FAILURE MAP
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FA-15241 / Numerics / Open access

Restricted growth strings: exact block count terminal · case 01

The exact restricted growth strings result violates the stated contract at exact block count terminal.

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

ROOT CAUSE

The exact block count terminal step uses m==B instead of m+1==B.

VERIFIED REPAIR

Use m+1==B at the exact block count terminal step.

Unsuccessful approach: The partial repair m+1<=B still violates the exact block count terminal invariant.

Case contract

Input length n (1..6), maximum blocks B>=1; return lexicographic restricted-growth strings a0=0, a_i<=1+max(prefix), using exactly B blocks.

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):
    n,B=x;out=[]
    def visit(prefix,m):
     if len(prefix)==n:
      if m==B:out.append(prefix)
      return
     for v in range(m+2):
      if v>=B:continue
      visit(prefix+[v],max(m,v))
    visit([0],0)
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[([1, 1], [[0]]), ([1, 2], []), ([6, 7], []), ([2, 1], [[0, 0]]), ([2, 2], [[0, 1]]), ([2, 3], []), ([3, 1], [[0, 0, 0]]), ([3, 2], [[0, 0, 1], [0, 1, 0], [0, 1, 1]])], [([2, 1], [[0, 0]]), ([3, 2], [[0, 0, 1], [0, 1, 0], [0, 1, 1]]), ([1, 1], [[0]]), ([6, 7], []), ([5, 4], [[0, 0, 1, 2, 3], [0, 1, 0, 2, 3], [0, 1, 1, 2, 3], [0, 1, 2, 0, 3], [0, 1, 2, 1, 3], [0, 1, 2, 2, 3], [0, 1, 2, 3, 0], [0, 1, 2, 3, 1], [0, 1, 2, 3, 2], [0, 1, 2, 3, 3]]), ([5, 5], [[0, 1, 2, 3, 4]]), ([5, 6], []), ([6, 1], [[0, 0, 0, 0, 0, 0]])], [([2, 2], [[0, 1]]), ([4, 2], [[0, 0, 0, 1], [0, 0, 1, 0], [0, 0, 1, 1], [0, 1, 0, 0], [0, 1, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1]]), ([1, 1], [[0]]), ([6, 7], []), ([3, 3], [[0, 1, 2]]), ([3, 4], []), ([4, 1], [[0, 0, 0, 0]]), ([4, 3], [[0, 0, 1, 2], [0, 1, 0, 2], [0, 1, 1, 2], [0, 1, 2, 0], [0, 1, 2, 1], [0, 1, 2, 2]])], [([3, 1], [[0, 0, 0]]), ([4, 5], []), ([1, 1], [[0]]), ([6, 7], []), ([6, 5], [[0, 0, 1, 2, 3, 4], [0, 1, 0, 2, 3, 4], [0, 1, 1, 2, 3, 4], [0, 1, 2, 0, 3, 4], [0, 1, 2, 1, 3, 4], [0, 1, 2, 2, 3, 4], [0, 1, 2, 3, 0, 4], [0, 1, 2, 3, 1, 4], [0, 1, 2, 3, 2, 4], [0, 1, 2, 3, 3, 4], [0, 1, 2, 3, 4, 0], [0, 1, 2, 3, 4, 1], [0, 1, 2, 3, 4, 2], [0, 1, 2, 3, 4, 3], [0, 1, 2, 3, 4, 4]]), ([6, 6], [[0, 1, 2, 3, 4, 5]]), ([1, 2], []), ([2, 1], [[0, 0]])], [([3, 2], [[0, 0, 1], [0, 1, 0], [0, 1, 1]]), ([5, 4], [[0, 0, 1, 2, 3], [0, 1, 0, 2, 3], [0, 1, 1, 2, 3], [0, 1, 2, 0, 3], [0, 1, 2, 1, 3], [0, 1, 2, 2, 3], [0, 1, 2, 3, 0], [0, 1, 2, 3, 1], [0, 1, 2, 3, 2], [0, 1, 2, 3, 3]]), ([1, 1], [[0]]), ([6, 7], []), ([5, 1], [[0, 0, 0, 0, 0]]), ([5, 2], [[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 0, 1, 1], [0, 0, 1, 0, 0], [0, 0, 1, 0, 1], [0, 0, 1, 1, 0], [0, 0, 1, 1, 1], [0, 1, 0, 0, 0], [0, 1, 0, 0, 1], [0, 1, 0, 1, 0], [0, 1, 0, 1, 1], [0, 1, 1, 0, 0], [0, 1, 1, 0, 1], [0, 1, 1, 1, 0], [0, 1, 1, 1, 1]]), ([5, 3], [[0, 0, 0, 1, 2], [0, 0, 1, 0, 2], [0, 0, 1, 1, 2], [0, 0, 1, 2, 0], [0, 0, 1, 2, 1], [0, 0, 1, 2, 2], [0, 1, 0, 0, 2], [0, 1, 0, 1, 2], [0, 1, 0, 2, 0], [0, 1, 0, 2, 1], [0, 1, 0, 2, 2], [0, 1, 1, 0, 2], [0, 1, 1, 1, 2], [0, 1, 1, 2, 0], [0, 1, 1, 2, 1], [0, 1, 1, 2, 2], [0, 1, 2, 0, 0], [0, 1, 2, 0, 1], [0, 1, 2, 0, 2], [0, 1, 2, 1, 0], [0, 1, 2, 1, 1], [0, 1, 2, 1, 2], [0, 1, 2, 2, 0], [0, 1, 2, 2, 1], [0, 1, 2, 2, 2]]), ([5, 5], [[0, 1, 2, 3, 4]])]]
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[][[0]]Failed
explicit oracle 1[][]Passed
explicit oracle 2[][]Passed
explicit oracle 3[][[0, 0]]Failed
explicit oracle 4[][[0, 1]]Failed
explicit oracle 5[][]Passed
explicit oracle 6[][[0, 0, 0]]Failed
explicit oracle 7[][[0, 0, 1], [0, 1, 0], [0, 1, 1]]Failed

