', 'allow', 'deny'], [1, 2, 0], [0, 25, -1]]Failed
slot index uses epoch[['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'allow'], [2, 1, 1, 1], [1, 0, 0, 3]][['allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'deny', 'deny'], [4, 1, 0, 0], [0, 1, 2, 3]]Failed
partial saturation reuse[['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'allow'], [2, 3], [2, 2]][['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny'], [4, 1], [2, 1]]Failed
random traffic[['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny'], [1, 1, 0, 1, 1], [15, 18, 18, 18, 16]][['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'deny'], [2, 1, 0, 1, 1], [15, 16, -1, 18, 4]]Failed

SHA-256 / a92b8f183db49e42e8a9893c62fa5dbd557cbb047526a774eb033415a4da6c6c

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    N = x['slots']
    B = x['slot_ms']
    lim = x['limit']
    cnt = [0] * N
    ep = [-1] * N
    out = []
    for t in x['requests']:
        e = t // B
        s = e % (N - 1)
        if ep[s] != e:
            ep[s] = e
            cnt[s] = 0
        total = sum(cnt[i] for i in range(N) if e - N < ep[i] <= e)
        if total < lim:
            cnt[s] += 1
            out.append('allow')
        else:
            out.append('deny')
    return [out, cnt, ep]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[['slot reused after a lap',
   {'limit': 3, 'requests': [0, 10, 20, 401, 410, 420, 430], 'slot_ms': 100, 'slots': 4},
   [['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny'], [3, 0, 0, 0], [4, -1, -1, -1]]],
  ['old slots leave the window',
   {'limit': 4, 'requests': [0, 100, 200, 300, 501, 610, 620, 630], 'slot_ms': 100, 'slots': 5},
   [['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'deny'],
    [1, 1, 1, 1, 0],
    [5, 6, 2, 3, -1]]],
  ['long idle gap',
   {'limit': 2, 'requests': [0, 250, 5001, 5010, 5020], 'slot_ms': 200, 'slots': 3},
   [['allow', 'allow', 'allow', 'allow', 'deny'], [1, 2, 0], [0, 25, -1]]],
  ['slot index uses epoch',
   {'limit': 5, 'requests': [0, 1, 2, 3, 252, 252, 503, 999], 'slot_ms': 250, 'slots': 4},
   [['allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'deny', 'deny'],
    [4, 1, 0, 0],
    [0, 1, 2, 3]]],
  ['partial saturation reuse',
   {'limit': 5, 'requests': [0, 1, 150, 201, 201, 202, 203, 204], 'slot_ms': 100, 'slots': 2},
   [['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny'], [4, 1], [2, 1]]],
  ['random traffic',
   {'limit': 4,
    'requests': [46, 120, 415, 554, 645, 818, 865, 1373, 1525, 1554, 1664, 1801, 1833, 1867],
    'slot_ms': 100,
    'slots': 5},
   [['allow',
     'allow',
     'allow',
     'allow',
     'allow',
     'allow',
     'deny',
     'allow',
     'allow',
     'allow',
     'allow',
     'allow',
     'deny',
     'deny'],
    [2, 1, 0, 1, 1],
    [15, 16, -1, 18, 4]]]],
 [['slot reused after a lap',
   {'limit': 3, 'requests': [0, 10, 20, 402, 410, 420, 430], 'slot_ms': 100, 'slots': 4},
   [['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny'], [3, 0, 0, 0], [4, -1, -1, -1]]],
  ['old slots leave the window',
   {'limit': 4, 'requests': [0, 100, 200, 300, 502, 610, 620, 630], 'slot_ms': 100, 'slots': 5},
   [['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'deny'],
    [1, 1, 1, 1, 0],
    [5, 6, 2, 3, -1]]],
  ['long idle gap',
   {'limit': 2, 'requests': [0, 250, 5002, 5010, 5020], 'slot_ms': 200, 'slots': 3},
   [['allow', 'allow', 'allow', 'allow', 'deny'], [1, 2, 0], [0, 25, -1]]],
  ['slot index uses epoch',
   {'limit': 5, 'requests': [0, 1, 2, 3, 253, 252, 503, 999], 'slot_ms': 250, 'slots': 4},
   [['allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'deny', 'deny'],
