FA-73101 / Probabilistic sketches / Open access
Weighted Misra-Gries frequent items: weighted decrement uses one unit · case 01
A heavy newcomer loses only one unit and stale counters linger, violating the weighted algorithm.
ROOT CAUSE
The decrement uses the unweighted step of one.
THE FAILURE
The decrement uses the unweighted step of one.
Unsuccessful approach: Decrementing by the full incoming weight can drive counters negative.
Case contract
Input {k, stream} of [item, positive weight]. Keep at most k counters. A tracked item adds its weight; an untracked item takes a free counter. Otherwise dec = min(smallest counter, weight) is subtracted from every counter and from the incoming weight, counters reaching 0 are dropped, and a positive remainder is inserted. removed accumulates dec*(k+1), the discarded mass. Return [sorted [item, count] pairs, removed].
Why this case matters
Heavy-hitter detection over weighted traffic (bytes per flow, spend per account) relies on the deterministic Misra-Gries error bound removed/(k+1).
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(x):
k = x['k']
C = {}
removed = 0
for item, wt in x['stream']:
if item in C:
C[item] += wt
elif len(C) < k:
C[item] = wt
else:
dec = 1
for key in list(C):
C[key] -= dec
if C[key] == 0:
del C[key]
wt -= dec
removed += dec * (k + 1)
if wt > 0:
C[item] = wt
return [sorted([key, v] for key, v in C.items()), removed]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[['weighted stream 0 k=2',
{'k': 2,
'stream': [['d', 4],
['c', 1],
['a', 3],
['d', 1],
['d', 3],
['a', 5],
['e', 2],
['d', 3],
['d', 4],
['a', 5],
['a', 4]]},
[[['a', 14], ['d', 12]], 9]],
['weighted stream 1 k=3',
{'k': 3,
'stream': [['e', 5],
['c', 5],
['b', 3],
['d', 2],
['c', 2],
['d', 2],
['d', 1],
['c', 3],
['a', 4],
['d', 4],
['f', 1]]},
[[['a', 1], ['c', 4], ['d', 3]], 24]],
['weighted stream 2 k=2',
{'k': 2,
'stream': [['d', 2],
['c', 2],
['c', 1],
['c', 4],
['a', 1],
['c', 4],
['d', 4],
['c', 5],
['c', 3],
['c', 4],
['a', 1]]},
[[['c', 21], ['d', 4]], 6]],
['weighted stream 3 k=4',
{'k': 4,
'stream': [['a', 5],
['a', 5],
['a', 2],
['a', 3],
['d', 4],
['a', 3],
['e', 4],
['e', 1],
['g', 4],
['g', 1],
['g', 3]]},
[[['a', 18], ['d', 4], ['e', 5], ['g', 8]], 0]],
['newcomer fully absorbed',
{'k': 2, 'stream': [['a', 5], ['b', 4], ['c', 3]]},
[[['a', 2], ['b', 1]], 9]],
['newcomer survives decrement',
{'k': 2, 'stream': [['a', 2], ['b', 3], ['c', 7]]},
[[['b', 1], ['c', 5]], 6]],
['exact capacity',
{'k': 3, 'stream': [['a', 1], ['b', 1], ['c', 1], ['a', 1]]},
[[['a', 2], ['b', 1], ['c', 1]], 0]]],
[['weighted stream 0 k=2',
{'k': 2,
'stream': [['d', 1],
['e', 5],
['d', 4],
['e', 5],
['b', 1],