SHA-256 / 68b96cc92c762d8eb88319f1810e946af954f7bdbe657bc9dedd1e732d34cb49

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):
    n,B=x;out=[]
    def visit(prefix,m):
     if len(prefix)==n:
      if m+1<=B:out.append(prefix)
      return
     for v in range(m+2):
      if v>=B:continue
      visit(prefix+[v],max(m,v))
    visit([0],0)
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[([1, 1], [[0]]), ([1, 2], []), ([6, 7], []), ([2, 1], [[0, 0]]), ([2, 2], [[0, 1]]), ([2, 3], []), ([3, 1], [[0, 0, 0]]), ([3, 2], [[0, 0, 1], [0, 1, 0], [0, 1, 1]])], [([2, 1], [[0, 0]]), ([3, 2], [[0, 0, 1], [0, 1, 0], [0, 1, 1]]), ([1, 1], [[0]]), ([6, 7], []), ([5, 4], [[0, 0, 1, 2, 3], [0, 1, 0, 2, 3], [0, 1, 1, 2, 3], [0, 1, 2, 0, 3], [0, 1, 2, 1, 3], [0, 1, 2, 2, 3], [0, 1, 2, 3, 0], [0, 1, 2, 3, 1], [0, 1, 2, 3, 2], [0, 1, 2, 3, 3]]), ([5, 5], [[0, 1, 2, 3, 4]]), ([5, 6], []), ([6, 1], [[0, 0, 0, 0, 0, 0]])], [([2, 2], [[0, 1]]), ([4, 2], [[0, 0, 0, 1], [0, 0, 1, 0], [0, 0, 1, 1], [0, 1, 0, 0], [0, 1, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1]]), ([1, 1], [[0]]), ([6, 7], []), ([3, 3], [[0, 1, 2]]), ([3, 4], []), ([4, 1], [[0, 0, 0, 0]]), ([4, 3], [[0, 0, 1, 2], [0, 1, 0, 2], [0, 1, 1, 2], [0, 1, 2, 0], [0, 1, 2, 1], [0, 1, 2, 2]])], [([3, 1], [[0, 0, 0]]), ([4, 5], []), ([1, 1], [[0]]), ([6, 7], []), ([6, 5], [[0, 0, 1, 2, 3, 4], [0, 1, 0, 2, 3, 4], [0, 1, 1, 2, 3, 4], [0, 1, 2, 0, 3, 4], [0, 1, 2, 1, 3, 4], [0, 1, 2, 2, 3, 4], [0, 1, 2, 3, 0, 4], [0, 1, 2, 3, 1, 4], [0, 1, 2, 3, 2, 4], [0, 1, 2, 3, 3, 4], [0, 1, 2, 3, 4, 0], [0, 1, 2, 3, 4, 1], [0, 1, 2, 3, 4, 2], [0, 1, 2, 3, 4, 3], [0, 1, 2, 3, 4, 4]]), ([6, 6], [[0, 1, 2, 3, 4, 5]]), ([1, 2], []), ([2, 1], [[0, 0]])], [([3, 2], [[0, 0, 1], [0, 1, 0], [0, 1, 1]]), ([5, 4], [[0, 0, 1, 2, 3], [0, 1, 0, 2, 3], [0, 1, 1, 2, 3], [0, 1, 2, 0, 3], [0, 1, 2, 1, 3], [0, 1, 2, 2, 3], [0, 1, 2, 3, 0], [0, 1, 2, 3, 1], [0, 1, 2, 3, 2], [0, 1, 2, 3, 3]]), ([1, 1], [[0]]), ([6, 7], []), ([5, 1], [[0, 0, 0, 0, 0]]), ([5, 2], [[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 0, 1, 1], [0, 0, 1, 0, 0], [0, 0, 1, 0, 1], [0, 0, 1, 1, 0], [0, 0, 1, 1, 1], [0, 1, 0, 0, 0], [0, 1, 0, 0, 1], [0, 1, 0, 1, 0], [0, 1, 0, 1, 1], [0, 1, 1, 0, 0], [0, 1, 1, 0, 1], [0, 1, 1, 1, 0], [0, 1, 1, 1, 1]]), ([5, 3], [[0, 0, 0, 1, 2], [0, 0, 1, 0, 2], [0, 0, 1, 1, 2], [0, 0, 1, 2, 0], [0, 0, 1, 2, 1], [0, 0, 1, 2, 2], [0, 1, 0, 0, 2], [0, 1, 0, 1, 2], [0, 1, 0, 2, 0], [0, 1, 0, 2, 1], [0, 1, 0, 2, 2], [0, 1, 1, 0, 2], [0, 1, 1, 1, 2], [0, 1, 1, 2, 0], [0, 1, 1, 2, 1], [0, 1, 1, 2, 2], [0, 1, 2, 0, 0], [0, 1, 2, 0, 1], [0, 1, 2, 0, 2], [0, 1, 2, 1, 0], [0, 1, 2, 1, 1], [0, 1, 2, 1, 2], [0, 1, 2, 2, 0], [0, 1, 2, 2, 1], [0, 1, 2, 2, 2]]), ([5, 5], [[0, 1, 2, 3, 4]])]]