    [4, 1, 0, 0],
    [0, 1, 2, 3]]],
  ['partial saturation reuse',
   {'limit': 5, 'requests': [0, 1, 150, 202, 201, 202, 203, 204], 'slot_ms': 100, 'slots': 2},
   [['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny'], [4, 1], [2, 1]]],
  ['random traffic',
   {'limit': 4,
    'requests': [98, 199, 284, 322, 376, 477, 477, 489, 1105, 1133, 1150, 1440, 1769, 1950],
    'slot_ms': 100,
    'slots': 5},
   [['allow',
     'allow',
     'allow',
     'allow',
     'deny',
     'deny',
     'deny',
     'deny',
     'allow',
     'allow',
     'allow',
     'allow',
     'allow',
     'allow'],
    [1, 3, 1, 1, 1],
    [0, 11, 17, 3, 19]]]],
 [['slot reused after a lap',
   {'limit': 3, 'requests': [0, 10, 20, 403, 410, 420, 430], 'slot_ms': 100, 'slots': 4},
   [['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny'], [3, 0, 0, 0], [4, -1, -1, -1]]],
  ['old slots leave the window',
   {'limit': 4, 'requests': [0, 100, 200, 300, 503, 610, 620, 630], 'slot_ms': 100, 'slots': 5},
   [['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'deny'],
    [1, 1, 1, 1, 0],
    [5, 6, 2, 3, -1]]],
  ['long idle gap',
   {'limit': 2, 'requests': [0, 250, 5003, 5010, 5020], 'slot_ms': 200, 'slots': 3},
   [['allow', 'allow', 'allow', 'allow', 'deny'], [1, 2, 0], [0, 25, -1]]],
  ['slot index uses epoch',
   {'limit': 5, 'requests': [0, 1, 2, 3, 254, 252, 503, 999], 'slot_ms': 250, 'slots': 4},
   [['allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'deny', 'deny'],
    [4, 1, 0, 0],
    [0, 1, 2, 3]]],
  ['partial saturation reuse',
   {'limit': 5, 'requests': [0, 1, 150, 203, 201, 202, 203, 204], 'slot_ms': 100, 'slots': 2},
   [['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny'], [4, 1], [2, 1]]],
  ['random traffic',
   {'limit': 4,
    'requests': [81, 356, 399, 715, 737, 761, 1248, 1286, 1450, 1484, 1518, 1539, 1635, 1691],
    'slot_ms': 100,
    'slots': 5},
   [['allow',
     'allow',
     'allow',
     'allow',
     'allow',
     'deny',
     'allow',
     'allow',
     'allow',
     'allow',
     'deny',
     'deny',
     'deny',
     'deny'],
    [0, 0, 2, 2, 2],
    [15, 16, 12, 3, 14]]]],
 [['slot reused after a lap',
   {'limit': 3, 'requests': [0, 10, 20, 404, 410, 420, 430], 'slot_ms': 100, 'slots': 4},
   [['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny'], [3, 0, 0, 0], [4, -1, -1, -1]]],
  ['old slots leave the window',
   {'limit': 4, 'requests': [0, 100, 200, 300, 504, 610, 620, 630], 'slot_ms': 100, 'slots': 5},
   [['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'deny'],
    [1, 1, 1, 1, 0],
    [5, 6, 2, 3, -1]]],
  ['long idle gap',
   {'limit': 2, 'requests': [0, 250, 5004, 5010, 5020], 'slot_ms': 200, 'slots': 3},
   [['allow', 'allow', 'allow', 'allow', 'deny'], [1, 2, 0], [0, 25, -1]]],
  ['slot index uses epoch',
   {'limit': 5, 'requests': [0, 1, 2, 3, 255, 252, 503, 999], 'slot_ms': 250, 'slots': 4},
   [['allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'deny', 'deny'],
    [4, 1, 0, 0],
    [0, 1, 2, 3]]],
  ['partial saturation reuse',
   {'limit': 5, 'requests': [0, 1, 150, 204, 201, 202, 203, 204], 'slot_ms': 100, 'slots': 2},
   [['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny'], [4, 1], [2, 1]]],
  ['random traffic',
   {'limit': 4,
    'requests': [39, 260, 414, 610, 686, 731, 892, 1075, 1107, 1491, 1496, 1594, 1832, 1860],
    'slot_ms': 100,
    'slots': 5},
   [['allow',
     'allow',
     'allow',
     'allow',
     'allow',
     'allow',
     'deny',
     'allow',
     'allow',
     'allow',
     'allow',
     'allow',
     'allow',
     'deny'],
