FA-83121 / Go territory scoring / Open access

False eyes need one opponent diagonal too many · case 01

Centre points with exactly two opponent diagonals are called real eyes.

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

ROOT CAUSE

The comparison uses > limit.

VERIFIED REPAIR

A point is false when bad >= limit.

Unsuccessful approach: Restricting false eyes to centre points ignores the edge rule.

Case contract

Input [board, row, col]. A point is an eye candidate of colour X if it is empty and every on-board orthogonal neighbour is X. It is false if opponent stones occupy >= 2 diagonals in the centre, or >= 1 diagonal on the edge/corner. Return "eye-X", "false-X" 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 = x
    n = len(board)
    m = len(board[0])
    if board[r][c] != '.':
        return 'none'
    orth = []
    for p, q in ((r - 1, c), (r + 1, c), (r, c - 1), (r, c + 1)):
        if 0 <= p < n and 0 <= q < m:
            orth.append(board[p][q])
    if not orth or orth.count(orth[0]) != len(orth) or orth[0] == '.':
        return 'none'
    col = orth[0]
    opp = 'W' if col == 'B' else 'B'
    bad = 0
    ondiag = 0
    for p, q in ((r - 1, c - 1), (r - 1, c + 1), (r + 1, c - 1), (r + 1, c + 1)):
        if 0 <= p < n and 0 <= q < m:
            ondiag += 1
            if board[p][q] == opp:
                bad += 1
    limit = 2 if ondiag == 4 else 1
    if bad > limit:
        return 'false-' + col
    return 'eye-' + col
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[[['...', '...', '...'], 0, 1], 'none'], [[['...', '...', '...'], 0, 2], 'none'], [[['...', '...', '...'], 1, 0], 'none'], [[['...', '...', '...'], 1, 1], 'none'], [[['...', '...', '...'], 1, 2], 'none'], [[['.B.', 'B.B', '.B.'], 0, 0], 'eye-B'], [[['.W.B.', 'W.WB.', '.WB..', 'WB...', 'B....'], 2, 0], 'false-W'], [[['B.B..', '.BWBB', '..WB.'], 0, 1], 'false-B']], [[[['.B.', 'B.B', '.B.'], 1, 1], 'eye-B'], [[['.B.', 'B.B', '.B.'], 2, 0], 'eye-B'], [[['.B.', 'B.B', '.B.'], 2, 2], 'eye-B'], [[['.B.', 