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[[0]][[0]]Passed
explicit oracle 1[[0]][]Failed
explicit oracle 2[[0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 2], [0, 0, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1], [0, 0, 0, 1, 0, 2], [0, 0, 0, 1, 1, 0], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 2], [0, 0, 0, 1, 2, 0], [0, 0, 0, 1, 2, 1], [0, 0, 0, 1, 2, 2], [0, 0, 0, 1, 2, 3], [0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 1], [0, 0, 1, 0, 0, 2], [0, 0, 1, 0, 1, 0], [0, 0, 1, 0, 1, 1], [0, 0, 1, 0, 1, 2], [0, 0, 1, 0, 2, 0], [0, 0, 1, 0, 2, 1], [0, 0, 1, 0, 2, 2], [0, 0, 1, 0, 2, 3], [0, 0, 1, 1, 0, 0], [0, 0, 1, 1, 0, 1], [0, 0, 1, 1, 0, 2], [0, 0, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 1, 2], [0, 0, 1, 1, 2, 0], [0, 0, 1, 1, 2, 1], [0, 0, 1, 1, 2, 2], [0, 0, 1, 1, 2, 3], [0, 0, 1, 2, 0, 0], [0, 0, 1, 2, 0, 1], [0, 0, 1, 2, 0, 2], [0, 0, 1, 2, 0, 3], [0, 0, 1, 2, 1, 0], [0, 0, 1, 2, 1, 1], [0, 0, 1, 2, 1, 2], [0, 0, 1, 2, 1, 3], [0, 0, 1, 2, 2, 0], [0, 0, 1, 2, 2, 1], [0, 0, 1, 2, 2, 2], [0, 0, 1, 2, 2, 3], [0, 0, 1, 2, 3, 0], [0, 0, 1, 2, 3, 1], [0, 0, 1, 2, 3, 2], [0, 0, 1, 2, 3, 3], [0, 0, 1, 2, 3, 4], [0, 1, 0, 0, 0, 0], [0, 1, 0, 0, 0, 1], [0, 1, 0, 0, 0, 2], [0, 1, 0, 0, 1, 0], [0, 1, 0, 0, 1, 1], [0, 1, 0, 0, 1, 2], [0, 1, 0, 0, 2, 0], [0, 1, 0, 0, 2, 1], [0, 1, 0, 0, 2, 2], [0, 1, 0, 0, 2, 3], [0, 1, 0, 1, 0, 0], [0, 1, 0, 1, 0, 1], [0, 1, 0, 1, 0, 2], [0, 1, 0, 1, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 0, 1, 1, 2], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 2, 1], [0, 1, 0, 1, 2, 2], [0, 1, 0, 1, 2, 3], [0, 1, 0, 2, 0, 0], [0, 1, 0, 2, 0, 1], [0, 1, 0, 2, 0, 2], [0, 1, 0, 2, 0, 3], [0, 1, 0, 2, 1, 0], [0, 1, 0, 2, 1, 1], [0, 1, 0, 2, 1, 2], [0, 1, 0, 2, 1, 3], [0, 1, 0, 2, 2, 0], [0, 1, 0, 2, 2, 1], [0, 1, 0, 2, 2, 2], [0, 1, 0, 2, 2, 3], [0, 1, 0, 2, 3, 0], [0, 1, 0, 2, 3, 1], [0, 1, 0, 2, 3, 2], [0, 1, 0, 2, 3, 3], [0, 1, 0, 2, 3, 4], [0, 1, 1, 0, 0, 0], [0, 1, 1, 0, 0, 1], [0, 1, 1, 0, 0, 2], [0, 1, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 1, 0, 1, 2], [0, 1, 1, 0, 2, 0], [0, 1, 1, 0, 2, 1], [0, 