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FA-82491 / Chess move legality / Open access

Knights below the king are invisible · case 01

The king may step next to a knight that attacks the square from below.

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

ROOT CAUSE

The knight-attack table only lists upward jumps.

THE FAILURE

The knight-attack table only lists upward jumps.

Unsuccessful approach: Listing only two diagonal quadrants still misses half the knight jumps.

Case contract

Input: {"board", "from": king square, "to": square}. Return true when the king move is legal: exactly one square in any direction, not onto a friendly piece, and the destination is not attacked by the opponent (including the enemy king) once the king has left its origin square. Captures of undefended enemy pieces are allowed.

Why this case matters

Move validators gate every move in engines, servers and arbiters; accepting an illegal move or rejecting a legal one corrupts the game record.

1 / The failure

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

N = 1
observations = []
def solve(x):
    def attacked(bd, sq, by_white):
        f,r=ord(sq[0])-97,int(sq[1])-1
        def at(ff,rr):
            return bd.get(chr(97+ff)+str(rr+1)) if 0<=ff<8 and 0<=rr<8 else None
        P,N,B,R,Q,K=('PNBRQK' if by_white else 'pnbrqk')
        pr=r-1 if by_white else r+1
        if at(f-1,pr)==P or at(f+1,pr)==P: return True
        for df,dr in ((1,2),(2,1),(-1,2),(-2,1)):
            if at(f+df,r+dr)==N: return True
        for df in (-1,0,1):
            for dr in (-1,0,1):
                if (df or dr) and at(f+df,r+dr)==K: return True
        for df,dr,kinds in ((1,0,(R,Q)),(-1,0,(R,Q)),(0,1,(R,Q)),(0,-1,(R,Q)),(1,1,(B,Q)),(1,-1,(B,Q)),(-1,1,(B,Q)),(-1,-1,(B,Q))):
            ff,rr=f+df,r+dr
            while 0<=ff<8 and 0<=rr<8:
                v=at(ff,rr)
                if v:
                    if v in kinds: return True
                    break
                ff+=df; rr+=dr
        return False
    
