FAILURE MAP
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MinHash Jaccard estimation: agreement normalised like a set Jaccard · case 01

Similarity estimates are systematically deflated for partially overlapping sets.

Verified by executionVariant 1 · 7 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Matching positions are divided by 2k - matches, treating the two signatures as sets to be unioned.

THE FAILURE

Matching positions are divided by 2k - matches, treating the two signatures as sets to be unioned.

Unsuccessful approach: Dividing by the number of distinct signature values mixes hash functions and is not the MinHash estimator.

Case contract

Input {k, A, B} integer sets. Signature component i is min over v of (A_i v + B_i) mod 2^31-1 with fixed coefficients. The estimate is the fraction of positions where both signatures agree, rounded to 4 decimals. Two empty sets have undefined similarity (None, with empty signatures); exactly one empty set gives 0.0. Return [sigA, sigB, estimate].

Why this case matters

Near-duplicate detection and set-similarity joins compare MinHash signatures instead of the sets; signature and comparison rules must match exactly across producers.

1 / The failure

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

N = 1
observations = []
def solve(x):
    k = x['k']
    P = 2147483647
    A = [1103515245, 1812433253, 1664525017, 2013265921, 1597334677, 1566083941, 69069, 22695477]
    Bc = [12345, 1013904223, 7, 99991, 31337, 424242, 1, 3]
    def sig(s):
        return [min((A[i] * v + Bc[i]) % P for v in s) for i in range(k)]
    a, b = x['A'], x['B']
    if not a and not b:
        return [[], [], None]
    if not a or not b:
        return [sig(a) if a else [], sig(b) if b else [], 0.0]
    sa, sb = sig(a), sig(b)
    matches = sum(1 for i in range(k) if sa[i] == sb[i])
    return [sa, sb, round(matches / (2 * k - matches), 4)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[['overlapping sets k=4',
   {'A': [185, 180, 93, 45, 14, 71, 154, 36, 166],
    'B': [45, 14, 71, 154, 36, 166, 145, 34, 146, 221],
    'k': 4},
   [[139386205, 618166001, 69675629, 268535474], [51964590, 359609062, 69675629, 268535474], 0.5]],
  ['overlapping sets k=6',
   {'A': [137, 9, 132, 163, 55, 20, 170, 179, 119],
    'B': [163, 55, 20, 170, 179, 119, 47, 41, 24, 251],
    'k': 6},
   [[321824033, 87781176, 406660754, 805406688, 307613469, 235695117],
    [146980803, 87781176, 509981506, 134317810, 307613469, 97986032],
    0.3333]],
  ['overlapping sets k=8',
   {'A': [148, 51, 156, 91, 149, 73, 41, 176, 152],
    'B': [91, 149, 73, 41, 176, 152, 140, 118, 113, 264],
    'k': 8},
   [[111511433, 27093348, 898627007, 100332, 76137897, 413810294, 2831830, 930514560],
    [143183504, 27093348, 898627007, 100332, 110223490, 114735638, 2831830, 417105257],
    0.5]],
  ['both empty', {'A': [], 'B': [], 'k': 4}, [[], [], None]],
  ['one empty', {'A': [6, 9], 'B': [], 'k': 3}, [[178652874, 145934324, 1397215521], [], 0.0]],
  ['identical sets',
   {'A': [3, 8, 14], 'B': [14, 8, 3], 'k': 5},
   [[238199717, 8753041, 431298261, 268535474, 497068074],
    [238199717, 8753041, 431298261, 268535474, 497068074],
    1.0]],
  ['large values',
   {'A': [1000000001, 7, 99], 'B': [1000000001, 8], 'k': 4},
   [[651916080, 56169922, 661849663, 1208059556],
    [238199717, 480984718, 431298261, 1073841830],
    0.0]]],
 [['overlapping sets k=4',
   {'A': [77, 180, 129, 27, 120, 79, 147, 135, 166],
    'B': [27, 120, 79, 147, 135, 166, 178, 114, 109, 210],
    'k': 4},
