FAILURE MAP
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FA-83096 / Go territory scoring / Open access

The board edge counts as liberties · case 01

Edge and corner chains report extra liberties.

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

ROOT CAUSE

Off-board neighbours pass the liberty test.

THE FAILURE

Off-board neighbours pass the liberty test.

Unsuccessful approach: An off-by-one upper bound still counts the bottom and right edges as liberties.

Case contract

Input [board, row, col]. Return [colour, chain_size, distinct_orthogonal_empty_liberties]; an empty point gives [".", 0, 0].

Why this case matters

Go servers and scoring tools compute this value automatically; a wrong answer changes a game result.

1 / The failure

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

N = 1
observations = []
def solve(x):
    board, r, c = x
    n = len(board)
    m = len(board[0])
    col = board[r][c]
    if col == '.':
        return ['.', 0, 0]
    chain = [(r, c)]
    k = 0
    while k < len(chain):
        i, j = chain[k]
        k += 1
        for p, q in ((i + 1, j), (i - 1, j), (i, j + 1), (i, j - 1)):
            if 0 <= p < n and 0 <= q < m and board[p][q] == col and (p, q) not in chain:
                chain.append((p, q))
    libs = set()
    for i, j in chain:
        for p, q in ((i, j - 1), (i, j + 1), (i - 1, j), (i + 1, j)):
            if not (0 <= p < n and 0 <= q < m) or board[p][q] == '.':
                libs.add((p, q))
    return [col, len(chain), len(libs)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[[['.B.', 'B.B', '.B.'], 1, 0], ['B', 1, 3]], [[['B..W', 'B..W', 'B..W', 'B..W'], 3, 3], ['W', 4, 4]], [[['B..W', 'B..W', 'B..W', 'B..W'], 3, 2], ['.', 0, 0]], [[['.BW.', '.BW.', '.BW.', '.BW.'], 3, 2], ['W', 4, 4]], [[['.BW.', '.BW.', '.BW.', '.BW.'], 3, 1], ['B', 4, 4]], [[['.BW.', '.BW.', '.BW.', '.BW.'], 1, 1], ['B', 4, 4]], [[['.BW.', '.BW.', '.BW.', '.BW.'], 2, 0], ['.', 0, 0]], [[['..B..', '..B..', 'BBBBB', 'WWWWW', '..W..'], 3, 3], ['W', 6, 4]]], [[[['B..W', 'B..W', 'B..W', 'B..W'], 1, 0], ['B', 4, 4]], [[['..B..', '..B..', 'BBBBB', 'WWWWW', '..W..'], 3, 1], ['W', 6, 4]], [[['..B..', '..B..', 'BBBBB', 'WWWWW', '..W..'], 1, 2], ['B', 