{"abstract":"The event trace violates the extra key rule and produces incorrect keyboard state or command output.","category":"Keyboard interactions","checks":9,"contract":"Case is [required_keys, events]. Down/up update held keys; cancel clears state. A chord fires on the first transition from incomplete to all required keys held, with no extra keys. It rearms after becoming incomplete. Empty chord never fires. Return fire count, sorted held, armed state, last triggering key and current completeness. Inputs are finite ordered event traces; return the stated deterministic state. Batch entries are independent. N varies the number of independent input transactions.","evaluation_group":"s3-keyboard-simultaneous-chord","failed_approach":"The partial repair changes this transition to bool(held & set(required)), which still violates the model contract on the explicit regression traces.","family":"s3-keyboard-interactions-simultaneous-chord-extra-key","id":"FA-30961","implementations":{"attempt":{"sha256":"7267dfd5fe4c8f25a16c07ebf6c170ea5fb1cf8688b8c1f12c7ebb9d4aeb7213","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(cases):\n    def run(c):\n        required,events=c\n        held=set(); armed=True; fires=0; last=None; complete=False\n        for kind,key in events:\n            if kind=='down': held.add(key)\n            elif kind=='up': held.discard(key)\n            elif kind=='cancel': held.clear()\n            complete=bool(required) and bool(held & set(required))\n            if complete and armed and kind=='down':\n                fires+=1\n                last=key\n                armed=False\n            elif not complete:\n                armed=True\n        return [fires,sorted(held),armed,last,complete]\n    return [run(c) for c in cases]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('simultaneous-chord scenario 0', solve([[[], []]] * N), [[0, [], True, None, False]] * N)\ncheck('simultaneous-chord scenario 1', solve([[[], [['down', 'x'], ['up', 'x'], ['down', 'x'], ['up', 'x']]]] * N), [[0, [], True, None, False]] * N)\ncheck('simultaneous-chord scenario 2', solve([[['A', 'B'], [['down', 'A'], ['down', 'B'], ['down', 'B']]]] * N), [[1, ['A', 'B'], False, 'B', True]] * N)\ncheck('simultaneous-chord scenario 3', solve([[['A', 'B'], [['down', 'A'], ['down', 'B'], ['up', 'B'], ['down', 'B']]]] * N), [[2, ['A', 'B'], False, 'B', True]] * N)\ncheck('simultaneous-chord scenario 4', solve([[['A', 'B'], [['down', 'A'], ['down', 'X'], ['down', 'B'], ['up', 'X']]]] * N), [[0, ['A', 'B'], True, None, True]] * N)\ncheck('simultaneous-chord scenario 5', solve([[['A', 'B'], [['down', 'A'], ['cancel', ''], ['down', 'B']]]] * N), [[0, ['B'], True, None, False]] * N)\ncheck('simultaneous-chord scenario 6', solve([[['A', 'B'], [['down', 'A'], ['up', 'X'], ['down', 'B']]]] * N), [[1, ['A', 'B'], False, 'B', True]] * N)\ncheck('simultaneous-chord scenario 7', solve([[['A'], [['down', 'A'], ['up', 'A'], ['down', 'A']]]] * N), [[2, ['A'], False, 'A', True]] * N)\ncheck('simultaneous-chord scenario 8', solve([[['A', 'B'], [['down', 'B'], ['down', 'A']]]] * N), [[1, ['A', 'B'], False, 'A', True]] * N)\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":"953df28379d002d74278f88b3a781388a27725d71f78d6d1cb94cce01f5b83bf","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(cases):\n    def run(c):\n        required,events=c\n        