FA-82081 / Poker hand evaluation / Open access
Lowball pot awarded to the stronger high hand · case 01
7-5-4-3-2 loses to a pair of deuces.
ROOT CAUSE
The comparison keeps the high-hand direction instead of inverting it.
VERIFIED REPAIR
The hand with the smaller high-hand key wins in lowball.
Unsuccessful approach: Inverting only the category comparison ignores rank order within a category.
Case contract
Input: [hand_a, hand_b] five distinct cards each. Deuce-to-seven lowball: aces are always high, A-2-3-4-5 is not a straight, straights and flushes count against the hand, and the standard high-hand ordering is inverted so the weaker high hand wins. Return 1 if hand_a wins, -1 if hand_b wins, 0 for a tie.
Why this case matters
Lowball variants reuse high-hand evaluators with inverted outcomes, a common source of subtle bugs.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import collections
N = 1
observations = []
def solve(x):
R='23456789TJQKA'
def key(h):
vals=sorted((R.index(c[0])+2 for c in h), reverse=True)
cnt=collections.Counter(vals)
order=sorted(cnt, key=lambda v:(cnt[v],v), reverse=True)
shape=sorted(cnt.values(), reverse=True)
straight=len(cnt)==5 and vals[0]-vals[4]==4
flush=len({c[1] for c in h})==1
if straight and flush: return (8,vals)
if shape==[4,1]: return (7,order)
if shape==[3,2]: return (6,order)
if flush: return (5,vals)
if straight: return (4,vals)
if shape==[3,1,1]: return (3,order)
if shape==[2,2,1]: return (2,order)
if shape==[2,1,1,1]: return (1,order)
return (0,vals)
ka,kb=key(x[0]),key(x[1])
if ka==kb: return 0
return 1 if ka>kb else -1
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('number one vs wheel', [['7h', '5d', '4c', '3s', '2h'], ['Ah', '2d', '3c', '4s', '5h']], 1),
('wheel is ace high', [['Ah', '2d', '3c', '4s', '5h'], ['Kh', 'Qd', 'Jc', '9s', '8h']], -1),
('seven low vs eight low', [['8h', '6d', '4c', '3s', '2h'], ['7c', '6h', '4d', '3c', '2d']], -1),
('flush counts against', [['2h', '4h', '5h', '6h', '8h'], ['9c', '6d', '4d', '3c', '2d']], -1),
('straight counts against', [['3h', '4d', '5c', '6s', '7h'], ['Kh', 'Qd', 'Jc', '9s', '7c']], -1),
('tie', [['7h', '5d', '4c', '3s', '2h'], ['7c', '5h', '4d', '3c', '2d']], 0),
('both pairs lower pair wins', [['4h', '4d', 'Kc', 'Qs', 'Jh'], ['5h', '5d', '2c', '3s', '7h']],
1),
('second tie', [['Kh', 'Jd', '9c', '6s', '3h'], ['Kc', 'Jh', '9d', '6c', '3d']], 0)],
[('wheel is ace high', [['Ah', '2d', '3c', '4s', '5h'], ['Kh', 'Qd', 'Jc', '9s', '8h']], -1),
('seven low vs eight low', [['8h', '6d', '4c', '3s', '2h'], ['7c', '6h', '4d', '3c', '2d']], -1),
('flush counts against', [['2h', '4h', '5h', '6h', '8h'], ['9c', '6d', '4d', '3c', '2d']], -1),
('straight counts against', [['3h', '4d', '5c', '6s', '7h'], ['Kh', 'Qd', 'Jc', '9s', '7c']], -1),