['e', 4],
['a', 5],
['b', 3],
['d', 1],
['d', 2],
['e', 1],
['d', 1]]},
[[['d', 2], ['e', 7]], 24]],
['weighted stream 1 k=3',
{'k': 3,
'stream': [['c', 2],
['b', 5],
['b', 5],
['c', 1],
['d', 1],
['a', 5],
['c', 2],
['f', 4],
['a', 2],
['f', 5],
['b', 2],
['d', 4]]},
[[['b', 5], ['d', 2], ['f', 3]], 28]],
['weighted stream 2 k=2',
{'k': 2,
'stream': [['c', 2],
['d', 2],
['c', 4],
['d', 5],
['d', 1],
['b', 2],
['b', 5],
['c', 3],
['e', 4],
['c', 5],
['e', 3],
['b', 2]]},
[[['c', 4], ['e', 4]], 30]],
['weighted stream 3 k=4',
{'k': 4,
'stream': [['a', 2],
['g', 1],
['c', 5],
['a', 3],
['b', 2],
['b', 1],
['d', 3],
['g', 2],
['e', 3],
['b', 4],
['d', 2],
['d', 4]]},
[[['b', 2], ['d', 4], ['e', 1]], 25]],
['newcomer fully absorbed',
{'k': 2, 'stream': [['a', 5], ['b', 4], ['c', 3]]},
[[['a', 2], ['b', 1]], 9]],
['newcomer survives decrement',
{'k': 2, 'stream': [['a', 2], ['b', 3], ['c', 8]]},
[[['b', 1], ['c', 6]], 6]],
['exact capacity',
{'k': 3, 'stream': [['a', 1], ['b', 1], ['c', 1], ['a', 2]]},
[[['a', 3], ['b', 1], ['c', 1]], 0]]],
[['weighted stream 0 k=2',
{'k': 2,
'stream': [['c', 3],
['e', 5],
['c', 1],
['a', 2],
['a', 2],
['a', 4],
['c', 3],
['d', 5],
['e', 3],
['a', 1],
['c', 1],
['b', 5],
['d', 1]]},
[[['b', 5], ['d', 1]], 30]],
['weighted stream 1 k=3',
{'k': 3,
'stream': [['a', 1],
['e', 4],
['e', 5],
['b', 2],
['f', 3],
['d', 3],
['b', 1],
['b', 1],
['f', 3],
['d', 2],
['c', 3],
['f', 3],
['c', 3]]},
[[['c', 4], ['e', 3], ['f', 3]], 24]],
['weighted stream 2 k=2',
{'k': 2,
'stream': [['e', 3],
['a', 1],
['c', 5],
['b', 5],
['c', 3],
['e', 4],
['b', 1],
['a', 5],
['e', 3],
['d', 1],
['e', 1],
['e', 1],
['e', 5]]},
[[['a', 3], ['e', 8]], 27]],
['weighted stream 3 k=4',
{'k': 4,
'stream': [['a', 3],
['f', 4],
['e', 4],
['b', 2],
['c', 1],
['g', 1],
['f', 4],
['e', 3],
['a', 1],
['e', 4],
['e', 2],
['b', 2],
['f', 1]]},
[[['a', 2], ['b', 2], ['e', 11], ['f', 7]], 10]],
['newcomer fully absorbed',
{'k': 2, 'stream': [['a', 5], ['b', 4], ['c', 3]]},
[[['a', 2], ['b', 1]], 9]],
['newcomer survives decrement',
{'k': 2, 'stream': [['a', 2], ['b', 3], ['c', 9]]},
[[['b', 1], ['c', 7]], 6]],
['exact capacity',
{'k': 3, 'stream': [['a', 1], ['b', 1], ['c', 1], ['a', 3]]},
[[['a', 4], ['b', 1], ['c', 1]], 0]]],
[['weighted stream 0 k=2',
{'k': 2,
'stream': [['d', 3],
['e', 1],
['d', 3],
['c', 1],
['c', 4],
['c', 3],
['e', 5],
['e', 2],
['b', 5],
['a', 2],
['e', 5],
['d', 3],
['a', 1],
['b', 4]]},
[[['b', 3]], 39]],
['weighted stream 1 k=3',
{'k': 3,
'stream': [['d', 3],
['a', 5],
['c', 2],
['d', 1],
['b', 2],
['d', 3],
['b', 3],
['d', 4],
['c', 1],
['f', 5],
['d', 1],
['e', 5],
['b', 2],
['d', 3]]},
[[['d', 8], ['e', 3], ['f', 1]], 28]],