   [[619558248, 314726861, 27022876, 134317872], [24089818, 314726861, 27022876, 134317872], 0.75]],
  ['overlapping sets k=6',
   {'A': [43, 26, 163, 158, 61, 6, 58, 100, 105],
    'B': [158, 61, 6, 58, 100, 105, 18, 10, 87, 294],
    'k': 6},
   [[178652874, 87781176, 327977509, 268535753, 216447956, 481067515],
    [163463678, 193351205, 604294635, 268535753, 216447956, 272647769],
    0.3333]],
  ['overlapping sets k=8',
   {'A': [119, 125, 38, 35, 22, 123, 186, 169, 60],
    'B': [35, 22, 123, 186, 169, 60, 55, 134, 69, 203],
    'k': 8},
   [[321824033, 24558668, 112328382, 402753417, 72170210, 94532592, 1519519, 499300497],
    [440917719, 24558668, 112328382, 536971019, 72170210, 87884509, 1519519, 312214540],
    0.5]],
  ['both empty', {'A': [], 'B': [], 'k': 4}, [[], [], None]],
  ['one empty', {'A': [7, 9], 'B': [], 'k': 3}, [[1282168119, 145934324, 914256891], [], 0.0]],
  ['identical sets',
   {'A': [3, 8, 15], 'B': [15, 8, 3], 'k': 5},
   [[238199717, 8753041, 431298261, 134317748, 337731375],
    [238199717, 8753041, 431298261, 134317748, 337731375],
    1.0]],
  ['large values',
   {'A': [1000000002, 7, 99], 'B': [1000000002, 8], 'k': 4},
   [[1282168119, 56169922, 178891033, 1208059556],
    [238199717, 480984718, 178891033, 1073841830],
    0.25]]],
 [['overlapping sets k=4',
   {'A': [21, 131, 85, 16, 192, 176, 186, 106, 14],
    'B': [16, 192, 176, 186, 106, 14, 154, 67, 112, 276],
    'k': 4},
   [[416840246, 27093348, 345992755, 100022], [290151962, 27093348, 345992755, 100022], 0.75]],
  ['overlapping sets k=6',
   {'A': [17, 173, 195, 128, 127, 162, 64, 34, 2],
    'B': [128, 127, 162, 64, 34, 2, 4, 31, 120, 261],
    'k': 6},
   [[59559188, 103586803, 200019250, 100115, 95164537, 302952338],
    [59559188, 343803435, 27022876, 100115, 125282443, 302952338],
    0.5]],
  ['overlapping sets k=8',
   {'A': [104, 160, 182, 180, 79, 129, 139, 39, 130],
    'B': [180, 79, 129, 139, 39, 130, 181, 110, 50, 200],
    'k': 8},
   [[87433960, 164274631, 36030499, 100301, 19057977, 161789813, 2693692, 212845964],
    [20292519, 314726861, 45038122, 134317872, 19057977, 161789813, 2693692, 244128109],
    0.375]],
  ['both empty', {'A': [], 'B': [], 'k': 4}, [[], [], None]],
  ['one empty', {'A': [8, 9], 'B': [], 'k': 3}, [[238199717, 145934324, 431298261], [], 0.0]],
  ['identical sets',
   {'A': [3, 8, 16], 'B': [16, 8, 3], 'k': 5},
   [[238199717, 8753041, 431298261, 100022, 497068074],
    [238199717, 8753041, 431298261, 100022, 497068074],
    1.0]],
  ['large values',
   {'A': [1000000003, 7, 99], 'B': [1000000003, 8], 'k': 4},
   [[711462923, 56169922, 914256891, 1208059556],
    [238199717, 318725747, 431298261, 1073841830],
    0.0]]],
 [['overlapping sets k=4',
   {'A': [47, 135, 53, 125, 192, 104, 165, 180, 91],
    'B': [125, 192, 104, 165, 180, 91, 144, 142, 45, 255],
    'k': 4},
   [[325621332, 298921234, 172996381, 100363], [76042063, 11287721, 139351251, 100270], 0.0]],
  ['overlapping sets k=6',
   {'A': [37, 42, 89, 127, 77, 170, 4, 111, 27],
    'B': [127, 77, 170, 4, 111, 27, 20, 114, 70, 228],
    'k': 6},
   [[27887117, 330532488, 78683252, 134317934, 178394676, 329803467],
    [83636661, 330532488, 78683252, 134317934, 144309083, 104634115],
    0.5]],
  ['overlapping sets k=8',
   {'A': [67, 151, 142, 156, 93, 90, 105, 112, 40],
    'B': [156, 93, 90, 105, 112, 40, 161, 43, 152, 287],
    'k': 8},
   [[349698805, 40364295, 9007630, 100208, 76137897, 255898163, 2762761, 235541441],
    [206527646, 193351205, 9007630, 100208, 76137897, 366756119, 2762761, 71150961],
    0.5]],