held=set(); armed=True; fires=0; last=None; complete=False\n        for kind,key in events:\n            if kind=='down': held.add(key)\n            elif kind=='up': held.discard(key)\n            elif kind=='cancel': held.clear()\n            complete=bool(required) and set(required).issubset(held)\n            if complete and armed and kind=='down':\n                fires+=1\n                last=key\n                armed=False\n            elif not complete:\n                armed=True\n        return [fires,sorted(held),armed,last,complete]\n    return [run(c) for c in cases]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('simultaneous-chord scenario 0', solve([[[], []]] * N), [[0, [], True, None, False]] * N)\ncheck('simultaneous-chord scenario 1', solve([[[], [['down', 'x'], ['up', 'x'], ['down', 'x'], ['up', 'x']]]] * N), [[0, [], True, None, False]] * N)\ncheck('simultaneous-chord scenario 2', solve([[['A', 'B'], [['down', 'A'], ['down', 'B'], ['down', 'B']]]] * N), [[1, ['A', 'B'], False, 'B', True]] * N)\ncheck('simultaneous-chord scenario 3', solve([[['A', 'B'], [['down', 'A'], ['down', 'B'], ['up', 'B'], ['down', 'B']]]] * N), [[2, ['A', 'B'], False, 'B', True]] * N)\ncheck('simultaneous-chord scenario 4', solve([[['A', 'B'], [['down', 'A'], ['down', 'X'], ['down', 'B'], ['up', 'X']]]] * N), [[0, ['A', 'B'], True, None, True]] * N)\ncheck('simultaneous-chord scenario 5', solve([[['A', 'B'], [['down', 'A'], ['cancel', ''], ['down', 'B']]]] * N), [[0, ['B'], True, None, False]] * N)\ncheck('simultaneous-chord scenario 6', solve([[['A', 'B'], [['down', 'A'], ['up', 'X'], ['down', 'B']]]] * N), [[1, ['A', 'B'], False, 'B', True]] * N)\ncheck('simultaneous-chord scenario 7', solve([[['A'], [['down', 'A'], ['up', 'A'], ['down', 'A']]]] * N), [[2, ['A'], False, 'A', True]] * N)\ncheck('simultaneous-chord scenario 8', solve([[['A', 'B'], [['down', 'B'], ['down', 'A']]]] * N), [[1, ['A', 'B'], False, 'A', True]] * N)\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"},"fixed":{"sha256":"562ac133d78ca0553becdae523cb3cdf4bbff15e9c721bccffa82f4e25a012d2","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(cases):\n    def run(c):\n        required,events=c\n        held=set(); armed=True; fires=0; last=None; complete=False\n        for kind,key in events:\n            if kind=='down': held.add(key)\n            elif kind=='up': held.discard(key)\n            elif kind=='cancel': held.clear()\n            complete=bool(required) and held==set(required)\n            if complete and armed and kind=='down':\n                fires+=1\n                last=key\n                armed=False\n            elif not complete:\n                armed=True\n        return [fires,sorted(held),armed,last,complete]\n    return [run(c) for c in cases]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('simultaneous-chord scenario 0', solve([[[], []]] * N), [[0, [], True, None, False]] * N)\ncheck('simultaneous-chord scenario 1', solve([[[], [['down', 'x'], ['up', 'x'], ['down', 'x'], ['up', 'x']]]] * N), [[0, [], True, None, False]] * N)\ncheck('simultaneous-chord scenario 2', solve([[['A', 'B'], [['down', 'A'], ['down', 'B'], ['down', 'B']]]] * N), [[1, ['A', 'B'], False, 'B', True]] * N)\ncheck('simultaneous-chord scenario 3', solve([[['A', 'B'], [['down', 'A'], ['down', 'B'], ['up', 'B'], ['down', 'B']]]] * N), [[2, ['A', 