    b=x['board']; fr,to=x['from'],x['to']; k=b[fr]; white=k=='K'
    df=ord(to[0])-ord(fr[0]); dr=int(to[1])-int(fr[1])
    if max(abs(df),abs(dr))!=1: return False
    occ=b.get(to)
    if occ and occ.isupper()==white: return False
    nb=dict(b); del nb[fr]; nb[to]=k
    return not attacked(nb, to, not white)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('retreat along rook file',
   {'board': {'a1': 'k', 'e4': 'K', 'e8': 'r'}, 'from': 'e4', 'to': 'e3'}, False),
  ('sidestep rook file', {'board': {'a1': 'k', 'e4': 'K', 'e8': 'r'}, 'from': 'e4', 'to': 'd3'},
   True),
  ('diagonal step', {'board': {'a8': 'k', 'e4': 'K'}, 'from': 'e4', 'to': 'f5'}, True),
  ('stand still', {'board': {'a8': 'k', 'e4': 'K'}, 'from': 'e4', 'to': 'e4'}, False),
  ('capture own', {'board': {'a8': 'k', 'e4': 'K', 'e5': 'P'}, 'from': 'e4', 'to': 'e5'}, False),
  ('capture undefended', {'board': {'a8': 'k', 'e4': 'K', 'e5': 'p'}, 'from': 'e4', 'to': 'e5'},
   True),
  ('knight below', {'board': {'a8': 'k', 'e4': 'K', 'f1': 'n'}, 'from': 'e4', 'to': 'e3'}, False),
  ('knight above', {'board': {'a8': 'k', 'd7': 'n', 'e4': 'K'}, 'from': 'e4', 'to': 'e5'}, False)],
 [('stand still', {'board': {'a8': 'k', 'e4': 'K'}, 'from': 'e4', 'to': 'e4'}, False),
  ('capture own', {'board': {'a8': 'k', 'e4': 'K', 'e5': 'P'}, 'from': 'e4', 'to': 'e5'}, False),
  ('capture undefended', {'board': {'a8': 'k', 'e4': 'K', 'e5': 'p'}, 'from': 'e4', 'to': 'e5'},
   True),
  ('capture defended',
   {'board': {'a8': 'k', 'd6': 'p', 'e4': 'K', 'e5': 'p'}, 'from': 'e4', 'to': 'e5'}, False),
  ('next to enemy king orthogonal', {'board': {'e4': 'K', 'e6': 'k'}, 'from': 'e4', 'to': 'e5'},
   False),
  ('next to enemy king diagonal', {'board': {'e4': 'K', 'g6': 'k'}, 'from': 'e4', 'to': 'f5'},
   False),
  ('knight below', {'board': {'a8': 'k', 'e4': 'K', 'f1': 'n'}, 'from': 'e4', 'to': 'e3'}, False),
  ('knight above', {'board': {'a8': 'k', 'd7': 'n', 'e4': 'K'}, 'from': 'e4', 'to': 'e5'}, False)],
 [('capture defended',
   {'board': {'a8': 'k', 'd6': 'p', 'e4': 'K', 'e5': 'p'}, 'from': 'e4', 'to': 'e5'}, False),
  ('next to enemy king orthogonal', {'board': {'e4': 'K', 'e6': 'k'}, 'from': 'e4', 'to': 'e5'},
   False),
  ('next to enemy king diagonal', {'board': {'e4': 'K', 'g6': 'k'}, 'from': 'e4', 'to': 'f5'},
   False),
  ('knight below', {'board': {'a8': 'k', 'e4': 'K', 'f1': 'n'}, 'from': 'e4', 'to': 'e3'}, False),
  ('knight above', {'board': {'a8': 'k', 'd7': 'n', 'e4': 'K'}, 'from': 'e4', 'to': 'e5'}, False),
  ('black king bishop diag retreat',
   {'board': {'b3': 'B', 'd5': 'k', 'h1': 'K'}, 'from': 'd5', 'to': 'e6'}, False),
  ('capture along check line',
   {'board': {'a1': 'k', 'e3': 'p', 'e4': 'K', 'e8': 'r'}, 'from': 'e4', 'to': 'e3'}, False),
  ('capture defended knight',
   {'board': {'a8': 'k', 'e4': 'K', 'e5': 'n', 'e7': 'r'}, 'from': 'e4', 'to': 'e5'}, False)],
 [('retreat along rook file',
   {'board': {'a1': 'k', 'e4': 'K', 'e8': 'r'}, 'from': 'e4', 'to': 'e3'}, False),
  ('knight below', {'board': {'a8': 'k', 'e4': 'K', 'f1': 'n'}, 'from': 'e4', 'to': 'e3'}, False),
  ('knight above', {'board': {'a8': 'k', 'd7': 'n', 'e4': 'K'}, 'from': 'e4', 'to': 'e5'}, False),
  ('black king bishop diag retreat',
   {'board': {'b3': 'B', 'd5': 'k', 'h1': 'K'}, 'from': 'd5', 'to': 'e6'}, False),
  ('capture along check line',
   {'board': {'a1': 'k', 'e3': 'p', 'e4': 'K', 'e8': 'r'}, 'from': 'e4', 'to': 'e3'}, False),
  ('capture defended knight',
   {'board': {'a8': 'k', 'e4': 'K', 'e5': 'n', 'e7': 'r'}, 'from': 'e4', 'to': 'e5'}, False),
  ('two squares', {'board': {'a8': 'k', 'e4': 'K'}, 'from': 'e4', 'to': 'e6'}, False),
  ('knight far below', {'board': {'a8': 'k', 'c4': 'n', 'e4': 'K'}, 'from': 'e4', 'to': 'd3'},
   True)],
 [('retreat along rook file',
   {'board': {'a1': 'k', 'e4': 'K', 'e8': 'r'}, 'from': 'e4', 'to': 'e3'}, False),
  ('sidestep rook file', {'board': {'a1': 'k', 'e4': 'K', 'e8': 'r'}, 'from': 'e4', 'to': 'd3'},
   True),
  ('diagonal step', {'board': {'a8': 'k', 'e4': 'K'}, 'from': 'e4', 'to': 'f5'}, True),
  ('stand still', {'board': {'a8': 'k', 'e4': 'K'}, 'from': 'e4', 'to': 'e4'}, False),
  ('knight below', {'board': {'a8': 'k', 'e4': 'K', 'f1': 'n'}, 'from': 'e4', 'to': 'e3'}, False),
  ('knight above', {'board': {'a8': 'k', 'd7': 'n', 'e4': 'K'}, 'from': 'e4', 'to': 'e5'}, False),
  ('two squares', {'board': {'a8': 'k', 'e4': 'K'}, 'from': 'e4', 'to': 'e6'}, False),
  ('knight far below', {'board': {'a8': 'k', 'c4': 'n', 'e4': 'K'}, 'from': 'e4', 'to': 'd3'},
   True)]]
for label, args, expected in fixtures[N-1]:
    try:
        actual = solve(args)
    except Exception as exc:
        actual = 'error:' + type(exc).__name__
    check(label, actual, 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
retreat along rook fileFalseFalsePassed
sidestep rook fileTrueTruePassed
diagonal stepTrueTruePassed
stand stillFalseFalsePassed
capture ownFalseFalsePassed
capture undefendedTrueTruePassed
knight belowTrueFalseFailed
knight aboveFalseFalsePassed