['weighted stream 2 k=2',
{'k': 2,
'stream': [['c', 5],
['b', 5],
['c', 2],
['c', 5],
['d', 4],
['a', 4],
['b', 4],
['c', 5],
['c', 1],
['e', 2],
['b', 3],
['e', 2],
['b', 3],
['d', 5]]},
[[['c', 3], ['d', 2]], 45]],
['weighted stream 3 k=4',
{'k': 4,
'stream': [['b', 5],
['d', 2],
['a', 4],
['f', 3],
['a', 1],
['b', 2],
['g', 1],
['c', 2],
['d', 3],
['d', 5],
['d', 3],
['e', 4],
['c', 3],
['g', 4]]},
[[['b', 1], ['d', 7], ['e', 1], ['g', 3]], 30]],
['newcomer fully absorbed',
{'k': 2, 'stream': [['a', 5], ['b', 4], ['c', 3]]},
[[['a', 2], ['b', 1]], 9]],
['newcomer survives decrement',
{'k': 2, 'stream': [['a', 2], ['b', 3], ['c', 10]]},
[[['b', 1], ['c', 8]], 6]],
['exact capacity',
{'k': 3, 'stream': [['a', 1], ['b', 1], ['c', 1], ['a', 4]]},
[[['a', 5], ['b', 1], ['c', 1]], 0]]],
[['weighted stream 0 k=2',
{'k': 2,
'stream': [['b', 4],
['d', 3],
['d', 4],
['e', 4],
['c', 1],
['a', 3],
['b', 2],
['b', 5],
['e', 5],
['e', 1],
['d', 4],
['e', 3],
['c', 3],
['d', 3],
['e', 5]]},
[[['d', 1], ['e', 7]], 42]],
['weighted stream 1 k=3',
{'k': 3,
'stream': [['d', 3],
['a', 5],
['b', 5],
['e', 3],
['c', 4],
['d', 4],
['e', 4],
['e', 2],
['b', 4],
['d', 1],
['a', 4],
['b', 3],
['f', 1],
['f', 2],
['d', 4]]},
[[['b', 1], ['d', 4]], 44]],
['weighted stream 2 k=2',
{'k': 2,
'stream': [['d', 3],
['a', 5],
['a', 5],
['e', 3],
['b', 4],
['c', 4],
['a', 2],
['e', 1],
['e', 2],
['a', 5],
['e', 1],
['c', 3],
['c', 4],
['c', 1],
['c', 3]]},
[[['a', 6], ['c', 7]], 33]],
['weighted stream 3 k=4',
{'k': 4,
'stream': [['b', 1],
['g', 4],
['f', 3],
['g', 1],
['f', 1],
['e', 1],
['g', 3],
['g', 5],
['g', 2],
['a', 4],
['d', 2],
['e', 2],
['d', 3],
['d', 3],
['e', 5]]},
[[['d', 5], ['e', 4], ['g', 11]], 20]],
['newcomer fully absorbed',
{'k': 2, 'stream': [['a', 5], ['b', 4], ['c', 3]]},
[[['a', 2], ['b', 1]], 9]],
['newcomer survives decrement',
{'k': 2, 'stream': [['a', 2], ['b', 3], ['c', 11]]},
[[['b', 1], ['c', 9]], 6]],
['exact capacity',
{'k': 3, 'stream': [['a', 1], ['b', 1], ['c', 1], ['a', 5]]},
[[['a', 6], ['b', 1], ['c', 1]], 0]]]]
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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| weighted stream 0 k=2 | [[['a', 15], ['d', 13], ['e', 1]], 6] | [[['a', 14], ['d', 12]], 9] | Failed |
| weighted stream 1 k=3 | [[['a', 2], ['c', 7], ['d', 6], ['e', 2]], 12] | [[['a', 1], ['c', 4], ['d', 3]], 24] | Failed |
| weighted stream 2 k=2 | [[['c', 21], ['d', 4]], 6] | [[['c', 21], ['d', 4]], 6] | Passed |
| weighted stream 3 k=4 | [[['a', 18], ['d', 4], ['e', 5], ['g', 8]], 0] | [[['a', 18], ['d', 4], ['e', 5], ['g', 8]], 0] | Passed |