'B'], False, 'B', True]] * N)\ncheck('simultaneous-chord scenario 4', solve([[['A', 'B'], [['down', 'A'], ['down', 'X'], ['down', 'B'], ['up', 'X']]]] * N), [[0, ['A', 'B'], True, None, True]] * N)\ncheck('simultaneous-chord scenario 5', solve([[['A', 'B'], [['down', 'A'], ['cancel', ''], ['down', 'B']]]] * N), [[0, ['B'], True, None, False]] * N)\ncheck('simultaneous-chord scenario 6', solve([[['A', 'B'], [['down', 'A'], ['up', 'X'], ['down', 'B']]]] * N), [[1, ['A', 'B'], False, 'B', True]] * N)\ncheck('simultaneous-chord scenario 7', solve([[['A'], [['down', 'A'], ['up', 'A'], ['down', 'A']]]] * N), [[2, ['A'], False, 'A', True]] * N)\ncheck('simultaneous-chord scenario 8', solve([[['A', 'B'], [['down', 'B'], ['down', 'A']]]] * N), [[1, ['A', 'B'], False, 'A', True]] * N)\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":"Offline stipulated event model, not a browser implementation or web standard conformance claim. 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":"s3-keyboard-interactions-simultaneous-chord-extra-key","generated_at":"2026-09-29T14:41:57.733836+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Controlled keyboard event processing model for debugging application event logic.","repair":"Use the contract transition `held==set(required)` at the extra key fault site; preserve the other state transitions.","root_cause":"Chord activation ignores extra depressed keys or missing members.","sha256":"bb5129a81a65a3671ca319da79779b3f6a867b2f2b57539c5163f6b2f0f32a2a","title":"Simultaneous chord edge recognizer: Chord activation ignores extra depressed keys or missing members · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":38.95,"exit_code":1,"observations":[{"actual":[[0,[],true,null,false]],"check":"simultaneous-chord scenario 0","expected":[[0,[],true,null,false]],"passed":true},{"actual":[[0,[],true,null,false]],"check":"simultaneous-chord scenario 1","expected":[[0,[],true,null,false]],"passed":true},{"actual":[[1,["A","B"],false,"A",true]],"check":"simultaneous-chord scenario 2","expected":[[1,["A","B"],false,"B",true]],"passed":false},{"actual":[[1,["A","B"],false,"A",true]],"check":"simultaneous-chord scenario 3","expected":[[2,["A","B"],false,"B",true]],"passed":false},{"actual":[[1,["A","B"],false,"A",true]],"check":"simultaneous-chord scenario 4","expected":[[0,["A","B"],true,null,true]],"passed":false},{"actual":[[2,["B"],false,"B",true]],"check":"simultaneous-chord scenario 5","expected":[[0,["B"],true,null,false]],"passed":false},{"actual":[[1,["A","B"],false,"A",true]],"check":"simultaneous-chord scenario 6","expected":[[1,["A","B"],false,"B",true]],"passed":false},{"actual":[[2,["A"],false,"A",true]],"check":"simultaneous-chord scenario 7","expected":[[2,["A"],false,"A",true]],"passed":true},{"actual":[[1,["A","B"],false,"B",true]],"check":"simultaneous-chord scenario 8","expected":[[1,["A","B"],false,"A",true]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"simultaneous-chord scenario 0\", \"actual\": [[0, [], true, null, false]], \"expected\": [[0, [], true, null, false]], \"passed\": true}, {\"check\": \"simultaneous-chord scenario 1\", \"actual\": [[0, [], true, null, false]], \"expected\": [[0, [], true, null, false]], \"passed\": true}, {\"check\": \"simultaneous-chord scenario 