{"abstract":"Stamina potions used near full are wasted.","category":"Game economy crafting balance","checks":8,"contract":"Stamina regenerates 1 per 300 s while below cap, anchored at last_tick. Events [time, amount] are applied in time order (then amount); before each event (and finally at now) regeneration catches up: if it reaches cap the value becomes cap and the anchor moves to the event time, otherwise the anchor advances by whole periods. While at or above cap the anchor follows the event time. Amounts may push stamina above cap up to 999; negative amounts are spends that are rejected if they would go below zero. Return [stamina, anchor].","contract_signature":"stamina, cap, last_tick, now, refills","evaluation_group":"w2-game-economy-crafting-balance-stamina-regen","failed_approach":"Clamping between cap and the ceiling refills a spend from overflow back up to cap.","family":"w2-game-economy-crafting-balance-stamina-regen-overflow-ceiling","id":"FA-86091","implementations":{"attempt":{"sha256":"b2e7f469689f20663f5d4d32d937a44af7d0902969d33e31167c409b31122cae","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(stamina, cap, last_tick, now, refills):\n    events = sorted(refills) + [[now, 0]]\n    t = last_tick\n    s = stamina\n    for at, amount in events:\n        if s < cap:\n            gained = (at - t) // 300\n            if s + gained >= cap:\n                s = cap\n                t = at\n            else:\n                s += gained\n                t += gained * 300\n        else:\n            t = at\n        if s + amount >= 0:\n            s = max(cap, min(999, s + amount))\n    return [s, t]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[('overflow potion persists #1', [5, 5, 0, 1200, [[100, 10]]], [15, 1200]),\n  ('spend from full restarts timer #1', [10, 10, 0, 1000, [[400, -4]]], [8, 1000]),\n  ('regression overflow ceiling #1', [23, 20, 972, 1572, [[1185, -20], [1315, -20], [1066, 20]]], [3, 1315]),\n  ('fault site overflow ceiling #1', [12, 13, 710, 1010, [[793, 7], [721, 13]]], [32, 1010]),\n  ('partial repair boundary #1', [9, 9, 266, 266, [[266, -9], [266, -10]]], [0, 266]),\n  ('partial repair boundary #2', [16, 17, 83, 1773, [[154, -6]]], [15, 1583]),\n  ('exact refill to cap #1', [3, 5, 0, 600, []], [5, 600]),\n  ('control #1', [0, 11, 224, 4427, []], [11, 4427])],\n [('overflow potion persists #1', [5, 5, 0, 1200, [[100, 10]]], [15, 1200]),\n  ('spend from full restarts timer #1', [10, 10, 0, 1000, [[400, -4]]], [8, 1000]),\n  ('fault site overflow ceiling #1', [12, 13, 710, 1010, [[793, 7], [721, 13]]], [32, 1010]),\n  ('fault site overflow ceiling #2', [11, 12, 57, 163, [[92, 12], [139, 12]]], [35, 163]),\n  ('regression overflow ceiling #1', [23, 20, 972, 1572, [[1185, -20], [1315, -20], [1066, 20]]], [3, 1315]),\n  ('partial repair boundary #1', [16, 17, 83, 1773, [[154, -6]]], [15, 1583]),\n  ('exact refill to cap #1', [3, 5, 0, 600, []], [5, 600]),\n  ('control #1', [0, 11, 224, 4427, []], [11, 4427])],\n [('overflow potion persists #1', [5, 5, 0, 1200, [[100, 10]]], [15, 1200]),\n  ('spend from full restarts timer #1', [10, 10, 0, 1000, [[400, -4]]], [8, 1000]),\n  ('fault site overflow ceiling #1', [4, 13, 569, 868, [[776, 10]]], [14, 868]),\n  ('regression overflow ceiling #1', [0, 15, 688, 1288, [[1231, 15], [743, 9], [808, 15]]], [39, 1288]),\n  ('partial repair boundary #1', [17, 18, 353, 353, []], [17, 353]),\n  ('partial repair boundary #2', [0, 18, 176, 176, []], [0, 176]),\n  ('exact refill to cap #1', [3, 5, 0, 600, []], [5, 600]),\n  ('control #1', [14, 15, 389, 2081, []], [15, 2081])],\n [('overflow potion persists #1', [5, 5, 0, 1200, [[100, 10]]], [15, 1200]),\n  ('spend from full restarts timer #1', [10, 10, 0, 1000, [[400, -4]]], [8, 1000]),\n  ('fault site overflow ceiling #1', [0, 7, 587, 587, [[587, 8], [587, 9]]], [17, 587]),\n  ('fault site overflow ceiling #2', [17, 17, 382, 982, [[483, 17], [862, -6], [923, 17]]], [45, 982]),\n  ('regression overflow ceiling #1', [0, 15, 688, 1288, [[1231, 15], [743, 9], [808, 15]]], [39, 1288]),\n  ('partial repair boundary #1', [8, 9, 913, 1212, [[1053, -9], [963, -6], [1014, -5]]], [2, 913]),\n  ('exact refill to cap #1', [3, 5, 0, 600, []], [5, 600]),\n  ('control #1', [0, 9, 303, 303, [[303, 9]]], [9, 303])],\n [('overflow potion persists #1', [5, 5, 0, 1200, [[100, 10]]], [15, 1200]),\n  ('spend from full restarts timer #1', [10, 10, 0, 1000, [[400, -4]]], [8, 1000]),\n  ('regression overflow ceiling #1', [4, 11, 767, 2462, [[2177, 7], [1959, -11], [1673, 11]]], [14, 2462]),\n  ('fault site overflow ceiling #1', [12, 12, 443, 1043, [[843, 12]]], [24, 1043]),\n  ('partial repair boundary #1', [17, 17, 907, 907, [[907, -12], [907, -17], [907, -17]]], [0, 907]),\n  ('partial repair boundary #2', [0, 14, 147, 147, []], [0, 147]),\n  ('exact refill to cap #1', [3, 5, 0, 600, []], [5, 600]),\n  ('control #1', [8, 8, 764, 764, [[764, 0]]], [8, 764])]]\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":"14784042d6a747cbbb041c841225c1d06a2236e924eac38a568e7e0b6a295c5f","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(stamina, cap, last_tick, now, refills):\n    events = sorted(refills) + [[now, 0]]\n    t = last_tick\n    s = stamina\n    for at, amount in events:\n        if s < cap:\n            gained = (at - t) // 300\n            if s + gained >= cap:\n                s = cap\n                t = at\n            else:\n                s += gained\n                t += gained * 300\n        else:\n            t = at\n        if s + amount >= 0:\n            s = min(cap, s + amount)\n    return [s, t]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[('overflow potion persists #1', [5, 5, 0, 1200, [[100, 10]]], [15, 1200]),\n  ('spend from full restarts timer #1', [10, 10, 0, 1000, [[400, -4]]], [8, 1000]),\n  ('regression overflow ceiling #1', [23, 20, 972, 1572, [[1185, -20], [1315, -20], [1066, 20]]], [3, 1315]),\n  ('fault site overflow ceiling #1', [12, 13, 710, 1010, [[793, 7], [721, 13]]], [32, 1010]),\n  ('partial repair boundary #1', [9, 9, 266, 266, [[266, -9], [266, -10]]], [0, 266]),\n  ('partial repair boundary #2', [16, 17, 83, 1773, [[154, -6]]], [15, 1583]),\n  ('exact refill to cap #1', [3, 5, 0, 600, []], [5, 600]),\n  ('control #1', [0, 11, 224, 4427, []], [11, 4427])],\n [('overflow potion persists #1', [5, 5, 0, 1200, [[100, 10]]], [15, 1200]),\n  ('spend