{"abstract":"Exchanging nothing produces a negative balance.","category":"Game economy crafting balance","checks":8,"contract":"rates map currency -> copper value. Same currency returns [amount, 0] without fee. Otherwise value = amount*rate[from]; fee = ceil(value*fee_bp/10000), at least 1 copper when value > 0 and fee_bp > 0 and 0 otherwise; net = value - fee; return [net // rate[to], net % rate[to]] (change in copper).","contract_signature":"amount, from_cur, to_cur, rates, fee_bp","evaluation_group":"w2-game-economy-crafting-balance-currency-exchange","failed_approach":"Gating only on value charges a fee at a zero-fee desk.","family":"w2-game-economy-crafting-balance-currency-exchange-minimum-fee-gate","id":"FA-86221","implementations":{"attempt":{"sha256":"a4f3542ea922a75702ca8f4c21106ebe5d2c6757a7e838b364766054f99f0d5a","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(amount, from_cur, to_cur, rates, fee_bp):\n    if from_cur == to_cur:\n        return [amount, 0]\n    value = amount * rates[from_cur]\n    fee = -(-value * fee_bp // 10000)\n    if value > 0:\n        fee = max(fee, 1)\n    net = value - fee\n    return [net // rates[to_cur], net % rates[to_cur]]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[('zero amount with fee #1', [0, 'gem', 'silver', {'copper': 1, 'silver': 100, 'gem': 250}, 50], [0, 0]),\n  ('fault site minimum fee gate #1',\n   [0, 'gem', 'gold', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 333],\n   [0, 0]),\n  ('fault site minimum fee gate #2',\n   [0, 'token', 'gold', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 150],\n   [0, 0]),\n  ('partial repair boundary #1',\n   [1, 'gold', 'silver', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 0],\n   [100, 0]),\n  ('partial repair boundary #2',\n   [3, 'silver', 'token', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 0],\n   [3, 0]),\n  ('same currency no fee #1',\n   [5, 'gold', 'gold', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250}, 150],\n   [5, 0]),\n  ('fee rounds up #1', [3, 'gem', 'silver', {'copper': 1, 'silver': 100, 'gem': 250}, 25], [7, 48]),\n  ('control #1',\n   [1, 'gem', 'token', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 1],\n   [2, 49])],\n [('zero amount with fee #1', [0, 'gem', 'silver', {'copper': 1, 'silver': 100, 'gem': 250}, 50], [0, 0]),\n  ('fault site minimum fee gate #1',\n   [0, 'token', 'gold', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 150],\n   [0, 0]),\n  ('fault site minimum fee gate #2',\n   [0, 'silver', 'gold', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 50],\n   [0, 0]),\n  ('partial repair boundary #1',\n   [40, 'token', 'silver', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 0],\n   [40, 0]),\n  ('partial repair boundary #2',\n   [1, 'gold', 'token', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 0],\n   [100, 0]),\n  ('same currency no fee #1',\n   [5, 'gold', 'gold', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250}, 150],\n   [5, 0]),\n  ('fee rounds up #1', [3, 'gem', 'silver', {'copper': 1, 'silver': 100, 'gem': 250}, 25], [7, 48]),\n  ('control #1',\n   [1, 'gem', 'token', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 1],\n   [2, 49])],\n [('zero amount with fee #1', [0, 'gem', 'silver', {'copper': 1, 'silver': 100, 'gem': 250}, 50], [0, 0]),\n  ('fault site minimum fee gate #1',\n   [0, 'copper', 'gold', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 333],\n   [0, 0]),\n  ('fault site minimum fee gate #2',\n   [0, 'copper', 'token', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 1],\n   [0, 0]),\n  ('partial repair boundary #1',\n   [40, 'gold', 'token', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 0],\n   [4000, 0]),\n  ('partial repair boundary #2',\n   [914, 'copper', 'gold', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 0],\n   [0, 914]),\n  ('same currency no fee #1',\n   [5, 'gold', 'gold', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250}, 150],\n   [5, 0]),\n  ('fee rounds up #1', [3, 'gem', 'silver', {'copper': 