FA-83106 / Go territory scoring / Open access

Edge eyes use the centre false-eye threshold · case 01

An edge eye with one opponent diagonal is reported as real.

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

ROOT CAUSE

The limit of two opponent diagonals is applied everywhere.

THE FAILURE

The limit of two opponent diagonals is applied everywhere.

Unsuccessful approach: Using limit 2 for any point with two or more diagonals still misclassifies edge eyes.

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 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'], [[['WWB.', '.WBW', 'WB.B', 'B..B'], 1, 0], 'false-W']], [[[['.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'], [[['WWB.', '.WBW', 'WB.B', 'B..B'], 1, 0], 'false-W'], [[['WB.BB', '..BWB', '...BB'], 0, 2], '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'], [[['WWB.', '.WBW', 'WB.B', 'B..B'], 1, 0], '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'], [[['WWB.', '.WBW', 'WB.B', 'B..B'], 1, 0], 'false-W'], [[['WBW', '.BW', 'BW.'], 2, 2], 'false-W']], [[[['..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'], [[['WWB.', '.WBW', 'WB.B', 'B..B'], 1, 0], '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-W`	`false-W`	Failed

SHA-256 / da6dc0df56b17cb2367eec4e39b3d7da15a3e39f3447e87079e40cdc8fcf9aba

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 >= 2 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'], [[['WWB.', '.WBW', 'WB.B', 'B..B'], 1, 0], 'false-W']], [[[['.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'], [[['WWB.', '.WBW', 'WB.B', 'B..B'], 1, 0], 'false-W'], [[['WB.BB', '..BWB', '...BB'], 0, 2], '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'], [[['WWB.', '.WBW', 'WB.B', 'B..B'], 1, 0], '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'], [[['WWB.', '.WBW', 'WB.B', 'B..B'], 1, 0], 'false-W'], [[['WBW', '.BW', 'BW.'], 2, 2], 'false-W']], [[[['..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'], [[['WWB.', '.WBW', 'WB.B', 'B..B'], 1, 0], '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-W`	`false-W`	Failed

SHA-256 / 062a8e13c483e9c9f37a29ed10f9e0df1a9e6b1a555513d4d6a0fe7eb791c36f

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 2026-09-29T14:50:18.613664+00:00.

Case digest / 58949e5449f6b6b713d7997b5e61d8afe518919fd06a59a71e239ba64e0be441