('pair loses to king high', [['2h', '2d', '4c', '5s', '7h'], ['Kh', '8d', '6c', '4s', '3h']], -1),
('ace-king gap hand', [['Ah', 'Kd', '7c', '4s', '2h'], ['Qh', 'Jd', 'Tc', '8s', '6h']], -1),
('both pairs lower pair wins', [['4h', '4d', 'Kc', 'Qs', 'Jh'], ['5h', '5d', '2c', '3s', '7h']],
1),
('nine vs ten', [['9h', '7d', '5c', '3s', '2h'], ['Th', '4d', '3c', '6s', '2c']], 1)],
[('number one vs wheel', [['7h', '5d', '4c', '3s', '2h'], ['Ah', '2d', '3c', '4s', '5h']], 1),
('seven low vs eight low', [['8h', '6d', '4c', '3s', '2h'], ['7c', '6h', '4d', '3c', '2d']], -1),
('flush counts against', [['2h', '4h', '5h', '6h', '8h'], ['9c', '6d', '4d', '3c', '2d']], -1),
('straight counts against', [['3h', '4d', '5c', '6s', '7h'], ['Kh', 'Qd', 'Jc', '9s', '7c']], -1),
('pair loses to king high', [['2h', '2d', '4c', '5s', '7h'], ['Kh', '8d', '6c', '4s', '3h']], -1),
('ace-king gap hand', [['Ah', 'Kd', '7c', '4s', '2h'], ['Qh', 'Jd', 'Tc', '8s', '6h']], -1),
('straight flush vs flush', [['2c', '3c', '4c', '5c', '6c'], ['9d', '7d', '5d', '3d', '2d']], -1),
('nine vs ten', [['9h', '7d', '5c', '3s', '2h'], ['Th', '4d', '3c', '6s', '2c']], 1)],
[('number one vs wheel', [['7h', '5d', '4c', '3s', '2h'], ['Ah', '2d', '3c', '4s', '5h']], 1),
('flush counts against', [['2h', '4h', '5h', '6h', '8h'], ['9c', '6d', '4d', '3c', '2d']], -1),
('straight counts against', [['3h', '4d', '5c', '6s', '7h'], ['Kh', 'Qd', 'Jc', '9s', '7c']], -1),
('straight flush vs flush', [['2c', '3c', '4c', '5c', '6c'], ['9d', '7d', '5d', '3d', '2d']], -1),
('ace high vs pair', [['Ah', 'Qd', '9c', '7s', '5h'], ['3h', '3d', '6c', '5s', '4h']], 1),
('both pairs lower pair wins', [['4h', '4d', 'Kc', 'Qs', 'Jh'], ['5h', '5d', '2c', '3s', '7h']],
1),
('wheel vs pair', [['Ah', '2d', '3c', '4s', '5h'], ['3h', '3d', '6c', '8s', '9h']], 1),
('ace-deuce span vs pair', [['Ah', 'Jd', '8c', '6s', '2h'], ['4h', '4d', '6d', '8d', '9s']], 1)],
[('straight counts against', [['3h', '4d', '5c', '6s', '7h'], ['Kh', 'Qd', 'Jc', '9s', '7c']], -1),
('pair loses to king high', [['2h', '2d', '4c', '5s', '7h'], ['Kh', '8d', '6c', '4s', '3h']], -1),
('tie', [['7h', '5d', '4c', '3s', '2h'], ['7c', '5h', '4d', '3c', '2d']], 0),
('both pairs lower pair wins', [['4h', '4d', 'Kc', 'Qs', 'Jh'], ['5h', '5d', '2c', '3s', '7h']],
1),
('wheel vs pair', [['Ah', '2d', '3c', '4s', '5h'], ['3h', '3d', '6c', '8s', '9h']], 1),
('ace-deuce span vs pair', [['Ah', 'Jd', '8c', '6s', '2h'], ['4h', '4d', '6d', '8d', '9s']], 1),
('ace high vs king high', [['Ah', '9d', '7c', '4s', '2h'], ['Kh', 'Qd', 'Jc', '9s', '8c']], -1),
('nine vs ten', [['9h', '7d', '5c', '3s', '2h'], ['Th', '4d', '3c', '6s', '2c']], 1)]]