    [1, 1, 1, 1, 2],
    [15, 11, 7, 18, 14]]]],
 [['slot reused after a lap',
   {'limit': 3, 'requests': [0, 10, 20, 405, 410, 420, 430], 'slot_ms': 100, 'slots': 4},
   [['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny'], [3, 0, 0, 0], [4, -1, -1, -1]]],
  ['old slots leave the window',
   {'limit': 4, 'requests': [0, 100, 200, 300, 505, 610, 620, 630], 'slot_ms': 100, 'slots': 5},
   [['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'deny'],
    [1, 1, 1, 1, 0],
    [5, 6, 2, 3, -1]]],
  ['long idle gap',
   {'limit': 2, 'requests': [0, 250, 5005, 5010, 5020], 'slot_ms': 200, 'slots': 3},
   [['allow', 'allow', 'allow', 'allow', 'deny'], [1, 2, 0], [0, 25, -1]]],
  ['slot index uses epoch',
   {'limit': 5, 'requests': [0, 1, 2, 3, 256, 252, 503, 999], 'slot_ms': 250, 'slots': 4},
   [['allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'deny', 'deny'],
    [4, 1, 0, 0],
    [0, 1, 2, 3]]],
  ['partial saturation reuse',
   {'limit': 5, 'requests': [0, 1, 150, 205, 201, 202, 203, 204], 'slot_ms': 100, 'slots': 2},
   [['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny'], [4, 1], [2, 1]]],
  ['random traffic',
   {'limit': 4,
    'requests': [2, 79, 224, 260, 340, 480, 497, 648, 755, 916, 1103, 1554, 1762, 1944],
    'slot_ms': 100,
    'slots': 5},
   [['allow',
     'allow',
     'allow',
     'allow',
     'deny',
     'deny',
     'deny',
     'allow',
     'allow',
     'allow',
     'allow',
     'allow',
     'allow',
     'allow'],
    [1, 1, 1, 0, 1],
    [15, 11, 17, 3, 19]]]]]
for label, args, expected in cases[N - 1]:
    check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
slot reused after a lap[['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny'], [3, 3, 0, 0], [0, 4, -1, -1]][['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny'], [3, 0, 0, 0], [4, -1, -1, -1]]Failed
old slots leave the window[['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny'], [1, 1, 2, 1, 0], [0, 5, 6, 3, -1]][['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'deny'], [1, 1, 1, 1, 0], [5, 6, 2, 3, -1]]Failed
long idle gap[['allow', 'allow', 'allow', 'allow', 'deny'], [1, 2, 0], [0, 25, -1]][['allow', 'allow', 'allow', 'allow', 'deny'], [1, 2, 0], [0, 25, -1]]Passed
slot index uses epoch[['allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'deny', 'allow'], [1, 1, 0, 0], [3, 1, 2, -1]][['allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'deny', 'deny'], [4, 1, 0, 0], [0, 1, 2, 3]]Failed
partial saturation reuse[['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'allow'], [5, 0], [2, -1]][['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny'], [4, 1], [2, 1]]Failed
random traffic[['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'deny'], [1, 1, 1, 2, 0], [16, 13, 18, 15, -1]][['allow', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'deny'], [2, 1, 0, 1, 1], [15, 16, -1, 18, 4]]Failed

SHA-256 / 8ae77cd062357751c13a826c9396316e6b13ab8a720c301208af2781aff120f3

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This mechanism has 6 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

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Verification & scope

A deterministic, bounded teaching model with stipulated constants and pre-hashed or explicitly hashed inputs; it is not a production implementation and makes no claim of conformance to any library or paper beyond the stated contract. 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.

Observations recorded using Python 3.12.14 at 2026-09-29T14:48:50.709786+00:00.

Case digest / 36ac9c90c92004107ee8dfe3bda4c2670fb6ab343851dfdd0690838eec9c5923