SHA-256 / 95f78ce093b5b1a58a9e799c72a9f92072bf18075d13c77ee93cb323aa8b4c74

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(x):
    def attacked(bd, sq, by_white):
        f,r=ord(sq[0])-97,int(sq[1])-1
        def at(ff,rr):
            return bd.get(chr(97+ff)+str(rr+1)) if 0<=ff<8 and 0<=rr<8 else None
        P,N,B,R,Q,K=('PNBRQK' if by_white else 'pnbrqk')
        pr=r-1 if by_white else r+1
        if at(f-1,pr)==P or at(f+1,pr)==P: return True
        for df,dr in ((1,2),(2,1),(-1,-2),(-2,-1)):
            if at(f+df,r+dr)==N: return True
        for df in (-1,0,1):
            for dr in (-1,0,1):
                if (df or dr) and at(f+df,r+dr)==K: return True
        for df,dr,kinds in ((1,0,(R,Q)),(-1,0,(R,Q)),(0,1,(R,Q)),(0,-1,(R,Q)),(1,1,(B,Q)),(1,-1,(B,Q)),(-1,1,(B,Q)),(-1,-1,(B,Q))):
            ff,rr=f+df,r+dr
            while 0<=ff<8 and 0<=rr<8:
                v=at(ff,rr)
                if v:
                    if v in kinds: return True
                    break
                ff+=df; rr+=dr
        return False
    