7, 6]], [[['..B..', '..B..', 'BBBBB', 'WWWWW', '..W..'], 1, 1], ['.', 0, 0]], [[['B.B.W', '.B.W.', 'B.BW.', 'BBW.W', '..W..'], 1, 1], ['B', 1, 4]], [[['B.B.W', '.B.W.', 'B.BW.', 'BBW.W', '..W..'], 2, 2], ['B', 1, 2]], [[['B.B.W', '.B.W.', 'B.BW.', 'BBW.W', '..W..'], 3, 0], ['B', 3, 4]], [[['W....', '.....', '.....', '.....', '....B'], 4, 4], ['B', 1, 2]]], [[[['.BW.', '.BW.', '.BW.', '.BW.'], 3, 2], ['W', 4, 4]], [[['W....', '.....', '.....', '.....', '....B'], 4, 4], ['B', 1, 2]], [[['W....', '.....', '.....', '.....', '....B'], 0, 0], ['W', 1, 2]], [[['W....', '.....', '.....', '.....', '....B'], 1, 0], ['.', 0, 0]], [[['.W.B.', 'W.WB.', '.WB..', 'WB...', 'B....'], 2, 1], ['W', 1, 2]], [[['.W.B.', 'W.WB.', '.WB..', 'WB...', 'B....'], 4, 0], ['B', 1, 1]], [[['.W.B.', 'W.WB.', '.WB..', 'WB...', 'B....'], 3, 0], ['W', 1, 1]], [[['WWW', 'W.W', 'WWW'], 2, 1], ['W', 8, 1]]], [[[['..B..', '..B..', 'BBBBB', 'WWWWW', '..W..'], 3, 3], ['W', 6, 4]], [[['BBBB', 'B..B', 'B..B', 'BBBB'], 3, 0], ['B', 12, 4]], [[['BBBB', 'B..B', 'B..B', 'BBBB'], 3, 2], ['B', 12, 4]], [[['BBBB', 'B..B', 'B..B', 'BBBB'], 0, 1], ['B', 12, 4]], [[['BBBB', 'B..B', 'B..B', 'BBBB'], 2, 2], ['.', 0, 0]], [[['WWW', 'W.W', 'WWW'], 2, 1], ['W', 8, 1]], [[['WWW', 'W.W', 'WWW'], 1, 2], ['W', 8, 1]], [[['.B...', 'B....', '.....', '....W', '...W.'], 4, 3], ['W', 1, 3]]], [[[['B.B.W', '.B.W.', 'B.BW.', 'BBW.W', '..W..'], 3, 0], ['B', 3, 4]], [[['WWW', 'W.W', 'WWW'], 1, 1], ['.', 0, 0]], [[['B.W', '...', 'W.B'], 0, 0], ['B', 1, 2]], [[['B.W', '...', 'W.B'], 0, 2], ['W', 1, 2]], [[['B.W', '...', 'W.B'], 2, 2], ['B', 1, 2]], [[['B.W', '...', 'W.B'], 1, 2], ['.', 0, 0]], [[['.B...', 'B....', '.....', '....W', '...W.'], 4, 3], ['W', 1, 3]], [[['WB.B', 'B.B.', '.B..', 'B...'], 3, 0], ['B', 1, 2]]]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check("chain case %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
chain case 0['B', 1, 4]['B', 1, 3]Failed
chain case 1['W', 4, 10]['W', 4, 4]Failed
chain case 2['.', 0, 0]['.', 0, 0]Passed
chain case 3['W', 4, 6]['W', 4, 4]Failed
chain case 4['B', 4, 6]['B', 4, 4]Failed
chain case 5['B', 4, 6]['B', 4, 4]Failed
chain case 6['.', 0, 0]['.', 0, 0]Passed
chain case 7['W', 6, 7]['W', 6, 4]Failed