'B.B', '.B.'], 0, 1], 'none'], [[['B..W', 'B..W', 'B..W', 'B..W'], 0, 1], 'none'], [[['B..W', 'B..W', 'B..W', 'B..W'], 0, 2], 'none'], [[['WB.BB', '..BWB', '...BB'], 0, 2], 'false-B'], [[['WW.WW', 'WB.B.', 'WBW.W', 'W.WBB', 'BBB.B'], 4, 3], 'false-B']], [[[['B..W', 'B..W', 'B..W', 'B..W'], 1, 2], 'none'], [[['B..W', 'B..W', 'B..W', 'B..W'], 2, 1], 'none'], [[['B..W', 'B..W', 'B..W', 'B..W'], 2, 2], 'none'], [[['B..W', 'B..W', 'B..W', 'B..W'], 0, 0], 'none'], [[['.BW.', '.BW.', '.BW.', '.BW.'], 0, 0], 'none'], [[['.BW.', '.BW.', '.BW.', '.BW.'], 0, 3], 'none'], [[['WBW', '.BW', 'BW.'], 2, 2], 'false-W'], [[['B.B..', '.BWBB', '..WB.'], 0, 1], 'false-B']], [[[['.BW.', '.BW.', '.BW.', '.BW.'], 1, 3], 'none'], [[['.BW.', '.BW.', '.BW.', '.BW.'], 2, 0], 'none'], [[['.BW.', '.BW.', '.BW.', '.BW.'], 2, 3], 'none'], [[['.BW.', '.BW.', '.BW.', '.BW.'], 0, 1], 'none'], [[['..B..', '..B..', 'BBBBB', 'WWWWW', '..W..'], 0, 0], 'none'], [[['..B..', '..B..', 'BBBBB', 'WWWWW', '..W..'], 0, 1], 'none'], [[['.W.B.', 'W.WB.', '.WB..', 'WB...', 'B....'], 2, 0], 'false-W'], [[['.BW', 'B.B', 'WB.'], 1, 1], 'false-B']], [[[['..B..', '..B..', 'BBBBB', 'WWWWW', '..W..'], 0, 4], 'none'], [[['..B..', '..B..', 'BBBBB', 'WWWWW', '..W..'], 1, 0], 'none'], [[['..B..', '..B..', 'BBBBB', 'WWWWW', '..W..'], 1, 1], 'none'], [[['..B..', '..B..', 'BBBBB', 'WWWWW', '..W..'], 0, 2], 'none'], [[['B.B.W', '.B.W.', 'B.BW.', 'BBW.W', '..W..'], 0, 1], 'eye-B'], [[['B.B.W', '.B.W.', 'B.BW.', 'BBW.W', '..W..'], 0, 3], 'none'], [[['WBW', '.BW', 'BW.'], 2, 2], 'false-W'], [[['..B.', '.BWB', '.BWW', '.BBW'], 0, 3], 'false-B']]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check("eye 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 fixture	Actual	Expected	Outcome
eye case 0	`none`	`none`	Passed
eye case 1	`none`	`none`	Passed
eye case 2	`none`	`none`	Passed
eye case 3	`none`	`none`	Passed
eye case 4	`none`	`none`	Passed
eye case 5	`eye-B`	`eye-B`	Passed
eye case 6	`eye-W`	`false-W`	Failed
eye case 7	`eye-B`	`false-B`	Failed