1, 1, 0, 2, 2], [0, 1, 1, 0, 2, 3], [0, 1, 1, 1, 0, 0], [0, 1, 1, 1, 0, 1], [0, 1, 1, 1, 0, 2], [0, 1, 1, 1, 1, 0], [0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 1, 2], [0, 1, 1, 1, 2, 0], [0, 1, 1, 1, 2, 1], [0, 1, 1, 1, 2, 2], [0, 1, 1, 1, 2, 3], [0, 1, 1, 2, 0, 0], [0, 1, 1, 2, 0, 1], [0, 1, 1, 2, 0, 2], [0, 1, 1, 2, 0, 3], [0, 1, 1, 2, 1, 0], [0, 1, 1, 2, 1, 1], [0, 1, 1, 2, 1, 2], [0, 1, 1, 2, 1, 3], [0, 1, 1, 2, 2, 0], [0, 1, 1, 2, 2, 1], [0, 1, 1, 2, 2, 2], [0, 1, 1, 2, 2, 3], [0, 1, 1, 2, 3, 0], [0, 1, 1, 2, 3, 1], [0, 1, 1, 2, 3, 2], [0, 1, 1, 2, 3, 3], [0, 1, 1, 2, 3, 4], [0, 1, 2, 0, 0, 0], [0, 1, 2, 0, 0, 1], [0, 1, 2, 0, 0, 2], [0, 1, 2, 0, 0, 3], [0, 1, 2, 0, 1, 0], [0, 1, 2, 0, 1, 1], [0, 1, 2, 0, 1, 2], [0, 1, 2, 0, 1, 3], [0, 1, 2, 0, 2, 0], [0, 1, 2, 0, 2, 1], [0, 1, 2, 0, 2, 2], [0, 1, 2, 0, 2, 3], [0, 1, 2, 0, 3, 0], [0, 1, 2, 0, 3, 1], [0, 1, 2, 0, 3, 2], [0, 1, 2, 0, 3, 3], [0, 1, 2, 0, 3, 4], [0, 1, 2, 1, 0, 0], [0, 1, 2, 1, 0, 1], [0, 1, 2, 1, 0, 2], [0, 1, 2, 1, 0, 3], [0, 1, 2, 1, 1, 0], [0, 1, 2, 1, 1, 1], [0, 1, 2, 1, 1, 2], [0, 1, 2, 1, 1, 3], [0, 1, 2, 1, 2, 0], [0, 1, 2, 1, 2, 1], [0, 1, 2, 1, 2, 2], [0, 1, 2, 1, 2, 3], [0, 1, 2, 1, 3, 0], [0, 1, 2, 1, 3, 1], [0, 1, 2, 1, 3, 2], [0, 1, 2, 1, 3, 3], [0, 1, 2, 1, 3, 4], [0, 1, 2, 2, 0, 0], [0, 1, 2, 2, 0, 1], [0, 1, 2, 2, 0, 2], [0, 1, 2, 2, 0, 3], [0, 1, 2, 2, 1, 0], [0, 1, 2, 2, 1, 1], [0, 1, 2, 2, 1, 2], [0, 1, 2, 2, 1, 3], [0, 1, 2, 2, 2, 0], [0, 1, 2, 2, 2, 1], [0, 1, 2, 2, 2, 2], [0, 1, 2, 2, 2, 3], [0, 1, 2, 2, 3, 0], [0, 1, 2, 2, 3, 1], [0, 1, 2, 2, 3, 2], [0, 1, 2, 2, 3, 3], [0, 1, 2, 2, 3, 4], [0, 1, 2, 3, 0, 0], [0, 1, 2, 3, 0, 1], [0, 1, 2, 3, 0, 2], [0, 1, 2, 3, 0, 3], [0, 1, 2, 3, 0, 4], [0, 1, 2, 3, 1, 0], [0, 1, 2, 3, 1, 1], [0, 1, 2, 3, 1, 2], [0, 1, 2, 3, 1, 3], [0, 1, 2, 3, 1, 4], [0, 1, 2, 3, 2, 0], [0, 1, 2, 3, 2, 1], [0, 1, 2, 3, 2, 2], [0, 1, 2, 3, 2, 3], [0, 1, 2, 3, 2, 4], [0, 1, 2, 3, 3, 0], [0, 1, 2, 3, 3, 1], [0, 1, 2, 3, 3, 2], [0, 1, 2, 3, 3, 3], [0, 1, 2, 3, 3, 4], [0, 1, 2, 3, 4, 0], [0, 1, 2, 3, 4, 1], [0, 1, 2, 3, 4, 2], [0, 1, 2, 3, 4, 3], [0, 1, 2, 3, 4, 4], [0, 1, 2, 3, 4, 5]][]Failed
explicit oracle 3[[0, 0]][[0, 0]]Passed
explicit oracle 4[[0, 0], [0, 1]][[0, 1]]Failed
explicit oracle 5[[0, 0], [0, 1]][]Failed
explicit oracle 6[[0, 0, 0]][[0, 0, 0]]Passed
explicit oracle 7[[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 1, 1]][[0, 0, 1], [0, 1, 0], [0, 1, 1]]Failed