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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| number one vs wheel | -1 | 1 | Failed |
| wheel is ace high | 1 | -1 | Failed |
| seven low vs eight low | 1 | -1 | Failed |
| flush counts against | 1 | -1 | Failed |
| straight counts against | 1 | -1 | Failed |
| tie | 0 | 0 | Passed |
| both pairs lower pair wins | -1 | 1 | Failed |
| second tie | 0 | 0 | Passed |
SHA-256 / 8b618950dc7ce2ff3eea375698bdbc80738d1aaa315ebf6540616a2baddc46d1
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import collections
N = 1
observations = []
def solve(x):
R='23456789TJQKA'
def key(h):
vals=sorted((R.index(c[0])+2 for c in h), reverse=True)
cnt=collections.Counter(vals)
order=sorted(cnt, key=lambda v:(cnt[v],v), reverse=True)
shape=sorted(cnt.values(), reverse=True)
straight=len(cnt)==5 and vals[0]-vals[4]==4
flush=len({c[1] for c in h})==1
if straight and flush: return (8,vals)
if shape==[4,1]: return (7,order)
if shape==[3,2]: return (6,order)
if flush: return (5,vals)
if straight: return (4,vals)
if shape==[3,1,1]: return (3,order)
if shape==[2,2,1]: return (2,order)
if shape==[2,1,1,1]: return (1,order)
return (0,vals)
ka,kb=key(x[0]),key(x[1])
if ka==kb: return 0
return 1 if ka[0]<kb[0] else -1
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('number one vs wheel', [['7h', '5d', '4c', '3s', '2h'], ['Ah', '2d', '3c', '4s', '5h']], 1),
('wheel is ace high', [['Ah', '2d', '3c', '4s', '5h'], ['Kh', 'Qd', 'Jc', '9s', '8h']], -1),
('seven low vs eight low', [['8h', '6d', '4c', '3s', '2h'], ['7c', '6h', '4d', '3c', '2d']], -1),
('flush counts against', [['2h', '4h', '5h', '6h', '8h'], ['9c', '6d', '4d', '3c', '2d']], -1),
('straight counts against', [['3h', '4d', '5c', '6s', '7h'], ['Kh', 'Qd', 'Jc', '9s', '7c']], -1),
('tie', [['7h', '5d', '4c', '3s', '2h'], ['7c', '5h', '4d', '3c', '2d']], 0),
('both pairs lower pair wins', [['4h', '4d', 'Kc', 'Qs', 'Jh'], ['5h', '5d', '2c', '3s', '7h']],
1),
('second tie', [['Kh', 'Jd', '9c', '6s', '3h'], ['Kc', 'Jh', '9d', '6c', '3d']], 0)],
[('wheel is ace high', [['Ah', '2d', '3c', '4s', '5h'], ['Kh', 'Qd', 'Jc', '9s', '8h']], -1),
('seven low vs eight low', [['8h', '6d', '4c', '3s', '2h'], ['7c', '6h', '4d', '3c', '2d']], -1),
('flush counts against', [['2h', '4h', '5h', '6h', '8h'], ['9c', '6d', '4d', '3c', '2d']], -1),
('straight counts against', [['3h', '4d', '5c', '6s', '7h'], ['Kh', 'Qd', 'Jc', '9s', '7c']], -1),
('pair loses to king high', [['2h', '2d', '4c', '5s', '7h'], ['Kh', '8d', '6c', '4s', '3h']], -1),
('ace-king gap hand', [['Ah', 'Kd', '7c', '4s', '2h'], ['Qh', 'Jd', 'Tc', '8s', '6h']], -1),
('both pairs lower pair wins', [['4h', '4d', 'Kc', 'Qs', 'Jh'], ['5h', '5d', '2c', '3s', '7h']],
1),
('nine vs ten', [['9h', '7d', '5c', '3s', '2h'], ['Th', '4d', '3c', '6s', '2c']], 1)],