SHA-256 / 8d86103ab395a4788edf11f27ad8b81936faf12a86105349ed9605a4b3a5d29b

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])
    if board[r][c] != '.':
        return 'none'
    orth = []
    for p, q in ((r - 1, c), (r + 1, c), (r, c - 1), (r, c + 1)):
        if 0 <= p < n and 0 <= q < m:
            orth.append(board[p][q])
    if not orth or orth.count(orth[0]) != len(orth) or orth[0] == '.':
        return 'none'
    col = orth[0]
    opp = 'W' if col == 'B' else 'B'
    bad = 0
    ondiag = 0
    for p, q in ((r - 1, c - 1), (r - 1, c + 1), (r + 1, c - 1), (r + 1, c + 1)):
        if 0 <= p < n and 0 <= q < m:
            ondiag += 1
            if board[p][q] == opp:
                bad += 1
    limit = 2 if ondiag == 4 else 1
    if bad >= limit and ondiag == 4:
        return 'false-' + col
    return 'eye-' + col
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[[['...', '...', '...'], 0, 1], 'none'], [[['...', '...', '...'], 0, 2], 'none'], [[['...', '...', '...'], 1, 0], 'none'], [[['...', '...', '...'], 1, 1], 'none'], [[['...', '...', '...'], 1, 2], 'none'], [[['.B.', 'B.B', '.B.'], 0, 0], 'eye-B'], [[['.W.B.', 'W.WB.', '.WB..', 'WB...', 'B....'], 2, 0], 'false-W'], [[['B.B..', '.BWBB', '..WB.'], 0, 1], 'false-B']], [[[['.B.', 'B.B', '.B.'], 1, 1], 'eye-B'], [[['.B.', 'B.B', '.B.'], 2, 0], 'eye-B'], [[['.B.', 'B.B', '.B.'], 2, 2], 'eye-B'], [[['.B.', 'B.B', '.B.'], 0, 1], 'none'], [[['B..W', 'B..W', 'B..W', 'B..W'], 0, 1], 'none'], [[['B..W', 'B..W', 'B..W', 'B..W'], 0, 2], 'none'], [[['WB.BB', '..BWB', '...BB'], 0, 2], 'false-B'], [[['WW.WW', 'WB.B.', 'WBW.W', 'W.WBB', 'BBB.B'], 4, 3], 'false-B']], [[[['B..W', 'B..W', 'B..W', 'B..W'], 1, 2], 'none'], [[['B..W', 'B..W', 'B..W', 'B..W'], 2, 1], 'none'], [[['B..W', 'B..W', 'B..W', 'B..W'], 2, 2], 'none'], [[['B..W', 'B..W', 'B..W', 'B..W'], 0, 0], 'none'], [[['.BW.', '.BW.', '.BW.', '.BW.'], 0, 0], 'none'], [[['.BW.', '.BW.', '.BW.', '.BW.'], 0, 3], 'none'], [[['WBW', '.BW', 'BW.'], 2, 2], 'false-W'], [[['B.B..', '.BWBB', '..WB.'], 0, 1], 'false-B']], [[[['.BW.', '.BW.', '.BW.', '.BW.'], 1, 3], 'none'], [[['.BW.', '.BW.', '.BW.', '.BW.'], 2, 0], 'none'], [[['.BW.', '.BW.', '.BW.', '.BW.'], 2, 3], 'none'], [[['.BW.', '.BW.', '.BW.', '.BW.'], 0, 1], 'none'], [[['..B..', '..B..', 'BBBBB', 'WWWWW', '..W..'], 0, 0], 'none'], [[['..B..', '..B..', 'BBBBB', 'WWWWW', '..W..'], 0, 1], 'none'], [[['.W.B.', 'W.WB.', '.WB..', 'WB...', 'B....'], 2, 0], 'false-W'], [[['.BW', 'B.B', 'WB.'], 1, 1], 'false-B']], [[[['..B..', '..B..', 'BBBBB', 'WWWWW', '..W..'], 0, 4], 'none'], [[['..B..', '..B..', 'BBBBB', 'WWWWW', '..W..'], 1, 0], 'none'], [[['..B..', '..B..', 'BBBBB', 'WWWWW', '..W..'], 1, 1], 'none'], [[['..B..', '..B..', 'BBBBB', 'WWWWW', '..W..'], 0, 2], 'none'], [[['B.B.W', '.B.W.', 'B.BW.', 'BBW.W', '..W..'], 0, 1], 'eye-B'], [[['B.B.W', '.B.W.', 'B.BW.', 'BBW.W', '..W..'], 0, 3], 'none'], [[['WBW', '.BW', 'BW.'], 2, 2], 'false-W'], [[['..B.', '.BWB', '.BWW', '.BBW'], 0, 3], 'false-B']]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check("eye 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 fixture	Actual	Expected	Outcome
eye case 0	`none`	`none`	Passed
eye case 1	`none`	`none`	Passed
eye case 2	`none`	`none`	Passed
eye case 3	`none`	`none`	Passed
eye case 4	`none`	`none`	Passed
eye case 5	`eye-B`	`eye-B`	Passed
eye case 6	`eye-W`	`false-W`	Failed
eye case 7	`eye-B`	`false-B`	Failed

