FAILURE MAP
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FA-14561 / Numerics / Open access

Calkin wilf successors: successor coordinate transfer · case 01

The exact calkin wilf successors result violates the stated contract at successor coordinate transfer.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The successor coordinate transfer step uses p,den instead of q,den.

THE FAILURE

The successor coordinate transfer step uses p,den instead of q,den.

Unsuccessful approach: The partial repair den,q still violates the successor coordinate transfer invariant.

Case contract

Input positive count k<=50; return first k reduced positive rationals in Calkin-Wilf breadth-first order.

Why this case matters

Exact discrete arithmetic with observable algorithmic state; no floating point approximation is used.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
import itertools
from fractions import Fraction
N = 1
observations = []
def solve(x):
    p,q=1,1
    out=[]
    for _ in range(x):
     out.append([p,q])
     if q==0:return None
     a=p//q
     den=(2*a+1)*q-p
     p,q=p,den
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[(3, [[1, 1], [1, 2], [2, 1]]), (2, [[1, 1], [1, 2]]), (1, [[1, 1]]), (50, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7], [7, 10], [10, 3], [3, 11], [11, 8], [8, 13], [13, 5], [5, 12], [12, 7], [7, 9], [9, 2], [2, 9], [9, 7], [7, 12]]), (4, [[1, 1], [1, 2], [2, 1], [1, 3]]), (5, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2]]), (6, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3]]), (7, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1]])], [(4, [[1, 1], [1, 2], [2, 1], [1, 3]]), (5, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2]]), (1, [[1, 1]]), (50, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7], [7, 10], [10, 3], [3, 11], [11, 8], [8, 13], [13, 5], [5, 12], [12, 7], [7, 9], [9, 2], [2, 9], [9, 7], [7, 12]]), (18, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7]]), (19, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3]]), (20, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8]]), (21, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5]])], [(5, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2]]), (8, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4]]), (1, [[1, 1]]), (50, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7], [7, 10], [10, 3], [3, 11], [11, 8], [8, 13], [13, 5], [5, 12], [12, 7], [7, 9], [9, 2], [2, 9], [9, 7], [7, 12]]), (35, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4]]), (36, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11]]), (37, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7]]), (38, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7], [7, 10]])], [(6, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3]]), (11, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2]]), (1, [[1, 1]]), (50, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7], [7, 10], [10, 3], [3, 11], [11, 8], [8, 13], [13, 5], [5, 12], [12, 7], [7, 9], [9, 2], [2, 9], [9, 7], [7, 12]]), (2, [[1, 1], [1, 2]]), (3, [[1, 1], [1, 2], [2, 1]]), (4, [[1, 1], [1, 2], [2, 1], [1, 3]]), (5, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2]])], [(7, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1]]), (14, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4]]), (1, [[1, 1]]), (50, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7], [7, 10], [10, 3], [3, 11], [11, 8], [8, 13], [13, 5], [5, 12], [12, 7], [7, 9], [9, 2], [2, 9], [9, 7], [7, 12]]), (19, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3]]), (20, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8]]), (21, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5]]), (22, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7]])]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check("explicit oracle %d" % i, 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
explicit oracle 0[[1, 1], [1, 2], [1, 1]][[1, 1], [1, 2], [2, 1]]Failed
explicit oracle 1[[1, 1], [1, 2]][[1, 1], [1, 2]]Passed
explicit oracle 2[[1, 1]][[1, 1]]Passed
explicit oracle 3[[1, 1], [1, 2], [1, 1], [1, 2], [1, 1], [1, 2], [1, 1], [1, 2], [1, 1], [1, 2], [1, 1], [1, 2], [1, 1], [1, 2], [1, 1], [1, 2], [1, 1], [1, 2], [1, 1], [1, 2], [1, 1], [1, 2], [1, 1], [1, 2], [1, 1], [1, 2], [1, 1], [1, 2], [1, 1], [1, 2], [1, 1], [1, 2], [1, 1], [1, 2], [1, 1], [1, 2], [1, 1], [1, 2], [1, 1], [1, 2], [1, 1], [1, 2], [1, 1], [1, 2], [1, 1], [1, 2], [1, 1], [1, 2], [1, 1], [1, 2]][[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7], [7, 10], [10, 3], [3, 11], [11, 8], [8, 13], [13, 5], [5, 12], [12, 7], [7, 9], [9, 2], [2, 9], [9, 7], [7, 12]]Failed
explicit oracle 4[[1, 1], [1, 2], [1, 1], [1, 2]][[1, 1], [1, 2], [2, 1], [1, 3]]Failed
explicit oracle 5[[1, 1], [1, 2], [1, 1], [1, 2], [1, 1]][[1, 1], [1, 2], [2, 1], [1, 3], [3, 2]]Failed
explicit oracle 6[[1, 1], [1, 2], [1, 1], [1, 2], [1, 1], [1, 2]][[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3]]Failed
explicit oracle 7[[1, 1], [1, 2], [1, 1], [1, 2], [1, 1], [1, 2], [1, 1]][[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1]]Failed