[('number one vs wheel', [['7h', '5d', '4c', '3s', '2h'], ['Ah', '2d', '3c', '4s', '5h']], 1),
('seven low vs eight low', [['8h', '6d', '4c', '3s', '2h'], ['7c', '6h', '4d', '3c', '2d']], -1),
('flush counts against', [['2h', '4h', '5h', '6h', '8h'], ['9c', '6d', '4d', '3c', '2d']], -1),
('straight counts against', [['3h', '4d', '5c', '6s', '7h'], ['Kh', 'Qd', 'Jc', '9s', '7c']], -1),
('pair loses to king high', [['2h', '2d', '4c', '5s', '7h'], ['Kh', '8d', '6c', '4s', '3h']], -1),
('ace-king gap hand', [['Ah', 'Kd', '7c', '4s', '2h'], ['Qh', 'Jd', 'Tc', '8s', '6h']], -1),
('straight flush vs flush', [['2c', '3c', '4c', '5c', '6c'], ['9d', '7d', '5d', '3d', '2d']], -1),
('nine vs ten', [['9h', '7d', '5c', '3s', '2h'], ['Th', '4d', '3c', '6s', '2c']], 1)],
[('number one vs wheel', [['7h', '5d', '4c', '3s', '2h'], ['Ah', '2d', '3c', '4s', '5h']], 1),
('flush counts against', [['2h', '4h', '5h', '6h', '8h'], ['9c', '6d', '4d', '3c', '2d']], -1),
('straight counts against', [['3h', '4d', '5c', '6s', '7h'], ['Kh', 'Qd', 'Jc', '9s', '7c']], -1),
('straight flush vs flush', [['2c', '3c', '4c', '5c', '6c'], ['9d', '7d', '5d', '3d', '2d']], -1),
('ace high vs pair', [['Ah', 'Qd', '9c', '7s', '5h'], ['3h', '3d', '6c', '5s', '4h']], 1),
('both pairs lower pair wins', [['4h', '4d', 'Kc', 'Qs', 'Jh'], ['5h', '5d', '2c', '3s', '7h']],
1),
('wheel vs pair', [['Ah', '2d', '3c', '4s', '5h'], ['3h', '3d', '6c', '8s', '9h']], 1),
('ace-deuce span vs pair', [['Ah', 'Jd', '8c', '6s', '2h'], ['4h', '4d', '6d', '8d', '9s']], 1)],
[('straight counts against', [['3h', '4d', '5c', '6s', '7h'], ['Kh', 'Qd', 'Jc', '9s', '7c']], -1),
('pair loses to king high', [['2h', '2d', '4c', '5s', '7h'], ['Kh', '8d', '6c', '4s', '3h']], -1),
('tie', [['7h', '5d', '4c', '3s', '2h'], ['7c', '5h', '4d', '3c', '2d']], 0),
('both pairs lower pair wins', [['4h', '4d', 'Kc', 'Qs', 'Jh'], ['5h', '5d', '2c', '3s', '7h']],
1),
('wheel vs pair', [['Ah', '2d', '3c', '4s', '5h'], ['3h', '3d', '6c', '8s', '9h']], 1),
('ace-deuce span vs pair', [['Ah', 'Jd', '8c', '6s', '2h'], ['4h', '4d', '6d', '8d', '9s']], 1),
('ace high vs king high', [['Ah', '9d', '7c', '4s', '2h'], ['Kh', 'Qd', 'Jc', '9s', '8c']], -1),
('nine vs ten', [['9h', '7d', '5c', '3s', '2h'], ['Th', '4d', '3c', '6s', '2c']], 1)]]
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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| number one vs wheel | -1 | 1 | Failed |
| wheel is ace high | -1 | -1 | Passed |
| seven low vs eight low | -1 | -1 | Passed |
| flush counts against | -1 | -1 | Passed |
| straight counts against | -1 | -1 | Passed |
| tie | 0 | 0 | Passed |
| both pairs lower pair wins | -1 | 1 | Failed |
| second tie | 0 | 0 | Passed |
SHA-256 / 6e2ad145db59bcb164440a794c7e265f5bebf03e3246d244e3cb6b36857b56f7