2\", \"actual\": [[1, [\"A\", \"B\"], false, \"A\", true]], \"expected\": [[1, [\"A\", \"B\"], false, \"B\", true]], \"passed\": false}, {\"check\": \"simultaneous-chord scenario 3\", \"actual\": [[1, [\"A\", \"B\"], false, \"A\", true]], \"expected\": [[2, [\"A\", \"B\"], false, \"B\", true]], \"passed\": false}, {\"check\": \"simultaneous-chord scenario 4\", \"actual\": [[1, [\"A\", \"B\"], false, \"A\", true]], \"expected\": [[0, [\"A\", \"B\"], true, null, true]], \"passed\": false}, {\"check\": \"simultaneous-chord scenario 5\", \"actual\": [[2, [\"B\"], false, \"B\", true]], \"expected\": [[0, [\"B\"], true, null, false]], \"passed\": false}, {\"check\": \"simultaneous-chord scenario 6\", \"actual\": [[1, [\"A\", \"B\"], false, \"A\", true]], \"expected\": [[1, [\"A\", \"B\"], false, \"B\", true]], \"passed\": false}, {\"check\": \"simultaneous-chord scenario 7\", \"actual\": [[2, [\"A\"], false, \"A\", true]], \"expected\": [[2, [\"A\"], false, \"A\", true]], \"passed\": true}, {\"check\": \"simultaneous-chord scenario 8\", \"actual\": [[1, [\"A\", \"B\"], false, \"B\", true]], \"expected\": [[1, [\"A\", \"B\"], false, \"A\", true]], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":42.576,"exit_code":1,"observations":[{"actual":[[0,[],true,null,false]],"check":"simultaneous-chord scenario 0","expected":[[0,[],true,null,false]],"passed":true},{"actual":[[0,[],true,null,false]],"check":"simultaneous-chord scenario 1","expected":[[0,[],true,null,false]],"passed":true},{"actual":[[1,["A","B"],false,"B",true]],"check":"simultaneous-chord scenario 2","expected":[[1,["A","B"],false,"B",true]],"passed":true},{"actual":[[2,["A","B"],false,"B",true]],"check":"simultaneous-chord scenario 3","expected":[[2,["A","B"],false,"B",true]],"passed":true},{"actual":[[1,["A","B"],false,"B",true]],"check":"simultaneous-chord scenario 4","expected":[[0,["A","B"],true,null,true]],"passed":false},{"actual":[[0,["B"],true,null,false]],"check":"simultaneous-chord scenario 5","expected":[[0,["B"],true,null,false]],"passed":true},{"actual":[[1,["A","B"],false,"B",true]],"check":"simultaneous-chord scenario 6","expected":[[1,["A","B"],false,"B",true]],"passed":true},{"actual":[[2,["A"],false,"A",true]],"check":"simultaneous-chord scenario 7","expected":[[2,["A"],false,"A",true]],"passed":true},{"actual":[[1,["A","B"],false,"A",true]],"check":"simultaneous-chord scenario 8","expected":[[1,["A","B"],false,"A",true]],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"simultaneous-chord scenario 0\", \"actual\": [[0, [], true, null, false]], \"expected\": [[0, [], true, null, false]], \"passed\": true}, {\"check\": \"simultaneous-chord scenario 1\", \"actual\": [[0, [], true, null, false]], \"expected\": [[0, [], true, null, false]], \"passed\": true}, {\"check\": \"simultaneous-chord scenario 2\", \"actual\": [[1, [\"A\", \"B\"], false, \"B\", true]], \"expected\": [[1, [\"A\", \"B\"], false, \"B\", true]], \"passed\": true}, {\"check\": \"simultaneous-chord scenario 3\", \"actual\": [[2, [\"A\", \"B\"], false, \"B\", true]], \"expected\": [[2, [\"A\", \"B\"], false, \"B\", true]], \"passed\": true}, {\"check\": \"simultaneous-chord scenario 4\", \"actual\": [[1, [\"A\", \"B\"], false, \"B\", true]], \"expected\": [[0, [\"A\", \"B\"], true, null, true]], \"passed\": false}, {\"check\": \"simultaneous-chord scenario 5\", \"actual\": [[0, [\"B\"], true, null, false]], \"expected\": [[0, [\"B\"], true, null, false]], \"passed\": true}, {\"check\": \"simultaneous-chord