  ['both empty', {'A': [], 'B': [], 'k': 4}, [[], [], None]],
  ['one empty', {'A': [9, 9], 'B': [], 'k': 3}, [[1341714962, 145934324, 2095823278], [], 0.0]],
  ['identical sets',
   {'A': [3, 8, 17], 'B': [17, 8, 3], 'k': 5},
   [[238199717, 8753041, 379637885, 1073841830, 497068074],
    [238199717, 8753041, 379637885, 1073841830, 497068074],
    1.0]],
  ['large values',
   {'A': [1000000004, 7, 99], 'B': [1000000004, 8], 'k': 4},
   [[1282168119, 56169922, 914256891, 1208059556],
    [238199717, 480984718, 431298261, 1073841830],
    0.0]]],
 [['overlapping sets k=4',
   {'A': [38, 155, 109, 179, 16, 111, 170, 114, 19],
    'B': [179, 16, 111, 170, 114, 19, 18, 198, 125, 300],
    'k': 4},
   [[24089818, 330532488, 78683252, 100022], [83636661, 330532488, 78683252, 100022], 0.75]],
  ['overlapping sets k=6',
   {'A': [10, 150, 23, 4, 69, 99, 130, 93, 198],
    'B': [4, 69, 99, 130, 93, 198, 145, 154, 30, 206],
    'k': 6},
   [[119106031, 56169922, 182004004, 402753355, 231506909, 423911817],
    [119106031, 56169922, 182004004, 268535505, 375784655, 423911817],
    0.6667]],
  ['overlapping sets k=8',
   {'A': [58, 185, 14, 110, 196, 126, 6, 158, 12],
    'B': [110, 196, 126, 6, 158, 12, 124, 92, 187, 209],
    'k': 8},
   [[139386205, 618166001, 561641882, 268535474, 303645782, 450762946, 414415, 136172865],
    [178652874, 254039033, 242672003, 268535660, 201389003, 198742465, 414415, 136172865],
    0.25]],
  ['both empty', {'A': [], 'B': [], 'k': 4}, [[], [], None]],
  ['one empty', {'A': [10, 9], 'B': [], 'k': 3}, [[297746560, 145934324, 1612864648], [], 0.0]],
  ['identical sets',
   {'A': [3, 8, 18], 'B': [18, 8, 3], 'k': 5},
   [[238199717, 8753041, 431298261, 1073841830, 497068074],
    [238199717, 8753041, 431298261, 1073841830, 497068074],
    1.0]],
  ['large values',
   {'A': [1000000005, 7, 99], 'B': [1000000005, 8], 'k': 4},
   [[771009766, 56169922, 877498790, 1208059556],
    [238199717, 480984718, 431298261, 1073841830],
    0.0]]]]
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 fixtureActualExpectedOutcome
overlapping sets k=4[[139386205, 618166001, 69675629, 268535474], [51964590, 359609062, 69675629, 268535474], 0.3333][[139386205, 618166001, 69675629, 268535474], [51964590, 359609062, 69675629, 268535474], 0.5]Failed
overlapping sets k=6[[321824033, 87781176, 406660754, 805406688, 307613469, 235695117], [146980803, 87781176, 509981506, 134317810, 307613469, 97986032], 0.2][[321824033, 87781176, 406660754, 805406688, 307613469, 235695117], [146980803, 87781176, 509981506, 134317810, 307613469, 97986032], 0.3333]Failed
overlapping sets k=8[[111511433, 27093348, 898627007, 100332, 76137897, 413810294, 2831830, 930514560], [143183504, 27093348, 898627007, 100332, 110223490, 114735638, 2831830, 417105257], 0.3333][[111511433, 27093348, 898627007, 100332, 76137897, 413810294, 2831830, 930514560], [143183504, 27093348, 898627007, 100332, 110223490, 114735638, 2831830, 417105257], 0.5]Failed
both empty[[], [], None][[], [], None]Passed
one empty[[178652874, 145934324, 1397215521], [], 0.0][[178652874, 145934324, 1397215521], [], 0.0]Passed
identical sets[[238199717, 8753041, 431298261, 268535474, 497068074], [238199717, 8753041, 431298261, 268535474, 497068074], 1.0][[238199717, 8753041, 431298261, 268535474, 497068074], [238199717, 8753041, 431298261, 268535474, 497068074], 1.0]Passed
large values[[651916080, 56169922, 661849663, 1208059556], [238199717, 480984718, 431298261, 1073841830], 0.0][[651916080, 56169922, 661849663, 1208059556], [238199717, 480984718, 431298261, 1073841830], 0.0]Passed

