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FA-82916 / Go territory scoring / Open access

Multi-stone captures create a ko ban · case 01

Capturing two stones marks the first captured point as a ko point.

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

ROOT CAUSE

The capture-size check accepts any non-empty capture.

THE FAILURE

The capture-size check accepts any non-empty capture.

Unsuccessful approach: Combining the size test with the liberty test using and lets a multi-stone capture through when the stone has one liberty.

Case contract

Input [board_after_move, row, col, captured_points]. A ko ban point exists only when exactly one stone was captured, the played stone has no friendly orthogonal neighbour, and it has exactly one liberty. Return the captured point or None.

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, captured = x
    n = len(board)
    m = len(board[0])
    color = board[r][c]
    same = 0
    libs = []
    for p, q in ((r + 1, c), (r - 1, c), (r, c + 1), (r, c - 1)):
        if 0 <= p < n and 0 <= q < m:
            if board[p][q] == color:
                same += 1
            elif board[p][q] == '.':
                libs.append([p, q])
    if not captured:
        return None
    if same:
        return None
    if len(libs) != 1:
        return None
    return captured[0]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[[['.W.B.', 'W.WB.', 'BWB..', '.B...', 'B....'], 2, 0, [[3, 0]]], [3, 0]], [[['.W.B.', 'W.WB.', '.WB..', 'WB...', '.W...'], 4, 1, [[4, 0]]], None], [[['BBBB', 'B..B', 'B.BB', 'BBBB'], 2, 2, []], None], [[['...', '.B.', '...'], 1, 1, [[0, 0], [0, 1], [0, 2], [1, 0], [1, 2], [2, 0], [2, 1], [2, 2]]], None], [[['B.W', '...', 'WWB'], 2, 1, []], None], [[['.B...', 'B....', '..W..', '....W', '...W.'], 2, 2, []], None], [[['.BBBW', 'W.BBW', 'BBWBB', 'WW.WW', 'BW.WW'], 2, 2, [[3, 2], [4, 2]]], None], [[['.BBBW', 'W.BBW', 'BBWBB', 'WW.WW', 'BW.WW'], 2, 2, [[3, 2], [4, 2]]], None]], [[[['.B...', 'B....', '.....', '...WW', '...W.'], 3, 3, []], None], [[['.....', '.BBB.', '.B.BB', '.BBB.', '.....'], 2, 4, []], None], [[['.....', '.BBB.', '.B.B.', 'WBBB.', '.....'], 3, 0, []], None], [[['B....B', '......', '..WWB.', '..WW..', '......', 'B....B'], 2, 4, []], None], [[['B....B', '......', '..WW..', '.WWW..', '......', 'B....B'], 3, 