    b=x['board']; fr,to=x['from'],x['to']; k=b[fr]; white=k=='K'
    df=ord(to[0])-ord(fr[0]); dr=int(to[1])-int(fr[1])
    if max(abs(df),abs(dr))!=1: return False
    occ=b.get(to)
    if occ and occ.isupper()==white: return False
    nb=dict(b); del nb[fr]; nb[to]=k
    return not attacked(nb, to, not white)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('retreat along rook file',
   {'board': {'a1': 'k', 'e4': 'K', 'e8': 'r'}, 'from': 'e4', 'to': 'e3'}, False),
  ('sidestep rook file', {'board': {'a1': 'k', 'e4': 'K', 'e8': 'r'}, 'from': 'e4', 'to': 'd3'},
   True),
  ('diagonal step', {'board': {'a8': 'k', 'e4': 'K'}, 'from': 'e4', 'to': 'f5'}, True),
  ('stand still', {'board': {'a8': 'k', 'e4': 'K'}, 'from': 'e4', 'to': 'e4'}, False),
  ('capture own', {'board': {'a8': 'k', 'e4': 'K', 'e5': 'P'}, 'from': 'e4', 'to': 'e5'}, False),
  ('capture undefended', {'board': {'a8': 'k', 'e4': 'K', 'e5': 'p'}, 'from': 'e4', 'to': 'e5'},
   True),
  ('knight below', {'board': {'a8': 'k', 'e4': 'K', 'f1': 'n'}, 'from': 'e4', 'to': 'e3'}, False),
  ('knight above', {'board': {'a8': 'k', 'd7': 'n', 'e4': 'K'}, 'from': 'e4', 'to': 'e5'}, False)],
 [('stand still', {'board': {'a8': 'k', 'e4': 'K'}, 'from': 'e4', 'to': 'e4'}, False),
  ('capture own', {'board': {'a8': 'k', 'e4': 'K', 'e5': 'P'}, 'from': 'e4', 'to': 'e5'}, False),
  ('capture undefended', {'board': {'a8': 'k', 'e4': 'K', 'e5': 'p'}, 'from': 'e4', 'to': 'e5'},
   True),
  ('capture defended',
   {'board': {'a8': 'k', 'd6': 'p', 'e4': 'K', 'e5': 'p'}, 'from': 'e4', 'to': 'e5'}, False),
  ('next to enemy king orthogonal', {'board': {'e4': 'K', 'e6': 'k'}, 'from': 'e4', 'to': 'e5'},
   False),
  ('next to enemy king diagonal', {'board': {'e4': 'K', 'g6': 'k'}, 'from': 'e4', 'to': 'f5'},
   False),
  ('knight below', {'board': {'a8': 'k', 'e4': 'K', 'f1': 'n'}, 'from': 'e4', 'to': 'e3'}, False),
  ('knight above', {'board': {'a8': 'k', 'd7': 'n', 'e4': 'K'}, 'from': 'e4', 'to': 'e5'}, False)],
 [('capture defended',
   {'board': {'a8': 'k', 'd6': 'p', 'e4': 'K', 'e5': 'p'}, 'from': 'e4', 'to': 'e5'}, False),
  ('next to enemy king orthogonal', {'board': {'e4': 'K', 'e6': 'k'}, 'from': 'e4', 'to': 'e5'},
   False),
  ('next to enemy king diagonal', {'board': {'e4': 'K', 'g6': 'k'}, 'from': 'e4', 'to': 'f5'},
   False),
  ('knight below', {'board': {'a8': 'k', 'e4': 'K', 'f1': 'n'}, 'from': 'e4', 'to': 'e3'}, False),
  ('knight above', {'board': {'a8': 'k', 'd7': 'n', 'e4': 'K'}, 'from': 'e4', 'to': 'e5'}, False),
  ('black king bishop diag retreat',
   {'board': {'b3': 'B', 'd5': 'k', 'h1': 'K'}, 'from': 'd5', 'to': 'e6'}, False),
  ('capture along check line',
   {'board': {'a1': 'k', 'e3': 'p', 'e4': 'K', 'e8': 'r'}, 'from': 'e4', 'to': 'e3'}, False),
  ('capture defended knight',
   {'board': {'a8': 'k', 'e4': 'K', 'e5': 'n', 'e7': 'r'}, 'from': 'e4', 'to': 'e5'}, False)],
 [('retreat along rook file',
   {'board': {'a1': 'k', 'e4': 'K', 'e8': 'r'}, 'from': 'e4', 'to': 'e3'}, False),
  ('knight below', {'board': {'a8': 'k', 'e4': 'K', 'f1': 'n'}, 'from': 'e4', 'to': 'e3'}, False),
  ('knight above', {'board': {'a8': 'k', 'd7': 'n', 'e4': 'K'}, 'from': 'e4', 'to': 'e5'}, False),
  ('black king bishop diag retreat',
   {'board': {'b3': 'B', 'd5': 'k', 'h1': 'K'}, 'from': 'd5', 'to': 'e6'}, False),
  ('capture along check line',
   {'board': {'a1': 'k', 'e3': 'p', 'e4': 'K', 'e8': 'r'}, 'from': 'e4', 'to': 'e3'}, False),
  ('capture defended knight',
   {'board': {'a8': 'k', 'e4': 'K', 'e5': 'n', 'e7': 'r'}, 'from': 'e4', 'to': 'e5'}, False),
  ('two squares', {'board': {'a8': 'k', 'e4': 'K'}, 'from': 'e4', 'to': 'e6'}, False),
  ('knight far below', {'board': {'a8': 'k', 'c4': 'n', 'e4': 'K'}, 'from': 'e4', 'to': 'd3'},
   True)],
 [('retreat along rook file',
   {'board': {'a1': 'k', 'e4': 'K', 'e8': 'r'}, 'from': 'e4', 'to': 'e3'}, False),
  ('sidestep rook file', {'board': {'a1': 'k', 'e4': 'K', 'e8': 'r'}, 'from': 'e4', 'to': 'd3'},
   True),
  ('diagonal step', {'board': {'a8': 'k', 'e4': 'K'}, 'from': 'e4', 'to': 'f5'}, True),
  ('stand still', {'board': {'a8': 'k', 'e4': 'K'}, 'from': 'e4', 'to': 'e4'}, False),
  ('knight below', {'board': {'a8': 'k', 'e4': 'K', 'f1': 'n'}, 'from': 'e4', 'to': 'e3'}, False),
  ('knight above', {'board': {'a8': 'k', 'd7': 'n', 'e4': 'K'}, 'from': 'e4', 'to': 'e5'}, False),
  ('two squares', {'board': {'a8': 'k', 'e4': 'K'}, 'from': 'e4', 'to': 'e6'}, False),
  ('knight far below', {'board': {'a8': 'k', 'c4': 'n', 'e4': 'K'}, 'from': 'e4', 'to': 'd3'},
   True)]]
for label, args, expected in fixtures[N-1]:
    try:
        actual = solve(args)
    except Exception as exc:
        actual = 'error:' + type(exc).__name__
    check(label, actual, 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
retreat along rook fileFalseFalsePassed
sidestep rook fileTrueTruePassed
diagonal stepTrueTruePassed
stand stillFalseFalsePassed
capture ownFalseFalsePassed
capture undefendedTrueTruePassed
knight belowTrueFalseFailed
knight aboveTrueFalseFailed

SHA-256 / f69d183ecc7310607e9473339b12223c8e9b45981dcac69adb989e9bc06843b8

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

A deterministic toy model with an explicitly stated contract; boards are {square: piece} with white upper-case and black lower-case pieces; no claim of full FIDE Laws conformance. 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 2026-09-29T14:50:12.708515+00:00.

Case digest / 616a93bc03ddc97321482be6bb941f3e95897e397c99c1141f8d2d501b2e2f1b