SHA-256 / 9f074e015d82b7e57c7886cbad7a01133db205a03dc7bffd3770dcd4321d8f10

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']
    P = 2147483647
    A = [1103515245, 1812433253, 1664525017, 2013265921, 1597334677, 1566083941, 69069, 22695477]
    Bc = [12345, 1013904223, 7, 99991, 31337, 424242, 1, 3]
    def sig(s):
        return [min((A[i] * v + Bc[i]) % P for v in s) for i in range(k)]
    a, b = x['A'], x['B']
    if not a and not b:
        return [[], [], None]
    if not a or not b:
        return [sig(a) if a else [], sig(b) if b else [], 0.0]
    sa, sb = sig(a), sig(b)
    matches = sum(1 for i in range(k) if sa[i] == sb[i])
    return [sa, sb, round(matches / len(set(sa + sb)), 4)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[['overlapping sets k=4',
   {'A': [185, 180, 93, 45, 14, 71, 154, 36, 166],
    'B': [45, 14, 71, 154, 36, 166, 145, 34, 146, 221],
    'k': 4},
   [[139386205, 618166001, 69675629, 268535474], [51964590, 359609062, 69675629, 268535474], 0.5]],
  ['overlapping sets k=6',
   {'A': [137, 9, 132, 163, 55, 20, 170, 179, 119],
    'B': [163, 55, 20, 170, 179, 119, 47, 41, 24, 251],
    'k': 6},
   [[321824033, 87781176, 406660754, 805406688, 307613469, 235695117],
    [146980803, 87781176, 509981506, 134317810, 307613469, 97986032],
    0.3333]],
  ['overlapping sets k=8',
   {'A': [148, 51, 156, 91, 149, 73, 41, 176, 152],
    'B': [91, 149, 73, 41, 176, 152, 140, 118, 113, 264],
    'k': 8},
   [[111511433, 27093348, 898627007, 100332, 76137897, 413810294, 2831830, 930514560],
    [143183504, 27093348, 898627007, 100332, 110223490, 114735638, 2831830, 417105257],
    0.5]],
  ['both empty', {'A': [], 'B': [], 'k': 4}, [[], [], None]],
  ['one empty', {'A': [6, 9], 'B': [], 'k': 3}, [[178652874, 145934324, 1397215521], [], 0.0]],
  ['identical sets',
   {'A': [3, 8, 14], 'B': [14, 8, 3], 'k': 5},
   [[238199717, 8753041, 431298261, 268535474, 497068074],
    [238199717, 8753041, 431298261, 268535474, 497068074],
    1.0]],
  ['large values',
   {'A': [1000000001, 7, 99], 'B': [1000000001, 8], 'k': 4},
   [[651916080, 56169922, 661849663, 1208059556],
    [238199717, 480984718, 431298261, 1073841830],
    0.0]]],
 [['overlapping sets k=4',
   {'A': [77, 180, 129, 27, 120, 79, 147, 135, 166],
    'B': [27, 120, 79, 147, 135, 166, 178, 114, 109, 210],
    'k': 4},
   [[619558248, 314726861, 27022876, 134317872], [24089818, 314726861, 27022876, 134317872], 0.75]],
  ['overlapping sets k=6',
   {'A': [43, 26, 163, 158, 61, 6, 58, 100, 105],
    'B': [158, 61, 6, 58, 100, 105, 18, 10, 87, 294],
    'k': 6},
   [[178652874, 87781176, 327977509, 268535753, 216447956, 481067515],
    [163463678, 193351205, 604294635, 268535753, 216447956, 272647769],
    0.3333]],
  ['overlapping sets k=8',
   {'A': [119, 125, 38, 35, 22, 123, 186, 169, 60],
    'B': [35, 22, 123, 186, 169, 60, 55, 134, 69, 203],
    'k': 8},
   [[321824033, 24558668, 112328382, 402753417, 72170210, 94532592, 1519519, 499300497],
    [440917719, 24558668, 112328382, 536971019, 72170210, 87884509, 1519519, 312214540],
    0.5]],
  ['both empty', {'A': [], 'B': [], 'k': 4}, [[], [], None]],
  ['one empty', {'A': [7, 9], 'B': [], 'k': 3}, [[1282168119, 145934324, 914256891], [], 0.0]],
  ['identical sets',
   {'A': [3, 8, 15], 'B': [15, 8, 3], 'k': 5},