from full restarts timer #1', [10, 10, 0, 1000, [[400, -4]]], [8, 1000]),\n  ('fault site overflow ceiling #1', [12, 13, 710, 1010, [[793, 7], [721, 13]]], [32, 1010]),\n  ('fault site overflow ceiling #2', [11, 12, 57, 163, [[92, 12], [139, 12]]], [35, 163]),\n  ('regression overflow ceiling #1', [23, 20, 972, 1572, [[1185, -20], [1315, -20], [1066, 20]]], [3, 1315]),\n  ('partial repair boundary #1', [16, 17, 83, 1773, [[154, -6]]], [15, 1583]),\n  ('exact refill to cap #1', [3, 5, 0, 600, []], [5, 600]),\n  ('control #1', [0, 11, 224, 4427, []], [11, 4427])],\n [('overflow potion persists #1', [5, 5, 0, 1200, [[100, 10]]], [15, 1200]),\n  ('spend from full restarts timer #1', [10, 10, 0, 1000, [[400, -4]]], [8, 1000]),\n  ('fault site overflow ceiling #1', [4, 13, 569, 868, [[776, 10]]], [14, 868]),\n  ('regression overflow ceiling #1', [0, 15, 688, 1288, [[1231, 15], [743, 9], [808, 15]]], [39, 1288]),\n  ('partial repair boundary #1', [17, 18, 353, 353, []], [17, 353]),\n  ('partial repair boundary #2', [0, 18, 176, 176, []], [0, 176]),\n  ('exact refill to cap #1', [3, 5, 0, 600, []], [5, 600]),\n  ('control #1', [14, 15, 389, 2081, []], [15, 2081])],\n [('overflow potion persists #1', [5, 5, 0, 1200, [[100, 10]]], [15, 1200]),\n  ('spend from full restarts timer #1', [10, 10, 0, 1000, [[400, -4]]], [8, 1000]),\n  ('fault site overflow ceiling #1', [0, 7, 587, 587, [[587, 8], [587, 9]]], [17, 587]),\n  ('fault site overflow ceiling #2', [17, 17, 382, 982, [[483, 17], [862, -6], [923, 17]]], [45, 982]),\n  ('regression overflow ceiling #1', [0, 15, 688, 1288, [[1231, 15], [743, 9], [808, 15]]], [39, 1288]),\n  ('partial repair boundary #1', [8, 9, 913, 1212, [[1053, -9], [963, -6], [1014, -5]]], [2, 913]),\n  ('exact refill to cap #1', [3, 5, 0, 600, []], [5, 600]),\n  ('control #1', [0, 9, 303, 303, [[303, 9]]], [9, 303])],\n [('overflow potion persists #1', [5, 5, 0, 1200, [[100, 10]]], [15, 1200]),\n  ('spend from full restarts timer #1', [10, 10, 0, 1000, [[400, -4]]], [8, 1000]),\n  ('regression overflow ceiling #1', [4, 11, 767, 2462, [[2177, 7], [1959, -11], [1673, 11]]], [14, 2462]),\n  ('fault site overflow ceiling #1', [12, 12, 443, 1043, [[843, 12]]], [24, 1043]),\n  ('partial repair boundary #1', [17, 17, 907, 907, [[907, -12], [907, -17], [907, -17]]], [0, 907]),\n  ('partial repair boundary #2', [0, 14, 147, 147, []], [0, 147]),\n  ('exact refill to cap #1', [3, 5, 0, 600, []], [5, 600]),\n  ('control #1', [8, 8, 764, 764, [[764, 0]]], [8, 764])]]\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-stamina-regen-overflow-ceiling","generated_at":"2026-09-29T14:50:46.336590+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":"Refills are clamped to the regeneration cap instead of the overflow ceiling.","sha256":"5e9e1b53c74708a8f72bb3ca2c7881cba5138ca53701ac27d5536a8d77a6a79d","title":"Stamina regeneration: Refills cannot exceed cap · 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":41.539,"exit_code":1,"observations":[{"actual":[15,1200],"check":"overflow potion persists #1","expected":[15,1200],"passed":true},{"actual":[10,1000],"check":"spend from full restarts timer #1","expected":[8,1000],"passed":false},{"actual":[20,1572],"check":"regression