1, 'silver': 100, 'gem': 250}, 25], [7, 48]),\n  ('control #1',\n   [1, 'gem', 'token', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 1],\n   [2, 49])],\n [('zero amount with fee #1', [0, 'gem', 'silver', {'copper': 1, 'silver': 100, 'gem': 250}, 50], [0, 0]),\n  ('fault site minimum fee gate #1',\n   [0, 'copper', 'silver', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 1],\n   [0, 0]),\n  ('fault site minimum fee gate #2',\n   [0, 'silver', 'token', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 150],\n   [0, 0]),\n  ('partial repair boundary #1',\n   [939, 'token', 'gem', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 0],\n   [375, 150]),\n  ('partial repair boundary #2',\n   [7, 'copper', 'gem', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 0],\n   [0, 7]),\n  ('same currency no fee #1',\n   [5, 'gold', 'gold', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250}, 150],\n   [5, 0]),\n  ('fee rounds up #1', [3, 'gem', 'silver', {'copper': 1, 'silver': 100, 'gem': 250}, 25], [7, 48]),\n  ('control #1',\n   [751, 'silver', 'silver', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 1],\n   [751, 0])],\n [('zero amount with fee #1', [0, 'gem', 'silver', {'copper': 1, 'silver': 100, 'gem': 250}, 50], [0, 0]),\n  ('fault site minimum fee gate #1',\n   [0, 'gold', 'copper', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 50],\n   [0, 0]),\n  ('fault site minimum fee gate #2',\n   [0, 'gem', 'copper', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 333],\n   [0, 0]),\n  ('partial repair boundary #1',\n   [7, 'gold', 'gem', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 0],\n   [280, 0]),\n  ('partial repair boundary #2',\n   [2596, 'silver', 'token', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 0],\n   [2596, 0]),\n  ('same currency no fee #1',\n   [5, 'gold', 'gold', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250}, 150],\n   [5, 0]),\n  ('fee rounds up #1', [3, 'gem', 'silver', {'copper': 1, 'silver': 100, 'gem': 250}, 25], [7, 48]),\n  ('control #1',\n   [7, 'gold', 'copper', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 333],\n   [67669, 0])]]\nfor label, args, expected in cases[N-1]:\n    check(label, solve(*args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"326f9fd0079d6bc553d18400c398e1557499cd8b5918d586a0c1402061fcb556","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(amount, from_cur, to_cur, rates, fee_bp):\n    if from_cur == to_cur:\n        return [amount, 0]\n    value = amount * rates[from_cur]\n    fee = -(-value * fee_bp // 10000)\n    if fee_bp > 0:\n        fee = max(fee, 1)\n    net = value - fee\n    return [net // rates[to_cur], net % rates[to_cur]]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[('zero amount with fee #1', [0, 'gem', 'silver', {'copper': 1, 'silver': 100, 'gem': 250}, 50], [0, 0]),\n  ('fault site minimum fee gate #1',\n   [0, 'gem', 'gold', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 333],\n   [0, 0]),\n  ('fault site minimum fee gate #2',\n   [0, 'token', 'gold', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 150],\n   [0, 0]),\n  ('partial repair boundary #1',\n   [1, 'gold', 'silver', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 0],\n   [100, 0]),\n  ('partial repair boundary #2',\n   [3, 'silver', 'token', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 0],\n   [3, 0]),\n  ('same currency no fee #1',\n   [5, 'gold', 'gold', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250}, 150],\n   [5, 0]),\n  ('fee rounds up #1', [3, 'gem', 'silver', {'copper': 1, 'silver': 100, 'gem': 250}, 25], [7, 48]),\n  ('control #1',\n   [1, 'gem', 'token', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 1],\n   [2, 49])],\n [('zero amount with fee #1', [0, 'gem', 'silver', {'copper': 1, 'silver': 100, 'gem': 250}, 50], [0, 0]),\n  ('fault site minimum fee gate #1',\n   [0, 'token', 'gold', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 150],\n   [0, 0]),\n  ('fault site minimum fee gate #2',\n   [0, 'silver', 