1, []], None], [[['B.B', '.B.', 'BWB', 'WBW', 'BB.'], 0, 2, [[1, 2], [0, 1]]], None], [[['.BBBW', 'W.BBW', 'BBWBB', 'WW.WW', 'BW.WW'], 2, 2, [[3, 2], [4, 2]]], None], [[['.BBBW', 'W.BBW', 'BBWBB', 'WW.WW', 'BW.WW'], 2, 2, [[3, 2], [4, 2]]], None]], [[[['BW.', '.BW', 'BWB', 'WB.', 'BBB'], 4, 2, [[3, 2]]], None], [[['BW.', '.BW', 'BWB', 'W.W', '..W'], 4, 2, [[3, 1], [4, 0], [4, 1]]], None], [[['..BWW', '....W', 'W..B.'], 2, 0, []], None], [[['W.W.B', '.WW..', '.W.BB'], 0, 0, [[1, 0], [2, 0], [0, 1]]], None], [[['..W..', 'B..WW', '...BW', 'W..B.', '..W.W'], 0, 2, [[0, 3], [0, 4]]], None], [[['.W..', 'W..W', '.B.W'], 0, 1, [[0, 0]]], None], [[['.BBBW', 'W.BBW', 'BBWBB', 'WW.WW', 'BW.WW'], 2, 2, [[3, 2], [4, 2]]], None], [[['.BBBW', 'W.BBW', 'BBWBB', 'WW.WW', 'BW.WW'], 2, 2, [[3, 2], [4, 2]]], None]], [[[['BW..', 'W.W.', 'BWW.', 'B.BW', 'B..W'], 1, 2, [[1, 1]]], None], [[['BW..', 'WB.B', 'BWW.', 'B.BW', 'B..W'], 1, 3, []], None], [[['.....', '..W..', 'W.WB.', 'BW.W.'], 2, 3, []], None], [[['..W', 'WWW', 'WBW', '...'], 0, 2, [[0, 0], [0, 1]]], None], [[['BB.', 'WWW', 'W.W', '.W.'], 3, 1, [[2, 1]]], None], [[['.BB', 'B.B', 'BWB', 'W.W'], 2, 1, [[3, 1]]], None], [[['.BBBW', 'W.BBW', 'BBWBB', 'WW.WW', 'BW.WW'], 2, 2, [[3, 2], [4, 2]]], None], [[['.BBBW', 'W.BBW', 'BBWBB', 'WW.WW', 'BW.WW'], 2, 2, [[3, 2], [4, 2]]], None]], [[[['W.WWB', '.WB.B', 'BW.BW', '.B.BW', '...WW'], 0, 2, [[0, 1]]], None], [[['.B.WB', 'BWB.B', 'BW.BW', '.B.BW', '...WW'], 1, 0, [[0, 0]]], None], [[['WB.W.', '.WBW.', 'BW.BW', '.B.BW', '...WW'], 1, 3, [[0, 4], [1, 4]]], None], [[['WB.WB', '.WB.B', 'BW.B.', '.B.B.', '..B..'], 4, 2, [[2, 4], [3, 4], [4, 3], [4, 4]]], None], [[['BB.', 'BBB', 'BB.', '..B', 'B.B'], 2, 1, [[3, 0], [3, 1], [4, 1]]], None], [[['BB.', 'BBB', 'B.W', 'WW.', 'BW.'], 2, 2, [[3, 2], [4, 2]]], None], [[['.BBBW', 'W.BBW', 'BBWBB', 'WW.WW', 'BW.WW'], 2, 2, [[3, 2], [4, 2]]], None], [[['.BBBW', 'W.BBW', 'BBWBB', 'WW.WW', 'BW.WW'], 2, 2, [[3, 2], [4, 2]]], None]]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check("ko point 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
ko point case 0[3, 0][3, 0]Passed
ko point case 1NoneNonePassed
ko point case 2NoneNonePassed
ko point case 3NoneNonePassed
ko point case 4NoneNonePassed
ko point case 5NoneNonePassed
ko point case 6[3, 2]NoneFailed
ko point case 7[3, 2]NoneFailed