SHA-256 / ca1deabb669ad0a52f84541c8116ed71358df443cb5b09ea16d0dd9e097dd536

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
import itertools
from fractions import Fraction
N = 1
observations = []
def solve(x):
    p,q=1,1
    out=[]
    for _ in range(x):
     out.append([p,q])
     if q==0:return None
     a=p//q
     den=(2*a+1)*q-p
     p,q=den,q
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[(3, [[1, 1], [1, 2], [2, 1]]), (2, [[1, 1], [1, 2]]), (1, [[1, 1]]), (50, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7], [7, 10], [10, 3], [3, 11], [11, 8], [8, 13], [13, 5], [5, 12], [12, 7], [7, 9], [9, 2], [2, 9], [9, 7], [7, 12]]), (4, [[1, 1], [1, 2], [2, 1], [1, 3]]), (5, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2]]), (6, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3]]), (7, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1]])], [(4, [[1, 1], [1, 2], [2, 1], [1, 3]]), (5, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2]]), (1, [[1, 1]]), (50, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7], [7, 10], [10, 3], [3, 11], [11, 8], [8, 13], [13, 5], [5, 12], [12, 7], [7, 9], [9, 2], [2, 9], [9, 7], [7, 12]]), (18, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7]]), (19, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3]]), (20, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8]]), (21, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5]])], [(5, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2]]), (8, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4]]), (1, [[1, 1]]), (50, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7], [7, 10], [10, 3], [3, 11], [11, 8], [8, 13], [13, 5], [5, 12], [12, 7], [7, 9], [9, 2], [2, 9], [9, 7], [7, 12]]), (35, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4]]), (36, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11]]), (37, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7]]), (38, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7], [7, 10]])], [(6, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3]]), (11, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2]]), (1, [[1, 1]]), (50, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7], [7, 10], [10, 3], [3, 11], [11, 8], [8, 13], [13, 5], [5, 12], [12, 7], [7, 9], [9, 2], [2, 9], [9, 7], [7, 12]]), (2, [[1, 1], [1, 2]]), (3, [[1, 1], [1, 2], [2, 1]]), (4, [[1, 1], [1, 2], [2, 1], [1, 3]]), (5, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2]])], [(7, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1]]), (14, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4]]), (1, [[1, 1]]), (50, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7], [7, 10], [10, 3], [3, 11], [11, 8], [8, 13], [13, 5], [5, 12], [12, 7], [7, 9], [9, 2], [2, 9], [9, 7], [7, 12]]), (19, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3]]), (20, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8]]), (21, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5]]), (22, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7]])]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check("explicit oracle %d" % i, 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
explicit oracle 0[[1, 1], [2, 1], [3, 1]][[1, 1], [1, 2], [2, 1]]Failed
explicit oracle 1[[1, 1], [2, 1]][[1, 1], [1, 2]]Failed
explicit oracle 2[[1, 1]][[1, 1]]Passed
explicit oracle 3[[1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1], [8, 1], [9, 1], [10, 1], [11, 1], [12, 1], [13, 1], [14, 1], [15, 1], [16, 1], [17, 1], [18, 1], [19, 1], [20, 1], [21, 1], [22, 1], [23, 1], [24, 1], [25, 1], [26, 1], [27, 1], [28, 1], [29, 1], [30, 1], [31, 1], [32, 1], [33, 1], [34, 1], [35, 1], [36, 1], [37, 1], [38, 1], [39, 1], [40, 1], [41, 1], [42, 1], [43, 1], [44, 1], [45, 1], [46, 1], [47, 1], [48, 1], [49, 1], [50, 1]][[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7], [7, 10], [10, 3], [3, 11], [11, 8], [8, 13], [13, 5], [5, 12], [12, 7], [7, 9], [9, 2], [2, 9], [9, 7], [7, 12]]Failed
explicit oracle 4[[1, 1], [2, 1], [3, 1], [4, 1]][[1, 1], [1, 2], [2, 1], [1, 3]]Failed
explicit oracle 5[[1, 1], [2, 1], [3, 1], [4, 1], [5, 1]][[1, 1], [1, 2], [2, 1], [1, 3], [3, 2]]Failed
explicit oracle 6[[1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1]][[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3]]Failed
explicit oracle 7[[1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1]][[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1]]Failed

SHA-256 / 7387dc531967dc835507292b15b4c0f93ce31b4d2c97d1c8c33fcac20c9d3d3d

HELD IN THE MEMBER ARCHIVE

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

This mechanism has 8 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. Inputs are restricted to the explicit contract; this is not a production algebra library. 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 2026-09-29T14:39:18.168421+00:00.

Case digest / 4f30556084e658dd55d9030af662c15f0ba73662051078176be783e118661235