SHA-256 / a2de408765d804734e9fdd3ec3c4f9c9b9badce298bc3dc7924cf348b2ac39e5

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json
import math
import itertools
from fractions import Fraction
N = 1
observations = []
def solve(x):
    n,B=x;out=[]
    def visit(prefix,m):
     if len(prefix)==n:
      if m+1==B:out.append(prefix)
      return
     for v in range(m+2):
      if v>=B:continue
      visit(prefix+[v],max(m,v))
    visit([0],0)
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[([1, 1], [[0]]), ([1, 2], []), ([6, 7], []), ([2, 1], [[0, 0]]), ([2, 2], [[0, 1]]), ([2, 3], []), ([3, 1], [[0, 0, 0]]), ([3, 2], [[0, 0, 1], [0, 1, 0], [0, 1, 1]])], [([2, 1], [[0, 0]]), ([3, 2], [[0, 0, 1], [0, 1, 0], [0, 1, 1]]), ([1, 1], [[0]]), ([6, 7], []), ([5, 4], [[0, 0, 1, 2, 3], [0, 1, 0, 2, 3], [0, 1, 1, 2, 3], [0, 1, 2, 0, 3], [0, 1, 2, 1, 3], [0, 1, 2, 2, 3], [0, 1, 2, 3, 0], [0, 1, 2, 3, 1], [0, 1, 2, 3, 2], [0, 1, 2, 3, 3]]), ([5, 5], [[0, 1, 2, 3, 4]]), ([5, 6], []), ([6, 1], [[0, 0, 0, 0, 0, 0]])], [([2, 2], [[0, 1]]), ([4, 2], [[0, 0, 0, 1], [0, 0, 1, 0], [0, 0, 1, 1], [0, 1, 0, 0], [0, 1, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1]]), ([1, 1], [[0]]), ([6, 7], []), ([3, 3], [[0, 1, 2]]), ([3, 4], []), ([4, 1], [[0, 0, 0, 0]]), ([4, 3], [[0, 0, 1, 2], [0, 1, 0, 2], [0, 1, 1, 2], [0, 1, 2, 0], [0, 1, 2, 1], [0, 1, 2, 2]])], [([3, 1], [[0, 0, 0]]), ([4, 5], []), ([1, 1], [[0]]), ([6, 7], []), ([6, 5], [[0, 0, 1, 2, 3, 4], [0, 1, 0, 2, 3, 4], [0, 1, 1, 2, 3, 4], [0, 1, 2, 0, 3, 4], [0, 1, 2, 1, 3, 4], [0, 1, 2, 2, 3, 4], [0, 1, 2, 3, 0, 4], [0, 1, 2, 3, 1, 4], [0, 1, 2, 3, 2, 4], [0, 1, 2, 3, 3, 4], [0, 1, 2, 3, 4, 0], [0, 1, 2, 3, 4, 1], [0, 1, 2, 3, 4, 2], [0, 1, 2, 3, 4, 3], [0, 1, 