SHA-256 / a6232d0890a1e39ce6e98b69c2956606b4e7471735d349396d7af91337f4b76d

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, captured = x
    n = len(board)
    m = len(board[0])
    color = board[r][c]
    same = 0
    libs = []
    for p, q in ((r + 1, c), (r - 1, c), (r, c + 1), (r, c - 1)):
        if 0 <= p < n and 0 <= q < m:
            if board[p][q] == color:
                same += 1
            elif board[p][q] == '.':
                libs.append([p, q])
    if len(captured) != 1 and len(libs) != 1:
        return None
    if same:
        return None
    if len(libs) != 1:
        return None
    return captured[0]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[[['.W.B.', 'W.WB.', 'BWB..', '.B...', 'B....'], 2, 0, [[3, 0]]], [3, 0]], [[['.W.B.', 'W.WB.', '.WB..', 'WB...', '.W...'], 4, 1, [[4, 0]]], None], [[['BBBB', 'B..B', 'B.BB', 'BBBB'], 2, 2, []], None], [[['...', '.B.', '...'], 1, 1, [[0, 0], [0, 1], [0, 2], [1, 0], [1, 2], [2, 0], [2, 1], [2, 2]]], None], [[['B.W', '...', 'WWB'], 2, 1, []], None], [[['.B...', 'B....', '..W..', '....W', '...W.'], 2, 2, []], None], [[['.BBBW', 'W.BBW', 'BBWBB', 'WW.WW', 'BW.WW'], 2, 2, [[3, 2], [4, 2]]], None], [[['.BBBW', 'W.BBW', 'BBWBB', 'WW.WW', 'BW.WW'], 2, 2, [[3, 2], [4, 2]]], None]], [[[['.B...', 'B....', '.....', '...WW', '...W.'], 3, 3, []], None], [[['.....', '.BBB.', '.B.BB', '.BBB.', '.....'], 2, 4, []], None], [[['.....', '.BBB.', '.B.B.', 'WBBB.', '.....'], 3, 0, []], None], [[['B....B', '......', '..WWB.', '..WW..', '......', 'B....B'], 2, 4, []], None], [[['B....B', '......', '..WW..', '.WWW..', '......', 'B....B'], 3, 1, []], None], [[['B.B', '.B.', 'BWB', 'WBW', 'BB.'], 0, 2, [[1, 2], [0, 1]]], None], [[['.BBBW', 'W.BBW', 'BBWBB', 'WW.WW', 'BW.WW'], 2, 2, [[3, 2], [4, 2]]], None], [[['.BBBW', 'W.BBW', 'BBWBB', 'WW.WW', 'BW.WW'], 2, 2, [[3, 2], [4, 2]]], None]], [[[['BW.', '.BW', 'BWB', 'WB.', 'BBB'], 4, 2, [[3, 2]]], None], [[['BW.', '.BW', 'BWB', 'W.W', '..W'], 4, 2, [[3, 1], [4, 0], [4, 1]]], None], [[['..BWW', '....W', 'W..B.'], 2, 0, []], None], [[['W.W.B', '.WW..', '.W.BB'], 0, 0, [[1, 0], [2, 0], [0, 1]]], None], [[['..W..', 'B..WW', '...BW', 'W..B.', '..W.W'], 0, 2, [[0, 3], [0, 4]]], None], [[['.W..', 'W..W', '.B.W'], 0, 1, [[0, 0]]], None], [[['.BBBW', 'W.BBW', 'BBWBB', 'WW.WW', 'BW.WW'], 2, 2, [[3, 2], [4, 2]]], None], [[['.BBBW', 'W.BBW', 'BBWBB', 'WW.WW', 'BW.WW'], 2, 2, [[3, 2], [4, 2]]], None]], [[[['BW..', 'W.W.', 'BWW.', 'B.BW', 'B..W'], 1, 2, [[1, 1]]], None], [[['BW..', 'WB.B', 'BWW.', 'B.BW', 'B..W'], 1, 3, []], None], [[['.....', '..W..', 'W.WB.', 'BW.W.'], 2, 3, []], None], [[['..W', 'WWW', 'WBW', '...'], 0, 2, [[0, 0], [0, 1]]], None], [[['BB.', 'WWW', 'W.W', '.W.'], 3, 1, [[2, 1]]], None], [[['.BB', 'B.B', 'BWB', 'W.W'], 2, 1, [[3, 1]]], None], [[['.BBBW', 'W.BBW', 'BBWBB', 'WW.WW', 'BW.WW'], 2, 2, [[3, 2], [4, 2]]], None], [[['.BBBW', 'W.BBW', 'BBWBB', 'WW.WW', 'BW.WW'], 2, 2, [[3, 2], [4, 2]]], None]], [[[['W.WWB', '.WB.B', 'BW.BW', '.B.BW', '...WW'], 0, 2, [[0, 1]]], None], [[['.B.WB', 'BWB.B', 'BW.BW', '.B.BW', '...WW'], 1, 0, [[0, 0]]], None], [[['WB.W.', '.WBW.', 'BW.BW', '.B.BW', '...WW'], 1, 3, [[0, 4], [1, 4]]], None], [[['WB.WB', '.WB.B', 'BW.B.', '.B.B.', '..B..'], 4, 2, [[2, 4], [3, 4], [4, 3], [4, 4]]], None], [[['BB.', 'BBB', 'BB.', '..B', 'B.B'], 2, 1, [[3, 0], [3, 1], [4, 1]]], None], [[['BB.', 'BBB', 'B.W', 'WW.', 'BW.'], 2, 2, [[3, 2], [4, 2]]], None], [[['.BBBW', 'W.BBW', 'BBWBB', 'WW.WW', 'BW.WW'], 2, 2, [[3, 2], [4, 2]]], None], [[['.BBBW', 'W.BBW', 'BBWBB', 'WW.WW', 'BW.WW'], 2, 2, [[3, 2], [4, 2]]], None]]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check("ko point 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
ko point case 0[3, 0][3, 0]Passed
ko point case 1NoneNonePassed
ko point case 2NoneNonePassed
ko point case 3NoneNonePassed
ko point case 4NoneNonePassed
ko point case 5NoneNonePassed
ko point case 6[3, 2]NoneFailed
ko point case 7[3, 2]NoneFailed

SHA-256 / e0d4ac21a9ccac87b7c8a48a1c8e4b2d63cfa685094729ba2cdead4a93faa20a

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 2026-09-29T14:50:16.576201+00:00.

Case digest / ccdf69006c3009dbdbde5c606e36e3dc332204dce77444c13a3bcddece0fd1ff