| newcomer fully absorbed | [[['a', 4], ['b', 3], ['c', 2]], 3] | [[['a', 2], ['b', 1]], 9] | Failed |
| newcomer survives decrement | [[['a', 1], ['b', 2], ['c', 6]], 3] | [[['b', 1], ['c', 5]], 6] | Failed |
| exact capacity | [[['a', 2], ['b', 1], ['c', 1]], 0] | [[['a', 2], ['b', 1], ['c', 1]], 0] | Passed |
SHA-256 / d4b9c731629438eca43aec1502da52347f8e552203b0234a5b5505ecde92f596
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(x):
k = x['k']
C = {}
removed = 0
for item, wt in x['stream']:
if item in C:
C[item] += wt
elif len(C) < k:
C[item] = wt
else:
dec = wt
for key in list(C):
C[key] -= dec
if C[key] == 0:
del C[key]
wt -= dec
removed += dec * (k + 1)
if wt > 0:
C[item] = wt
return [sorted([key, v] for key, v in C.items()), removed]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[['weighted stream 0 k=2',
{'k': 2,
'stream': [['d', 4],
['c', 1],
['a', 3],
['d', 1],
['d', 3],
['a', 5],
['e', 2],
['d', 3],
['d', 4],
['a', 5],
['a', 4]]},
[[['a', 14], ['d', 12]], 9]],
['weighted stream 1 k=3',
{'k': 3,
'stream': [['e', 5],
['c', 5],
['b', 3],
['d', 2],
['c', 2],
['d', 2],
['d', 1],
['c', 3],
['a', 4],
['d', 4],
['f', 1]]},
[[['a', 1], ['c', 4], ['d', 3]], 24]],
['weighted stream 2 k=2',
{'k': 2,
'stream': [['d', 2],
['c', 2],
['c', 1],
['c', 4],
['a', 1],
['c', 4],
['d', 4],
['c', 5],
['c', 3],
['c', 4],
['a', 1]]},
[[['c', 21], ['d', 4]], 6]],
['weighted stream 3 k=4',
{'k': 4,
'stream': [['a', 5],
['a', 5],
['a', 2],
['a', 3],
['d', 4],
['a', 3],
['e', 4],
['e', 1],
['g', 4],
['g', 1],
['g', 3]]},
[[['a', 18], ['d', 4], ['e', 5], ['g', 8]], 0]],
['newcomer fully absorbed',
{'k': 2, 'stream': [['a', 5], ['b', 4], ['c', 3]]},
[[['a', 2], ['b', 1]], 9]],
['newcomer survives decrement',
{'k': 2, 'stream': [['a', 2], ['b', 3], ['c', 7]]},
[[['b', 1], ['c', 5]], 6]],
['exact capacity',
{'k': 3, 'stream': [['a', 1], ['b', 1], ['c', 1], ['a', 1]]},
[[['a', 2], ['b', 1], ['c', 1]], 0]]],
[['weighted stream 0 k=2',
{'k': 2,
'stream': [['d', 1],
['e', 5],
['d', 4],
['e', 5],
['b', 1],
['e', 4],
['a', 5],
['b', 3],
['d', 1],
['d', 2],
['e', 1],
['d', 1]]},
[[['d', 2], ['e', 7]], 24]],
['weighted stream 1 k=3',
{'k': 3,
'stream': [['c', 2],
['b', 5],
['b', 5],
['c', 1],
['d', 1],
['a', 5],
['c', 2],
['f', 4],
['a', 2],
['f', 5],
['b', 2],
['d', 4]]},
[[['b', 5], ['d', 2], ['f', 3]], 28]],
['weighted stream 2 k=2',
{'k': 2,
'stream': [['c', 2],
['d', 2],
['c', 4],
['d', 5],
['d', 1],
['b', 2],
['b', 5],
['c', 3],
['e', 4],
['c', 5],
['e', 3],
['b', 2]]},
[[['c', 4], ['e', 4]], 30]],
['weighted stream 3 k=4',
{'k': 4,
'stream': [['a', 2],
['g', 1],
['c', 5],
['a', 3],
['b', 2],
['b', 1],
['d', 3],
['g', 2],
['e', 3],
['b', 4],
['d', 2],
['d', 4]]},
