{"abstract":"Freshly made gems do not cascade to the next tier.","category":"Game economy crafting balance","checks":8,"contract":"gems[t] = count of tier t gems for t = 0..max_tier. Tiers are processed upward: three tier t gems make one tier t+1 gem at a cost of (t+1)*10 gold each, limited by the remaining gold budget; newly made gems can cascade into the next tier. Max-tier gems never combine. Returns [counts, gold_spent].","contract_signature":"gems, max_tier, budget","evaluation_group":"w2-game-economy-crafting-balance-gem-combine","failed_approach":"Stopping one tier early skips the combine into the max tier.","family":"w2-game-economy-crafting-balance-gem-combine-cascade-direction","id":"FA-86191","implementations":{"attempt":{"sha256":"8a842520119a41cf9afa6430b70f36f4ac2a0b7cae4f5a8ab8a83b25d4051ea9","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(gems, max_tier, budget):\n    g = list(gems)\n    gold = 0\n    for t in range(max_tier - 1):\n        price = (t + 1) * 10\n        made = min(g[t] // 3, (budget - gold) // price)\n        g[t] -= made * 3\n        g[t + 1] += made\n        gold += made * price\n    return [g, gold]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[('two level cascade #1', [[9, 0, 0], 2, 1000], [[0, 0, 1], 50]),\n  ('regression cascade direction #1', [[9, 3, 2], 2, 1000], [[0, 0, 4], 70]),\n  ('fault site cascade direction #1', [[4, 4, 3, 3, 9], 4, 29], [[1, 5, 3, 3, 9], 10]),\n  ('regression cascade direction #2', [[4, 2, 0, 3, 6], 4, 201], [[1, 0, 1, 0, 7], 70]),\n  ('partial repair boundary #1', [[4, 22], 1, 30], [[1, 23], 10]),\n  ('budget stops second tier #1', [[9, 1, 0], 2, 30], [[0, 4, 0], 30]),\n  ('max tier untouched #1', [[0, 6], 1, 1000], [[0, 6], 0]),\n  ('control #1', [[27, 2, 2], 2, 60], [[9, 8, 2], 60])],\n [('two level cascade #1', [[9, 0, 0], 2, 1000], [[0, 0, 1], 50]),\n  ('fault site cascade direction #1', [[4, 4, 3, 3, 9], 4, 29], [[1, 5, 3, 3, 9], 10]),\n  ('fault site cascade direction #2', [[3, 9, 8, 3], 3, 60], [[0, 4, 10, 3], 50]),\n  ('regression cascade direction #1', [[4, 2, 0, 3, 6], 4, 201], [[1, 0, 1, 0, 7], 70]),\n  ('partial repair boundary #1', [[4, 22], 1, 30], [[1, 23], 10]),\n  ('budget stops second tier #1', [[9, 1, 0], 2, 30], [[0, 4, 0], 30]),\n  ('max tier untouched #1', [[0, 6], 1, 1000], [[0, 6], 0]),\n  ('control #1', [[27, 2, 2], 2, 60], [[9, 8, 2], 60])],\n [('two level cascade #1', [[9, 0, 0], 2, 1000], [[0, 0, 1], 50]),\n  ('fault site cascade direction #1', [[4, 4, 0, 9, 8], 4, 60], [[1, 2, 1, 9, 8], 30]),\n  ('regression cascade direction #1', [[4, 2, 0, 3, 6], 4, 201], [[1, 0, 1, 0, 7], 70]),\n  ('regression cascade direction #2', [[9, 8, 2, 9], 3, 277], [[0, 2, 2, 10], 120]),\n  ('partial repair boundary #1', [[8, 2], 1, 60], [[2, 4], 20]),\n  ('budget stops second tier #1', [[9, 1, 0], 2, 30], [[0, 4, 0], 30]),\n  ('max tier untouched #1', [[0, 6], 1, 1000], [[0, 6], 0]),\n  ('control #1', [[27, 2, 2], 2, 60], [[9, 8, 2], 60])],\n [('two level cascade #1', [[9, 0, 0], 2, 1000], [[0, 0, 1], 50]),\n  ('regression cascade direction #1', [[9, 8, 2, 9], 3, 277], [[0, 2, 2, 10], 120]),\n  ('fault site cascade direction #1', [[8, 8, 4, 0, 0], 4, 30], [[2, 10, 4, 0, 0], 20]),\n  ('partial repair boundary #1', [[24, 3], 1, 1000], [[0, 11], 80]),\n  ('regression cascade direction #2', [[8, 2, 0], 2, 83], [[2, 1, 1], 40]),\n  ('budget stops second tier #1', [[9, 1, 0], 2, 30], [[0, 4, 0], 30]),\n  ('max tier untouched #1', [[0, 6], 1, 1000], [[0, 6], 0]),\n  ('control #1', [[9, 28, 24], 2, 10], [[6, 29, 24], 10])],\n [('two level cascade #1', [[9, 0, 0], 2, 1000], [[0, 0, 1], 50]),\n  ('fault site cascade direction #1', [[27, 3, 9], 2, 30], [[18, 6, 9], 30]),\n  ('regression cascade direction #1', [[8, 2, 0], 2, 83], [[2, 1, 1], 40]),\n  ('partial repair boundary #1', [[3, 3], 1, 30], [[0, 4], 10]),\n  ('partial repair boundary #2', [[24, 10], 1, 133], [[0, 18], 80]),\n  ('budget stops second tier #1', [[9, 1, 0], 2, 30], [[0, 4, 0], 30]),\n  ('max tier untouched #1', [[0, 6], 1, 1000], [[0, 6], 0]),\n  ('control #1', [[0, 4, 7, 4], 3, 29], [[0, 1, 8, 4], 20])]]\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":"1ce47717489269b7ad78e2b8dbe6c2085b001e1665a7dbc419ec7afe5269a588","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(gems, max_tier, budget):\n    g = list(gems)\n    gold = 0\n    for t in reversed(range(max_tier)):\n        price = (t + 1) * 10\n        made = min(g[t] // 3, (budget - gold) // price)\n        g[t] -= made * 3\n        g[t + 1] += made\n        gold += made * price\n    return [g, gold]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[('two level cascade #1', [[9, 0, 0], 2, 1000], [[0, 0, 1], 50]),\n  ('regression cascade direction #1', [[9, 3, 2], 2, 1000], [[0, 0, 4], 70]),\n  ('fault site cascade direction #1', [[4, 4, 3, 3, 9], 4, 29], [[1, 5, 3, 3, 9], 10]),\n  ('regression cascade direction #2', [[4, 2, 0, 3, 6], 4, 201], [[1, 0, 1, 0, 7], 70]),\n  ('partial repair boundary #1', [[4, 22], 1, 30], [[1, 23], 10]),\n  ('budget stops second tier #1', [[9, 1, 0], 2, 30], [[0, 4, 0], 30]),\n  ('max tier untouched #1', [[0, 6], 1, 1000], [[0, 6], 0]),\n  ('control #1', [[27, 2, 2], 2, 60], [[9, 8, 2], 60])],\n [('two level cascade #1', [[9, 0, 0], 2, 1000], [[0, 0, 1], 50]),\n  ('fault site cascade direction #1', [[4, 4, 3, 3, 9], 4, 29], [[1, 5, 3, 3, 9], 10]),\n  ('fault site cascade direction #2', [[3, 9, 8, 3], 3, 60], [[0, 4, 10, 3], 50]),\n  ('regression cascade direction #1', [[4, 2, 0, 3, 6], 4, 201], [[1, 0, 1, 0, 7], 70]),\n  ('partial repair boundary #1', [[4, 22], 1, 30], [[1, 23], 10]),\n  ('budget stops second tier #1', [[9, 1, 0], 2, 30], [[0, 4, 0], 30]),\n  ('max tier untouched #1', [[0, 6], 1, 1000], [[0, 6], 0]),\n  ('control #1', [[27, 2, 2], 2, 60], [[9, 8, 2], 60])],\n [('two level cascade #1', [[9, 0, 0], 2, 1000], [[0, 0, 