overflow ceiling #1","expected":[3,1315],"passed":false},{"actual":[32,1010],"check":"fault site overflow ceiling #1","expected":[32,1010],"passed":true},{"actual":[9,266],"check":"partial repair boundary #1","expected":[0,266],"passed":false},{"actual":[17,1773],"check":"partial repair boundary #2","expected":[15,1583],"passed":false},{"actual":[5,600],"check":"exact refill to cap #1","expected":[5,600],"passed":true},{"actual":[11,4427],"check":"control #1","expected":[11,4427],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"overflow potion persists #1\", \"actual\": [15, 1200], \"expected\": [15, 1200], \"passed\": true}, {\"check\": \"spend from full restarts timer #1\", \"actual\": [10, 1000], \"expected\": [8, 1000], \"passed\": false}, {\"check\": \"regression overflow ceiling #1\", \"actual\": [20, 1572], \"expected\": [3, 1315], \"passed\": false}, {\"check\": \"fault site overflow ceiling #1\", \"actual\": [32, 1010], \"expected\": [32, 1010], \"passed\": true}, {\"check\": \"partial repair boundary #1\", \"actual\": [9, 266], \"expected\": [0, 266], \"passed\": false}, {\"check\": \"partial repair boundary #2\", \"actual\": [17, 1773], \"expected\": [15, 1583], \"passed\": false}, {\"check\": \"exact refill to cap #1\", \"actual\": [5, 600], \"expected\": [5, 600], \"passed\": true}, {\"check\": \"control #1\", \"actual\": [11, 4427], \"expected\": [11, 4427], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":38.95,"exit_code":1,"observations":[{"actual":[5,1200],"check":"overflow potion persists #1","expected":[15,1200],"passed":false},{"actual":[8,1000],"check":"spend from full restarts timer #1","expected":[8,1000],"passed":true},{"actual":[1,1485],"check":"regression overflow ceiling #1","expected":[3,1315],"passed":false},{"actual":[13,1010],"check":"fault site overflow ceiling #1","expected":[32,1010],"passed":false},{"actual":[0,266],"check":"partial repair boundary #1","expected":[0,266],"passed":true},{"actual":[15,1583],"check":"partial repair boundary #2","expected":[15,1583],"passed":true},{"actual":[5,600],"check":"exact refill to cap #1","expected":[5,600],"passed":true},{"actual":[11,4427],"check":"control #1","expected":[11,4427],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"overflow potion persists #1\", \"actual\": [5, 1200], \"expected\": [15, 1200], \"passed\": false}, {\"check\": \"spend from full restarts timer #1\", \"actual\": [8, 1000], \"expected\": [8, 1000], \"passed\": true}, {\"check\": \"regression overflow ceiling #1\", \"actual\": [1, 1485], \"expected\": [3, 1315], \"passed\": false}, {\"check\": \"fault site overflow ceiling #1\", \"actual\": [13, 1010], \"expected\": [32, 1010], \"passed\": false}, {\"check\": \"partial repair boundary #1\", \"actual\": [0, 266], \"expected\": [0, 266], \"passed\": true}, {\"check\": \"partial repair boundary #2\", \"actual\": [15, 1583], \"expected\": [15, 1583], \"passed\": true}, {\"check\": \"exact refill to cap #1\", \"actual\": [5, 600], \"expected\": [5, 600], \"passed\": true}, {\"check\": \"control #1\", \"actual\": [11, 4427], \"expected\": [11, 4427], \"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."}}