[[['b', 2], ['d', 4], ['e', 1]], 25]],
['newcomer fully absorbed',
{'k': 2, 'stream': [['a', 5], ['b', 4], ['c', 3]]},
[[['a', 2], ['b', 1]], 9]],
['newcomer survives decrement',
{'k': 2, 'stream': [['a', 2], ['b', 3], ['c', 8]]},
[[['b', 1], ['c', 6]], 6]],
['exact capacity',
{'k': 3, 'stream': [['a', 1], ['b', 1], ['c', 1], ['a', 2]]},
[[['a', 3], ['b', 1], ['c', 1]], 0]]],
[['weighted stream 0 k=2',
{'k': 2,
'stream': [['c', 3],
['e', 5],
['c', 1],
['a', 2],
['a', 2],
['a', 4],
['c', 3],
['d', 5],
['e', 3],
['a', 1],
['c', 1],
['b', 5],
['d', 1]]},
[[['b', 5], ['d', 1]], 30]],
['weighted stream 1 k=3',
{'k': 3,
'stream': [['a', 1],
['e', 4],
['e', 5],
['b', 2],
['f', 3],
['d', 3],
['b', 1],
['b', 1],
['f', 3],
['d', 2],
['c', 3],
['f', 3],
['c', 3]]},
[[['c', 4], ['e', 3], ['f', 3]], 24]],
['weighted stream 2 k=2',
{'k': 2,
'stream': [['e', 3],
['a', 1],
['c', 5],
['b', 5],
['c', 3],
['e', 4],
['b', 1],
['a', 5],
['e', 3],
['d', 1],
['e', 1],
['e', 1],
['e', 5]]},
[[['a', 3], ['e', 8]], 27]],
['weighted stream 3 k=4',
{'k': 4,
'stream': [['a', 3],
['f', 4],
['e', 4],
['b', 2],
['c', 1],
['g', 1],
['f', 4],
['e', 3],
['a', 1],
['e', 4],
['e', 2],
['b', 2],
['f', 1]]},
[[['a', 2], ['b', 2], ['e', 11], ['f', 7]], 10]],
['newcomer fully absorbed',
{'k': 2, 'stream': [['a', 5], ['b', 4], ['c', 3]]},
[[['a', 2], ['b', 1]], 9]],
['newcomer survives decrement',
{'k': 2, 'stream': [['a', 2], ['b', 3], ['c', 9]]},
[[['b', 1], ['c', 7]], 6]],
['exact capacity',
{'k': 3, 'stream': [['a', 1], ['b', 1], ['c', 1], ['a', 3]]},
[[['a', 4], ['b', 1], ['c', 1]], 0]]],
[['weighted stream 0 k=2',
{'k': 2,
'stream': [['d', 3],
['e', 1],
['d', 3],
['c', 1],
['c', 4],
['c', 3],
['e', 5],
['e', 2],
['b', 5],
['a', 2],
['e', 5],
['d', 3],
['a', 1],
['b', 4]]},
[[['b', 3]], 39]],
['weighted stream 1 k=3',
{'k': 3,
'stream': [['d', 3],
['a', 5],
['c', 2],
['d', 1],
['b', 2],
['d', 3],
['b', 3],
['d', 4],
['c', 1],
['f', 5],
['d', 1],
['e', 5],
['b', 2],
['d', 3]]},
[[['d', 8], ['e', 3], ['f', 1]], 28]],
['weighted stream 2 k=2',
{'k': 2,
'stream': [['c', 5],
['b', 5],
['c', 2],
['c', 5],
['d', 4],
['a', 4],
['b', 4],
['c', 5],
['c', 1],
['e', 2],
['b', 3],
['e', 2],
['b', 3],
['d', 5]]},
[[['c', 3], ['d', 2]], 45]],
['weighted stream 3 k=4',
{'k': 4,
'stream': [['b', 5],
['d', 2],
['a', 4],
['f', 3],
['a', 1],
['b', 2],
['g', 1],
['c', 2],
['d', 3],
['d', 5],
['d', 3],
['e', 4],
['c', 3],
['g', 4]]},
[[['b', 1], ['d', 7], ['e', 1], ['g', 3]], 30]],
['newcomer fully absorbed',
{'k': 2, 'stream': [['a', 5], ['b', 4], ['c', 3]]},
[[['a', 2], ['b', 1]], 9]],
['newcomer survives decrement',
{'k': 2, 'stream': [['a', 2], ['b', 3], ['c', 10]]},
[[['b', 1], ['c', 8]], 6]],