   [[238199717, 8753041, 431298261, 134317748, 337731375],
    [238199717, 8753041, 431298261, 134317748, 337731375],
    1.0]],
  ['large values',
   {'A': [1000000002, 7, 99], 'B': [1000000002, 8], 'k': 4},
   [[1282168119, 56169922, 178891033, 1208059556],
    [238199717, 480984718, 178891033, 1073841830],
    0.25]]],
 [['overlapping sets k=4',
   {'A': [21, 131, 85, 16, 192, 176, 186, 106, 14],
    'B': [16, 192, 176, 186, 106, 14, 154, 67, 112, 276],
    'k': 4},
   [[416840246, 27093348, 345992755, 100022], [290151962, 27093348, 345992755, 100022], 0.75]],
  ['overlapping sets k=6',
   {'A': [17, 173, 195, 128, 127, 162, 64, 34, 2],
    'B': [128, 127, 162, 64, 34, 2, 4, 31, 120, 261],
    'k': 6},
   [[59559188, 103586803, 200019250, 100115, 95164537, 302952338],
    [59559188, 343803435, 27022876, 100115, 125282443, 302952338],
    0.5]],
  ['overlapping sets k=8',
   {'A': [104, 160, 182, 180, 79, 129, 139, 39, 130],
    'B': [180, 79, 129, 139, 39, 130, 181, 110, 50, 200],
    'k': 8},
   [[87433960, 164274631, 36030499, 100301, 19057977, 161789813, 2693692, 212845964],
    [20292519, 314726861, 45038122, 134317872, 19057977, 161789813, 2693692, 244128109],
    0.375]],
  ['both empty', {'A': [], 'B': [], 'k': 4}, [[], [], None]],
  ['one empty', {'A': [8, 9], 'B': [], 'k': 3}, [[238199717, 145934324, 431298261], [], 0.0]],
  ['identical sets',
   {'A': [3, 8, 16], 'B': [16, 8, 3], 'k': 5},
   [[238199717, 8753041, 431298261, 100022, 497068074],
    [238199717, 8753041, 431298261, 100022, 497068074],
    1.0]],
  ['large values',
   {'A': [1000000003, 7, 99], 'B': [1000000003, 8], 'k': 4},
   [[711462923, 56169922, 914256891, 1208059556],
    [238199717, 318725747, 431298261, 1073841830],
    0.0]]],
 [['overlapping sets k=4',
   {'A': [47, 135, 53, 125, 192, 104, 165, 180, 91],
    'B': [125, 192, 104, 165, 180, 91, 144, 142, 45, 255],
    'k': 4},
   [[325621332, 298921234, 172996381, 100363], [76042063, 11287721, 139351251, 100270], 0.0]],
  ['overlapping sets k=6',
   {'A': [37, 42, 89, 127, 77, 170, 4, 111, 27],
    'B': [127, 77, 170, 4, 111, 27, 20, 114, 70, 228],
    'k': 6},
   [[27887117, 330532488, 78683252, 134317934, 178394676, 329803467],
    [83636661, 330532488, 78683252, 134317934, 144309083, 104634115],
    0.5]],
  ['overlapping sets k=8',
   {'A': [67, 151, 142, 156, 93, 90, 105, 112, 40],
    'B': [156, 93, 90, 105, 112, 40, 161, 43, 152, 287],
    'k': 8},
   [[349698805, 40364295, 9007630, 100208, 76137897, 255898163, 2762761, 235541441],
    [206527646, 193351205, 9007630, 100208, 76137897, 366756119, 2762761, 71150961],
    0.5]],
  ['both empty', {'A': [], 'B': [], 'k': 4}, [[], [], None]],
  ['one empty', {'A': [9, 9], 'B': [], 'k': 3}, [[1341714962, 145934324, 2095823278], [], 0.0]],
  ['identical sets',
   {'A': [3, 8, 17], 'B': [17, 8, 3], 'k': 5},
   [[238199717, 8753041, 379637885, 1073841830, 497068074],
    [238199717, 8753041, 379637885, 1073841830, 497068074],
    1.0]],
  ['large values',
   {'A': [1000000004, 7, 99], 'B': [1000000004, 8], 'k': 4},
   [[1282168119, 56169922, 914256891, 1208059556],
    [238199717, 480984718, 431298261, 1073841830],
    0.0]]],
 [['overlapping sets k=4',
   {'A': [38, 155, 109, 179, 16, 111, 170, 114, 19],
    'B': [179, 16, 111, 170, 114, 19, 18, 198, 125, 300],
    'k': 4},