scenario 6\", \"actual\": [[1, [\"A\", \"B\"], false, \"B\", true]], \"expected\": [[1, [\"A\", \"B\"], false, \"B\", true]], \"passed\": true}, {\"check\": \"simultaneous-chord scenario 7\", \"actual\": [[2, [\"A\"], false, \"A\", true]], \"expected\": [[2, [\"A\"], false, \"A\", true]], \"passed\": true}, {\"check\": \"simultaneous-chord scenario 8\", \"actual\": [[1, [\"A\", \"B\"], false, \"A\", true]], \"expected\": [[1, [\"A\", \"B\"], false, \"A\", true]], \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":39.297,"exit_code":0,"observations":[{"actual":[[0,[],true,null,false]],"check":"simultaneous-chord scenario 0","expected":[[0,[],true,null,false]],"passed":true},{"actual":[[0,[],true,null,false]],"check":"simultaneous-chord scenario 1","expected":[[0,[],true,null,false]],"passed":true},{"actual":[[1,["A","B"],false,"B",true]],"check":"simultaneous-chord scenario 2","expected":[[1,["A","B"],false,"B",true]],"passed":true},{"actual":[[2,["A","B"],false,"B",true]],"check":"simultaneous-chord scenario 3","expected":[[2,["A","B"],false,"B",true]],"passed":true},{"actual":[[0,["A","B"],true,null,true]],"check":"simultaneous-chord scenario 4","expected":[[0,["A","B"],true,null,true]],"passed":true},{"actual":[[0,["B"],true,null,false]],"check":"simultaneous-chord scenario 5","expected":[[0,["B"],true,null,false]],"passed":true},{"actual":[[1,["A","B"],false,"B",true]],"check":"simultaneous-chord scenario 6","expected":[[1,["A","B"],false,"B",true]],"passed":true},{"actual":[[2,["A"],false,"A",true]],"check":"simultaneous-chord scenario 7","expected":[[2,["A"],false,"A",true]],"passed":true},{"actual":[[1,["A","B"],false,"A",true]],"check":"simultaneous-chord scenario 8","expected":[[1,["A","B"],false,"A",true]],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"simultaneous-chord scenario 0\", \"actual\": [[0, [], true, null, false]], \"expected\": [[0, [], true, null, false]], \"passed\": true}, {\"check\": \"simultaneous-chord scenario 1\", \"actual\": [[0, [], true, null, false]], \"expected\": [[0, [], true, null, false]], \"passed\": true}, {\"check\": \"simultaneous-chord scenario 2\", \"actual\": [[1, [\"A\", \"B\"], false, \"B\", true]], \"expected\": [[1, [\"A\", \"B\"], false, \"B\", true]], \"passed\": true}, {\"check\": \"simultaneous-chord scenario 3\", \"actual\": [[2, [\"A\", \"B\"], false, \"B\", true]], \"expected\": [[2, [\"A\", \"B\"], false, \"B\", true]], \"passed\": true}, {\"check\": \"simultaneous-chord scenario 4\", \"actual\": [[0, [\"A\", \"B\"], true, null, true]], \"expected\": [[0, [\"A\", \"B\"], true, null, true]], \"passed\": true}, {\"check\": \"simultaneous-chord scenario 5\", \"actual\": [[0, [\"B\"], true, null, false]], \"expected\": [[0, [\"B\"], true, null, false]], \"passed\": true}, {\"check\": \"simultaneous-chord scenario 6\", \"actual\": [[1, [\"A\", \"B\"], false, \"B\", true]], \"expected\": [[1, [\"A\", \"B\"], false, \"B\", true]], \"passed\": true}, {\"check\": \"simultaneous-chord scenario 7\", \"actual\": [[2, [\"A\"], false, \"A\", true]], \"expected\": [[2, [\"A\"], false, \"A\", true]], \"passed\": true}, {\"check\": \"simultaneous-chord scenario 8\", \"actual\": [[1, [\"A\", \"B\"], false, \"A\", true]], \"expected\": [[1, [\"A\", \"B\"], false, \"A\", true]], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}