['exact capacity',
{'k': 3, 'stream': [['a', 1], ['b', 1], ['c', 1], ['a', 4]]},
[[['a', 5], ['b', 1], ['c', 1]], 0]]],
[['weighted stream 0 k=2',
{'k': 2,
'stream': [['b', 4],
['d', 3],
['d', 4],
['e', 4],
['c', 1],
['a', 3],
['b', 2],
['b', 5],
['e', 5],
['e', 1],
['d', 4],
['e', 3],
['c', 3],
['d', 3],
['e', 5]]},
[[['d', 1], ['e', 7]], 42]],
['weighted stream 1 k=3',
{'k': 3,
'stream': [['d', 3],
['a', 5],
['b', 5],
['e', 3],
['c', 4],
['d', 4],
['e', 4],
['e', 2],
['b', 4],
['d', 1],
['a', 4],
['b', 3],
['f', 1],
['f', 2],
['d', 4]]},
[[['b', 1], ['d', 4]], 44]],
['weighted stream 2 k=2',
{'k': 2,
'stream': [['d', 3],
['a', 5],
['a', 5],
['e', 3],
['b', 4],
['c', 4],
['a', 2],
['e', 1],
['e', 2],
['a', 5],
['e', 1],
['c', 3],
['c', 4],
['c', 1],
['c', 3]]},
[[['a', 6], ['c', 7]], 33]],
['weighted stream 3 k=4',
{'k': 4,
'stream': [['b', 1],
['g', 4],
['f', 3],
['g', 1],
['f', 1],
['e', 1],
['g', 3],
['g', 5],
['g', 2],
['a', 4],
['d', 2],
['e', 2],
['d', 3],
['d', 3],
['e', 5]]},
[[['d', 5], ['e', 4], ['g', 11]], 20]],
['newcomer fully absorbed',
{'k': 2, 'stream': [['a', 5], ['b', 4], ['c', 3]]},
[[['a', 2], ['b', 1]], 9]],
['newcomer survives decrement',
{'k': 2, 'stream': [['a', 2], ['b', 3], ['c', 11]]},
[[['b', 1], ['c', 9]], 6]],
['exact capacity',
{'k': 3, 'stream': [['a', 1], ['b', 1], ['c', 1], ['a', 5]]},
[[['a', 6], ['b', 1], ['c', 1]], 0]]]]
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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| weighted stream 0 k=2 | [[['c', -23], ['e', -14]], 72] | [[['a', 14], ['d', 12]], 9] | Failed |
| weighted stream 1 k=3 | [[['b', -6], ['c', 1], ['f', 1]], 36] | [[['a', 1], ['c', 4], ['d', 3]], 24] | Failed |
| weighted stream 2 k=2 | [[['c', 21], ['d', 4]], 6] | [[['c', 21], ['d', 4]], 6] | Passed |
| weighted stream 3 k=4 | [[['a', 18], ['d', 4], ['e', 5], ['g', 8]], 0] | [[['a', 18], ['d', 4], ['e', 5], ['g', 8]], 0] | Passed |
| newcomer fully absorbed | [[['a', 2], ['b', 1]], 9] | [[['a', 2], ['b', 1]], 9] | Passed |
| newcomer survives decrement | [[['a', -5], ['b', -4]], 21] | [[['b', 1], ['c', 5]], 6] | Failed |
| exact capacity | [[['a', 2], ['b', 1], ['c', 1]], 0] | [[['a', 2], ['b', 1], ['c', 1]], 0] | Passed |
SHA-256 / 86fc25a94ec5e26c37e59125e51d056ec7b9a6003e7bcff42e156573edab9953
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This mechanism has 7 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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Sign in to the archive ↗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 2026-09-29T14:48:44.546719+00:00.
Case digest / f7f4ff9e0a8df6c5e9490b812c6cc735e3672e7f08171638544dbea81e9ef904