SHA-256 / 1cfb264bc3efce941cc250b8f469ee006f4d60ea4bf8599e8bfd905de0d88611

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(x):
    board, r, c = x
    n = len(board)
    m = len(board[0])
    col = board[r][c]
    if col == '.':
        return ['.', 0, 0]
    chain = [(r, c)]
    k = 0
    while k < len(chain):
        i, j = chain[k]
        k += 1
        for p, q in ((i + 1, j), (i - 1, j), (i, j + 1), (i, j - 1)):
            if 0 <= p < n and 0 <= q < m and board[p][q] == col and (p, q) not in chain:
                chain.append((p, q))
    libs = set()
    for i, j in chain:
        for p, q in ((i, j - 1), (i, j + 1), (i - 1, j), (i + 1, j)):
            if 0 <= p <= n and 0 <= q <= m and (p == n or q == m or board[p][q] == '.'):
                libs.add((p, q))
    return [col, len(chain), len(libs)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[[['.B.', 'B.B', '.B.'], 1, 0], ['B', 1, 3]], [[['B..W', 'B..W', 'B..W', 'B..W'], 3, 3], ['W', 4, 4]], [[['B..W', 'B..W', 'B..W', 'B..W'], 3, 2], ['.', 0, 0]], [[['.BW.', '.BW.', '.BW.', '.BW.'], 3, 2], ['W', 4, 4]], [[['.BW.', '.BW.', '.BW.', '.BW.'], 3, 1], ['B', 4, 4]], [[['.BW.', '.BW.', '.BW.', '.BW.'], 1, 1], ['B', 4, 4]], [[['.BW.', '.BW.', '.BW.', '.BW.'], 2, 0], ['.', 0, 0]], [[['..B..', '..B..', 'BBBBB', 'WWWWW', '..W..'], 3, 3], ['W', 6, 4]]], [[[['B..W', 'B..W', 'B..W', 'B..W'], 1, 0], ['B', 4, 4]], [[['..B..', '..B..', 'BBBBB', 'WWWWW', '..W..'], 3, 1], ['W', 6, 4]], [[['..B..', '..B..', 'BBBBB', 'WWWWW', '..W..'], 1, 2], ['B', 7, 6]], [[['..B..', '..B..', 'BBBBB', 'WWWWW', '..W..'], 1, 1], ['.', 0, 0]], [[['B.B.W', '.B.W.', 'B.BW.', 'BBW.W', '..W..'], 1, 1], ['B', 1, 4]], [[['B.B.W', '.B.W.', 'B.BW.', 'BBW.W', '..W..'], 2, 2], ['B', 1, 2]], [[['B.B.W', '.B.W.', 'B.BW.', 'BBW.W', '..W..'], 3, 0], ['B', 3, 4]], [[['W....', '.....', '.....', '.....', '....B'], 4, 4], ['B', 1, 2]]], [[[['.BW.', '.BW.', '.BW.', '.BW.'], 3, 2], ['W', 4, 4]], [[['W....', '.....', '.....', '.....', '....B'], 4, 4], ['B', 1, 2]], [[['W....', '.....', '.....', '.....', '....B'], 0, 0], ['W', 1, 2]], [[['W....', '.....', '.....', '.....', '....B'], 1, 0], ['.', 0, 0]], [[['.W.B.', 'W.WB.', '.WB..', 'WB...', 'B....'], 2, 1], ['W', 1, 2]], [[['.W.B.', 'W.WB.', '.WB..', 'WB...', 'B....'], 4, 0], ['B', 1, 1]], [[['.W.B.', 'W.WB.', '.WB..', 'WB...', 'B....'], 3, 0], ['W', 1, 1]], [[['WWW', 'W.W', 'WWW'], 2, 1], ['W', 8, 1]]], [[[['..B..', '..B..', 'BBBBB', 'WWWWW', '..W..'], 3, 3], ['W', 6, 4]], [[['BBBB', 'B..B', 'B..B', 'BBBB'], 3, 0], ['B', 12, 4]], [[['BBBB', 'B..B', 'B..B', 'BBBB'], 3, 2], ['B', 12, 4]], [[['BBBB', 'B..B', 'B..B', 'BBBB'], 0, 1], ['B', 12, 4]], [[['BBBB', 'B..B', 'B..B', 'BBBB'], 2, 2], ['.', 0, 0]], [[['WWW', 'W.W', 'WWW'], 2, 1], ['W', 8, 1]], [[['WWW', 'W.W', 'WWW'], 1, 2], ['W', 8, 1]], [[['.B...', 'B....', '.....', '....W', '...W.'], 4, 3], ['W', 1, 3]]], [[[['B.B.W', '.B.W.', 'B.BW.', 'BBW.W', '..W..'], 3, 0], ['B', 3, 4]], [[['WWW', 'W.W', 'WWW'], 1, 1], ['.', 0, 0]], [[['B.W', '...', 'W.B'], 0, 0], ['B', 1, 2]], [[['B.W', '...', 'W.B'], 0, 2], ['W', 1, 2]], [[['B.W', '...', 'W.B'], 2, 2], ['B', 1, 2]], [[['B.W', '...', 'W.B'], 1, 2], ['.', 0, 0]], [[['.B...', 'B....', '.....', '....W', '...W.'], 4, 3], ['W', 1, 3]], [[['WB.B', 'B.B.', '.B..', 'B...'], 3, 0], ['B', 1, 2]]]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check("chain case %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
chain case 0['B', 1, 3]['B', 1, 3]Passed
chain case 1['W', 4, 9]['W', 4, 4]Failed
chain case 2['.', 0, 0]['.', 0, 0]Passed
chain case 3['W', 4, 5]['W', 4, 4]Failed
chain case 4['B', 4, 5]['B', 4, 4]Failed
chain case 5['B', 4, 5]['B', 4, 4]Failed
chain case 6['.', 0, 0]['.', 0, 0]Passed
chain case 7['W', 6, 6]['W', 6, 4]Failed

SHA-256 / eb1cfdcd9326ef08de1016eacfd2dfebe197e4b9d5eaa31cc8bb6456aa8e2be4

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

Small rectangular toy boards given as strings of B, W and dot; a bounded teaching model of one scoring or bookkeeping rule, not a complete rules engine or server implementation. 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 2026-09-29T14:50:18.452995+00:00.

Case digest / 340b6005998e413fa9f77dc069e73013f3e38d15110bf4ca0bbd6c51c719dd2b