1], 50]),\n  ('fault site cascade direction #1', [[4, 4, 0, 9, 8], 4, 60], [[1, 2, 1, 9, 8], 30]),\n  ('regression cascade direction #1', [[4, 2, 0, 3, 6], 4, 201], [[1, 0, 1, 0, 7], 70]),\n  ('regression cascade direction #2', [[9, 8, 2, 9], 3, 277], [[0, 2, 2, 10], 120]),\n  ('partial repair boundary #1', [[8, 2], 1, 60], [[2, 4], 20]),\n  ('budget stops second tier #1', [[9, 1, 0], 2, 30], [[0, 4, 0], 30]),\n  ('max tier untouched #1', [[0, 6], 1, 1000], [[0, 6], 0]),\n  ('control #1', [[27, 2, 2], 2, 60], [[9, 8, 2], 60])],\n [('two level cascade #1', [[9, 0, 0], 2, 1000], [[0, 0, 1], 50]),\n  ('regression cascade direction #1', [[9, 8, 2, 9], 3, 277], [[0, 2, 2, 10], 120]),\n  ('fault site cascade direction #1', [[8, 8, 4, 0, 0], 4, 30], [[2, 10, 4, 0, 0], 20]),\n  ('partial repair boundary #1', [[24, 3], 1, 1000], [[0, 11], 80]),\n  ('regression cascade direction #2', [[8, 2, 0], 2, 83], [[2, 1, 1], 40]),\n  ('budget stops second tier #1', [[9, 1, 0], 2, 30], [[0, 4, 0], 30]),\n  ('max tier untouched #1', [[0, 6], 1, 1000], [[0, 6], 0]),\n  ('control #1', [[9, 28, 24], 2, 10], [[6, 29, 24], 10])],\n [('two level cascade #1', [[9, 0, 0], 2, 1000], [[0, 0, 1], 50]),\n  ('fault site cascade direction #1', [[27, 3, 9], 2, 30], [[18, 6, 9], 30]),\n  ('regression cascade direction #1', [[8, 2, 0], 2, 83], [[2, 1, 1], 40]),\n  ('partial repair boundary #1', [[3, 3], 1, 30], [[0, 4], 10]),\n  ('partial repair boundary #2', [[24, 10], 1, 133], [[0, 18], 80]),\n  ('budget stops second tier #1', [[9, 1, 0], 2, 30], [[0, 4, 0], 30]),\n  ('max tier untouched #1', [[0, 6], 1, 1000], [[0, 6], 0]),\n  ('control #1', [[0, 4, 7, 4], 3, 29], [[0, 1, 8, 4], 20])]]\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-gem-combine-cascade-direction","generated_at":"2026-09-29T14:50:47.374967+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":"Tiers are processed from the top, so new gems miss their cascade.","sha256":"1457b39457490a7018f35acfbf05f8fefee8239df8cedbc294f24d6396956011","title":"Gem combining cascade: Combining runs top-down · 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":41.946,"exit_code":1,"observations":[{"actual":[[0,3,0],30],"check":"two level cascade #1","expected":[[0,0,1],50],"passed":false},{"actual":[[0,6,2],30],"check":"regression cascade direction #1","expected":[[0,0,4],70],"passed":false},{"actual":[[1,5,3,3,9],10],"check":"fault site cascade direction #1","expected":[[1,5,3,3,9],10],"passed":true},{"actual":[[1,0,1,3,6],30],"check":"regression cascade direction #2","expected":[[1,0,1,0,7],70],"passed":false},{"actual":[[4,22],0],"check":"partial repair boundary #1","expected":[[1,23],10],"passed":false},{"actual":[[0,4,0],30],"check":"budget stops second tier #1","expected":[[0,4,0],30],"passed":true},{"actual":[[0,6],0],"check":"max tier untouched #1","expected":[[0,6],0],"passed":true},{"actual":[[9,8,2],60],"check":"control #1","expected":[[9,8,2],60],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"two level cascade #1\", \"actual\": [[0, 3, 0], 30], \"expected\": [[0, 0, 1], 50], \"passed\": false}, {\"check\": \"regression cascade direction #1\", \"actual\": [[0, 6, 2], 30], \"expected\": [[0, 0, 4], 70], \"passed\": false}, {\"check\": \"fault site cascade direction #1\", \"actual\": [[1, 5, 3, 3, 9], 10], \"expected\": [[1, 5, 3, 3, 9], 10], \"passed\": true}, {\"check\": \"regression cascade direction #2\", \"actual\": [[1, 0, 1, 3, 6], 30], \"expected\": [[1, 0, 1, 0, 7], 70], \"passed\": false}, {\"check\": \"partial repair boundary #1\", \"actual\": [[4, 22], 0], \"expected\": [[1, 23], 10], \"passed\": false}, {\"check\": \"budget stops second tier #1\", \"actual\": [[0, 4, 0], 30], \"expected\": [[0, 4, 0], 30], \"passed\": true}, {\"check\": \"max tier untouched #1\", \"actual\": [[0, 6], 0], \"expected\": [[0, 6], 0], \"passed\": true}, {\"check\": \"control #1\", \"actual\": [[9, 8, 2], 60], \"expected\": [[9, 8, 2], 60], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":39.715,"exit_code":1,"observations":[{"actual":[[0,3,0],30],"check":"two level cascade #1","expected":[[0,0,1],50],"passed":false},{"actual":[[0,3,3],50],"check":"regression cascade direction #1","expected":[[0,0,4],70],"passed":false},{"actual":[[4,1,4,3,9],20],"check":"fault site cascade direction #1","expected":[[1,5,3,3,9],10],"passed":false},{"actual":[[1,3,0,0,7],50],"check":"regression cascade direction #2","expected":[[1,0,1,0,7],70],"passed":false},{"actual":[[1,23],10],"check":"partial repair boundary #1","expected":[[1,23],10],"passed":true},{"actual":[[0,4,0],30],"check":"budget stops second tier #1","expected":[[0,4,0],30],"passed":true},{"actual":[[0,6],0],"check":"max tier untouched #1","expected":[[0,6],0],"passed":true},{"actual":[[9,8,2],60],"check":"control #1","expected":[[9,8,2],60],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"two level cascade #1\", \"actual\": [[0, 3, 0], 30], \"expected\": [[0, 0, 1], 50], \"passed\": false}, {\"check\": \"regression cascade direction #1\", \"actual\": [[0, 3, 3], 50], \"expected\": [[0, 0, 4], 70], \"passed\": false}, {\"check\": \"fault site cascade direction #1\", \"actual\": [[4, 1, 4, 3, 9], 20], \"expected\": [[1, 5, 3, 3, 9], 10], \"passed\": false}, {\"check\": \"regression cascade direction #2\", \"actual\": [[1, 3, 0, 0, 7], 50], \"expected\": [[1, 0, 1, 0, 7], 70], \"passed\": false}, {\"check\": \"partial repair boundary #1\", \"actual\": [[1, 23], 10], \"expected\": [[1, 23], 10], \"passed\": true}, {\"check\": \"budget stops second tier #1\", \"actual\": [[0, 4, 0], 30], \"expected\": [[0, 4, 0], 30], \"passed\": true}, {\"check\": \"max tier untouched #1\", \"actual\": [[0, 6], 0], \"expected\": [[0, 6], 0], \"passed\": true}, {\"check\": \"control #1\", \"actual\": [[9, 8, 2], 60], \"expected\": [[9, 8, 2], 60], \"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."}}