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
import collections
N = 1
observations = []
def solve(x):
R='23456789TJQKA'
def key(h):
vals=sorted((R.index(c[0])+2 for c in h), reverse=True)
cnt=collections.Counter(vals)
order=sorted(cnt, key=lambda v:(cnt[v],v), reverse=True)
shape=sorted(cnt.values(), reverse=True)
straight=len(cnt)==5 and vals[0]-vals[4]==4
flush=len({c[1] for c in h})==1
if straight and flush: return (8,vals)
if shape==[4,1]: return (7,order)
if shape==[3,2]: return (6,order)
if flush: return (5,vals)
if straight: return (4,vals)
if shape==[3,1,1]: return (3,order)
if shape==[2,2,1]: return (2,order)
if shape==[2,1,1,1]: return (1,order)
return (0,vals)
ka,kb=key(x[0]),key(x[1])
if ka==kb: return 0
return 1 if ka<kb else -1
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('number one vs wheel', [['7h', '5d', '4c', '3s', '2h'], ['Ah', '2d', '3c', '4s', '5h']], 1),
('wheel is ace high', [['Ah', '2d', '3c', '4s', '5h'], ['Kh', 'Qd', 'Jc', '9s', '8h']], -1),
('seven low vs eight low', [['8h', '6d', '4c', '3s', '2h'], ['7c', '6h', '4d', '3c', '2d']], -1),
('flush counts against', [['2h', '4h', '5h', '6h', '8h'], ['9c', '6d', '4d', '3c', '2d']], -1),
('straight counts against', [['3h', '4d', '5c', '6s', '7h'], ['Kh', 'Qd', 'Jc', '9s', '7c']], -1),
('tie', [['7h', '5d', '4c', '3s', '2h'], ['7c', '5h', '4d', '3c', '2d']], 0),
('both pairs lower pair wins', [['4h', '4d', 'Kc', 'Qs', 'Jh'], ['5h', '5d', '2c', '3s', '7h']],
1),
('second tie', [['Kh', 'Jd', '9c', '6s', '3h'], ['Kc', 'Jh', '9d', '6c', '3d']], 0)],
[('wheel is ace high', [['Ah', '2d', '3c', '4s', '5h'], ['Kh', 'Qd', 'Jc', '9s', '8h']], -1),
('seven low vs eight low', [['8h', '6d', '4c', '3s', '2h'], ['7c', '6h', '4d', '3c', '2d']], -1),
('flush counts against', [['2h', '4h', '5h', '6h', '8h'], ['9c', '6d', '4d', '3c', '2d']], -1),
('straight counts against', [['3h', '4d', '5c', '6s', '7h'], ['Kh', 'Qd', 'Jc', '9s', '7c']], -1),
('pair loses to king high', [['2h', '2d', '4c', '5s', '7h'], ['Kh', '8d', '6c', '4s', '3h']], -1),
('ace-king gap hand', [['Ah', 'Kd', '7c', '4s', '2h'], ['Qh', 'Jd', 'Tc', '8s', '6h']], -1),
('both pairs lower pair wins', [['4h', '4d', 'Kc', 'Qs', 'Jh'], ['5h', '5d', '2c', '3s', '7h']],
1),
('nine vs ten', [['9h', '7d', '5c', '3s', '2h'], ['Th', '4d', '3c', '6s', '2c']], 1)],
[('number one vs wheel', [['7h', '5d', '4c', '3s', '2h'], ['Ah', '2d', '3c', '4s', '5h']], 1),
('seven low vs eight low', [['8h', '6d', '4c', '3s', '2h'], ['7c', '6h', '4d', '3c', '2d']], -1),
('flush counts against', [['2h', '4h', '5h', '6h', '8h'], ['9c', '6d', '4d', '3c', '2d']], -1),
('straight counts against', [['3h', '4d', '5c', '6s', '7h'], ['Kh', 'Qd', 'Jc', '9s', '7c']], -1),