SHA-256 / 0499d8d124c8237eaed21f821525e711eed270db46256696871f31534e58eff0

3 / The verified repair

Exit 0

"""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])
    if board[r][c] != '.':
        return 'none'
    orth = []
    for p, q in ((r - 1, c), (r + 1, c), (r, c - 1), (r, c + 1)):
        if 0 <= p < n and 0 <= q < m:
            orth.append(board[p][q])
    if not orth or orth.count(orth[0]) != len(orth) or orth[0] == '.':
        return 'none'
    col = orth[0]
    opp = 'W' if col == 'B' else 'B'
    bad = 0
    ondiag = 0
    for p, q in ((r - 1, c - 1), (r - 1, c + 1), (r + 1, c - 1), (r + 1, c + 1)):
        if 0 <= p < n and 0 <= q < m:
            ondiag += 1
            if board[p][q] == opp:
                bad += 1
    limit = 2 if ondiag == 4 else 1
    if bad >= limit:
        return 'false-' + col
    return 'eye-' + col
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[[['...', '...', '...'], 0, 1], 'none'], [[['...', '...', '...'], 0, 2], 'none'], [[['...', '...', '...'], 1, 0], 'none'], [[['...', '...', '...'], 1, 1], 'none'], [[['...', '...', '...'], 1, 2], 'none'], [[['.B.', 'B.B', '.B.'], 0, 0], 'eye-B'], [[['.W.B.', 'W.WB.', '.WB..', 'WB...', 'B....'], 2, 0], 'false-W'], [[['B.B..', '.BWBB', '..WB.'], 0, 1], 'false-B']], [[[['.B.', 'B.B', '.B.'], 1, 1], 'eye-B'], [[['.B.', 'B.B', '.B.'], 2, 0], 'eye-B'], [[['.B.', 'B.B', '.B.'], 2, 2], 'eye-B'], [[['.B.', 'B.B', '.B.'], 0, 1], 'none'], [[['B..W', 'B..W', 'B..W', 'B..W'], 0, 1], 'none'], [[['B..W', 'B..W', 'B..W', 'B..W'], 0, 2], 'none'], [[['WB.BB', '..BWB', '...BB'], 0, 2], 'false-B'], [[['WW.WW', 'WB.B.', 'WBW.W', 'W.WBB', 'BBB.B'], 4, 3], 'false-B']], [[[['B..W', 'B..W', 'B..W', 'B..W'], 1, 2], 'none'], [[['B..W', 'B..W', 'B..W', 'B..W'], 2, 1], 'none'], [[['B..W', 'B..W', 'B..W', 'B..W'], 2, 2], 'none'], [[['B..W', 'B..W', 'B..W', 'B..W'], 0, 0], 'none'], [[['.BW.', '.BW.', '.BW.', '.BW.'], 0, 0], 'none'], [[['.BW.', '.BW.', '.BW.', '.BW.'], 0, 3], 'none'], [[['WBW', '.BW', 'BW.'], 2, 2], 'false-W'], [[['B.B..', '.BWBB', '..WB.'], 0, 1], 'false-B']], [[[['.BW.', '.BW.', '.BW.', '.BW.'], 1, 3], 'none'], [[['.BW.', '.BW.', '.BW.', '.BW.'], 2, 0], 'none'], [[['.BW.', '.BW.', '.BW.', '.BW.'], 2, 3], 'none'], [[['.BW.', '.BW.', '.BW.', '.BW.'], 0, 1], 'none'], [[['..B..', '..B..', 'BBBBB', 'WWWWW', '..W..'], 0, 0], 'none'], [[['..B..', '..B..', 'BBBBB', 'WWWWW', '..W..'], 0, 1], 'none'], [[['.W.B.', 'W.WB.', '.WB..', 'WB...', 'B....'], 2, 0], 'false-W'], [[['.BW', 'B.B', 'WB.'], 1, 1], 'false-B']], [[[['..B..', '..B..', 'BBBBB', 'WWWWW', '..W..'], 0, 4], 'none'], [[['..B..', '..B..', 'BBBBB', 'WWWWW', '..W..'], 1, 0], 'none'], [[['..B..', '..B..', 'BBBBB', 'WWWWW', '..W..'], 1, 1], 'none'], [[['..B..', '..B..', 'BBBBB', 'WWWWW', '..W..'], 0, 2], 'none'], [[['B.B.W', '.B.W.', 'B.BW.', 'BBW.W', '..W..'], 0, 1], 'eye-B'], [[['B.B.W', '.B.W.', 'B.BW.', 'BBW.W', '..W..'], 0, 3], 'none'], [[['WBW', '.BW', 'BW.'], 2, 2], 'false-W'], [[['..B.', '.BWB', '.BWW', '.BBW'], 0, 3], 'false-B']]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check("eye 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 fixture	Actual	Expected	Outcome
eye case 0	`none`	`none`	Passed
eye case 1	`none`	`none`	Passed
eye case 2	`none`	`none`	Passed
eye case 3	`none`	`none`	Passed
eye case 4	`none`	`none`	Passed
eye case 5	`eye-B`	`eye-B`	Passed
eye case 6	`false-W`	`false-W`	Passed
eye case 7	`false-B`	`false-B`	Passed

SHA-256 / 75d02ab07d55294180b6e07639ac58462d23ce5956f82b68490c592cba1f040d

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 2026-09-29T14:50:18.727791+00:00.

Case digest / 48b101d7527eda290151c27af4acb705e88e9675dae2b68abf309c09fb9ef565