2, 3, 4, 4]]), ([6, 6], [[0, 1, 2, 3, 4, 5]]), ([1, 2], []), ([2, 1], [[0, 0]])], [([3, 2], [[0, 0, 1], [0, 1, 0], [0, 1, 1]]), ([5, 4], [[0, 0, 1, 2, 3], [0, 1, 0, 2, 3], [0, 1, 1, 2, 3], [0, 1, 2, 0, 3], [0, 1, 2, 1, 3], [0, 1, 2, 2, 3], [0, 1, 2, 3, 0], [0, 1, 2, 3, 1], [0, 1, 2, 3, 2], [0, 1, 2, 3, 3]]), ([1, 1], [[0]]), ([6, 7], []), ([5, 1], [[0, 0, 0, 0, 0]]), ([5, 2], [[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 0, 1, 1], [0, 0, 1, 0, 0], [0, 0, 1, 0, 1], [0, 0, 1, 1, 0], [0, 0, 1, 1, 1], [0, 1, 0, 0, 0], [0, 1, 0, 0, 1], [0, 1, 0, 1, 0], [0, 1, 0, 1, 1], [0, 1, 1, 0, 0], [0, 1, 1, 0, 1], [0, 1, 1, 1, 0], [0, 1, 1, 1, 1]]), ([5, 3], [[0, 0, 0, 1, 2], [0, 0, 1, 0, 2], [0, 0, 1, 1, 2], [0, 0, 1, 2, 0], [0, 0, 1, 2, 1], [0, 0, 1, 2, 2], [0, 1, 0, 0, 2], [0, 1, 0, 1, 2], [0, 1, 0, 2, 0], [0, 1, 0, 2, 1], [0, 1, 0, 2, 2], [0, 1, 1, 0, 2], [0, 1, 1, 1, 2], [0, 1, 1, 2, 0], [0, 1, 1, 2, 1], [0, 1, 1, 2, 2], [0, 1, 2, 0, 0], [0, 1, 2, 0, 1], [0, 1, 2, 0, 2], [0, 1, 2, 1, 0], [0, 1, 2, 1, 1], [0, 1, 2, 1, 2], [0, 1, 2, 2, 0], [0, 1, 2, 2, 1], [0, 1, 2, 2, 2]]), ([5, 5], [[0, 1, 2, 3, 4]])]]
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[[0]][[0]]Passed
explicit oracle 1[][]Passed
explicit oracle 2[][]Passed
explicit oracle 3[[0, 0]][[0, 0]]Passed
explicit oracle 4[[0, 1]][[0, 1]]Passed
explicit oracle 5[][]Passed
explicit oracle 6[[0, 0, 0]][[0, 0, 0]]Passed
explicit oracle 7[[0, 0, 1], [0, 1, 0], [0, 1, 1]][[0, 0, 1], [0, 1, 0], [0, 1, 1]]Passed

SHA-256 / 4217b140a930d01f9e050e930594f1745ef07e3b2daf996d1585b73aefba87d4

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 2026-09-29T14:39:24.751085+00:00.

Case digest / 998b9b5f1e134da180ac70a4f40d04e207934a380ea402f92bb44ce50d4e9bbc