('pair loses to king high', [['2h', '2d', '4c', '5s', '7h'], ['Kh', '8d', '6c', '4s', '3h']], -1),
('ace-king gap hand', [['Ah', 'Kd', '7c', '4s', '2h'], ['Qh', 'Jd', 'Tc', '8s', '6h']], -1),
('straight flush vs flush', [['2c', '3c', '4c', '5c', '6c'], ['9d', '7d', '5d', '3d', '2d']], -1),
('nine vs ten', [['9h', '7d', '5c', '3s', '2h'], ['Th', '4d', '3c', '6s', '2c']], 1)],
[('number one vs wheel', [['7h', '5d', '4c', '3s', '2h'], ['Ah', '2d', '3c', '4s', '5h']], 1),
('flush counts against', [['2h', '4h', '5h', '6h', '8h'], ['9c', '6d', '4d', '3c', '2d']], -1),
('straight counts against', [['3h', '4d', '5c', '6s', '7h'], ['Kh', 'Qd', 'Jc', '9s', '7c']], -1),
('straight flush vs flush', [['2c', '3c', '4c', '5c', '6c'], ['9d', '7d', '5d', '3d', '2d']], -1),
('ace high vs pair', [['Ah', 'Qd', '9c', '7s', '5h'], ['3h', '3d', '6c', '5s', '4h']], 1),
('both pairs lower pair wins', [['4h', '4d', 'Kc', 'Qs', 'Jh'], ['5h', '5d', '2c', '3s', '7h']],
1),
('wheel vs pair', [['Ah', '2d', '3c', '4s', '5h'], ['3h', '3d', '6c', '8s', '9h']], 1),
('ace-deuce span vs pair', [['Ah', 'Jd', '8c', '6s', '2h'], ['4h', '4d', '6d', '8d', '9s']], 1)],
[('straight counts against', [['3h', '4d', '5c', '6s', '7h'], ['Kh', 'Qd', 'Jc', '9s', '7c']], -1),
('pair loses to king high', [['2h', '2d', '4c', '5s', '7h'], ['Kh', '8d', '6c', '4s', '3h']], -1),
('tie', [['7h', '5d', '4c', '3s', '2h'], ['7c', '5h', '4d', '3c', '2d']], 0),
('both pairs lower pair wins', [['4h', '4d', 'Kc', 'Qs', 'Jh'], ['5h', '5d', '2c', '3s', '7h']],
1),
('wheel vs pair', [['Ah', '2d', '3c', '4s', '5h'], ['3h', '3d', '6c', '8s', '9h']], 1),
('ace-deuce span vs pair', [['Ah', 'Jd', '8c', '6s', '2h'], ['4h', '4d', '6d', '8d', '9s']], 1),
('ace high vs king high', [['Ah', '9d', '7c', '4s', '2h'], ['Kh', 'Qd', 'Jc', '9s', '8c']], -1),
('nine vs ten', [['9h', '7d', '5c', '3s', '2h'], ['Th', '4d', '3c', '6s', '2c']], 1)]]
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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| number one vs wheel | 1 | 1 | Passed |
| wheel is ace high | -1 | -1 | Passed |
| seven low vs eight low | -1 | -1 | Passed |
| flush counts against | -1 | -1 | Passed |
| straight counts against | -1 | -1 | Passed |
| tie | 0 | 0 | Passed |
| both pairs lower pair wins | 1 | 1 | Passed |
| second tie | 0 | 0 | Passed |
SHA-256 / 985524538e9dfb95f23e1c4d47f1447d093ff72752e07ec77755fe60ff6ce2d2
Verification & scope
A deterministic toy model with an explicitly stated contract; card strings are rank+suit (for example "As", "Td"); no claim of conformance to any casino or tournament rulebook. 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 2026-09-29T14:50:08.881176+00:00.
Case digest / 395309a95af056cfe836e00ef4be5c917d81fb7d21b929e3d631da3a46c7c2b2