   [[24089818, 330532488, 78683252, 100022], [83636661, 330532488, 78683252, 100022], 0.75]],
  ['overlapping sets k=6',
   {'A': [10, 150, 23, 4, 69, 99, 130, 93, 198],
    'B': [4, 69, 99, 130, 93, 198, 145, 154, 30, 206],
    'k': 6},
   [[119106031, 56169922, 182004004, 402753355, 231506909, 423911817],
    [119106031, 56169922, 182004004, 268535505, 375784655, 423911817],
    0.6667]],
  ['overlapping sets k=8',
   {'A': [58, 185, 14, 110, 196, 126, 6, 158, 12],
    'B': [110, 196, 126, 6, 158, 12, 124, 92, 187, 209],
    'k': 8},
   [[139386205, 618166001, 561641882, 268535474, 303645782, 450762946, 414415, 136172865],
    [178652874, 254039033, 242672003, 268535660, 201389003, 198742465, 414415, 136172865],
    0.25]],
  ['both empty', {'A': [], 'B': [], 'k': 4}, [[], [], None]],
  ['one empty', {'A': [10, 9], 'B': [], 'k': 3}, [[297746560, 145934324, 1612864648], [], 0.0]],
  ['identical sets',
   {'A': [3, 8, 18], 'B': [18, 8, 3], 'k': 5},
   [[238199717, 8753041, 431298261, 1073841830, 497068074],
    [238199717, 8753041, 431298261, 1073841830, 497068074],
    1.0]],
  ['large values',
   {'A': [1000000005, 7, 99], 'B': [1000000005, 8], 'k': 4},
   [[771009766, 56169922, 877498790, 1208059556],
    [238199717, 480984718, 431298261, 1073841830],
    0.0]]]]
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 fixtureActualExpectedOutcome
overlapping sets k=4[[139386205, 618166001, 69675629, 268535474], [51964590, 359609062, 69675629, 268535474], 0.3333][[139386205, 618166001, 69675629, 268535474], [51964590, 359609062, 69675629, 268535474], 0.5]Failed
overlapping sets k=6[[321824033, 87781176, 406660754, 805406688, 307613469, 235695117], [146980803, 87781176, 509981506, 134317810, 307613469, 97986032], 0.2][[321824033, 87781176, 406660754, 805406688, 307613469, 235695117], [146980803, 87781176, 509981506, 134317810, 307613469, 97986032], 0.3333]Failed
overlapping sets k=8[[111511433, 27093348, 898627007, 100332, 76137897, 413810294, 2831830, 930514560], [143183504, 27093348, 898627007, 100332, 110223490, 114735638, 2831830, 417105257], 0.3333][[111511433, 27093348, 898627007, 100332, 76137897, 413810294, 2831830, 930514560], [143183504, 27093348, 898627007, 100332, 110223490, 114735638, 2831830, 417105257], 0.5]Failed
both empty[[], [], None][[], [], None]Passed
one empty[[178652874, 145934324, 1397215521], [], 0.0][[178652874, 145934324, 1397215521], [], 0.0]Passed
identical sets[[238199717, 8753041, 431298261, 268535474, 497068074], [238199717, 8753041, 431298261, 268535474, 497068074], 1.0][[238199717, 8753041, 431298261, 268535474, 497068074], [238199717, 8753041, 431298261, 268535474, 497068074], 1.0]Passed
large values[[651916080, 56169922, 661849663, 1208059556], [238199717, 480984718, 431298261, 1073841830], 0.0][[651916080, 56169922, 661849663, 1208059556], [238199717, 480984718, 431298261, 1073841830], 0.0]Passed

SHA-256 / b786436c4ae1fff01b4c859a11d2bc5e2833dd96d90fa110553af964ae47af09

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

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.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

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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 2026-09-29T14:48:45.359942+00:00.

Case digest / d9aaf7a9c527ad8c6dc5cbaa3375ddb61d43b3a07e8ec6111e092dd073aa0519