'gold', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 50],\n   [0, 0]),\n  ('partial repair boundary #1',\n   [40, 'token', 'silver', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 0],\n   [40, 0]),\n  ('partial repair boundary #2',\n   [1, 'gold', 'token', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 0],\n   [100, 0]),\n  ('same currency no fee #1',\n   [5, 'gold', 'gold', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250}, 150],\n   [5, 0]),\n  ('fee rounds up #1', [3, 'gem', 'silver', {'copper': 1, 'silver': 100, 'gem': 250}, 25], [7, 48]),\n  ('control #1',\n   [1, 'gem', 'token', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 1],\n   [2, 49])],\n [('zero amount with fee #1', [0, 'gem', 'silver', {'copper': 1, 'silver': 100, 'gem': 250}, 50], [0, 0]),\n  ('fault site minimum fee gate #1',\n   [0, 'copper', 'gold', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 333],\n   [0, 0]),\n  ('fault site minimum fee gate #2',\n   [0, 'copper', 'token', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 1],\n   [0, 0]),\n  ('partial repair boundary #1',\n   [40, 'gold', 'token', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 0],\n   [4000, 0]),\n  ('partial repair boundary #2',\n   [914, 'copper', 'gold', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 0],\n   [0, 914]),\n  ('same currency no fee #1',\n   [5, 'gold', 'gold', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250}, 150],\n   [5, 0]),\n  ('fee rounds up #1', [3, 'gem', 'silver', {'copper': 1, 'silver': 100, 'gem': 250}, 25], [7, 48]),\n  ('control #1',\n   [1, 'gem', 'token', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 1],\n   [2, 49])],\n [('zero amount with fee #1', [0, 'gem', 'silver', {'copper': 1, 'silver': 100, 'gem': 250}, 50], [0, 0]),\n  ('fault site minimum fee gate #1',\n   [0, 'copper', 'silver', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 1],\n   [0, 0]),\n  ('fault site minimum fee gate #2',\n   [0, 'silver', 'token', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 150],\n   [0, 0]),\n  ('partial repair boundary #1',\n   [939, 'token', 'gem', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 0],\n   [375, 150]),\n  ('partial repair boundary #2',\n   [7, 'copper', 'gem', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 0],\n   [0, 7]),\n  ('same currency no fee #1',\n   [5, 'gold', 'gold', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250}, 150],\n   [5, 0]),\n  ('fee rounds up #1', [3, 'gem', 'silver', {'copper': 1, 'silver': 100, 'gem': 250}, 25], [7, 48]),\n  ('control #1',\n   [751, 'silver', 'silver', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 1],\n   [751, 0])],\n [('zero amount with fee #1', [0, 'gem', 'silver', {'copper': 1, 'silver': 100, 'gem': 250}, 50], [0, 0]),\n  ('fault site minimum fee gate #1',\n   [0, 'gold', 'copper', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 50],\n   [0, 0]),\n  ('fault site minimum fee gate #2',\n   [0, 'gem', 'copper', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 333],\n   [0, 0]),\n  ('partial repair boundary #1',\n   [7, 'gold', 'gem', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 0],\n   [280, 0]),\n  ('partial repair boundary #2',\n   [2596, 'silver', 'token', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 0],\n   [2596, 0]),\n  ('same currency no fee #1',\n   [5, 'gold', 'gold', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250}, 150],\n   [5, 0]),\n  ('fee rounds up #1', [3, 'gem', 'silver', {'copper': 1, 'silver': 100, 'gem': 250}, 25], [7, 48]),\n  ('control #1',\n   [7, 'gold', 'copper', {'copper': 1, 'silver': 100, 'gold': 10000, 'gem': 250, 'token': 100}, 333],\n   [67669, 0])]]\nfor label, args, expected in cases[N-1]:\n    check(label, solve(*args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":"Deterministic toy contract stipulated for this model; integer or exact arithmetic only, not a reproduction of any specific game engine. 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.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"w2-game-economy-crafting-balance-currency-exchange-minimum-fee-gate","generated_at":"2026-09-29T14:50:47.587088+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Game economies leak or destroy currency when one crafting or pricing rule is off by one boundary, rounding stage or state update; the defect is observable in exact integer outcomes.","root_cause":"The minimum fee applies even when no value is exchanged.","sha256":"09b921b4d89e0185a1ac2dcf69518f55108e19ad3510e8bd29fb8e12ec411236","title":"Currency exchange desk: Empty exchange charges the minimum fee · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":39.637,"exit_code":1,"observations":[{"actual":[0,0],"check":"zero amount with fee #1","expected":[0,0],"passed":true},{"actual":[0,0],"check":"fault site minimum fee gate #1","expected":[0,0],"passed":true},{"actual":[0,0],"check":"fault site minimum fee gate #2","expected":[0,0],"passed":true},{"actual":[99,99],"check":"partial repair boundary #1","expected":[100,0],"passed":false},{"actual":[2,99],"check":"partial repair boundary #2","expected":[3,0],"passed":false},{"actual":[5,0],"check":"same currency no fee #1","expected":[5,0],"passed":true},{"actual":[7,48],"check":"fee rounds up #1","expected":[7,48],"passed":true},{"actual":[2,49],"check":"control #1","expected":[2,49],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"zero amount with fee #1\", \"actual\": [0, 0], \"expected\": [0, 0], \"passed\": true}, {\"check\": \"fault site minimum fee gate #1\", \"actual\": [0, 0], \"expected\": [0, 0], \"passed\": true}, {\"check\": \"fault site minimum fee gate #2\", \"actual\": [0, 0], \"expected\": [0, 0], \"passed\": true}, {\"check\": \"partial repair boundary #1\", \"actual\": [99, 99], \"expected\": [100, 0], \"passed\": false}, {\"check\": \"partial repair boundary #2\", \"actual\": [2, 99], \"expected\": [3, 0], \"passed\": false}, {\"check\": \"same currency no fee #1\", \"actual\": [5, 0], \"expected\": [5, 0], \"passed\": true}, {\"check\": \"fee rounds up #1\", \"actual\": [7, 48], \"expected\": [7, 48], \"passed\": true}, {\"check\": \"control #1\", \"actual\": [2, 49], \"expected\": [2, 49], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":40.362,"exit_code":1,"observations":[{"actual":[-1,99],"check":"zero amount with fee #1","expected":[0,0],"passed":false},{"actual":[-1,9999],"check":"fault site minimum fee gate #1","expected":[0,0],"passed":false},{"actual":[-1,9999],"check":"fault site minimum fee gate #2","expected":[0,0],"passed":false},{"actual":[100,0],"check":"partial repair boundary #1","expected":[100,0],"passed":true},{"actual":[3,0],"check":"partial repair boundary #2","expected":[3,0],"passed":true},{"actual":[5,0],"check":"same currency no fee #1","expected":[5,0],"passed":true},{"actual":[7,48],"check":"fee rounds up #1","expected":[7,48],"passed":true},{"actual":[2,49],"check":"control #1","expected":[2,49],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"zero amount with fee #1\", \"actual\": [-1, 99], \"expected\": [0, 0], \"passed\": false}, {\"check\": \"fault site minimum fee gate #1\", \"actual\": [-1, 9999], \"expected\": [0, 0], \"passed\": false}, {\"check\": \"fault site minimum fee gate #2\", \"actual\": [-1, 9999], \"expected\": [0, 0], \"passed\": false}, {\"check\": \"partial repair boundary #1\", \"actual\": [100, 0], \"expected\": [100, 0], \"passed\": true}, {\"check\": \"partial repair boundary #2\", \"actual\": [3, 0], \"expected\": [3, 0], \"passed\": true}, {\"check\": \"same currency no fee #1\", \"actual\": [5, 0], \"expected\": [5, 0], \"passed\": true}, {\"check\": \"fee rounds up #1\", \"actual\": [7, 48], \"expected\": [7, 48], \"passed\": true}, {\"check\": \"control #1\", \"actual\": [2, 49], \"expected\": [2, 49], \"passed\": true}], \"passed\": false}\n"}},"member_only":{"stages":["fixed"],"fields":["implementations.fixed","verification.fixed","harness","repair"],"note":"The verified repair, its recorded checks, the repair description, and the scoring harness are available to members."}}