{
    "6": {
        "score": 0.6833333333333332,
        "success": {
            "8": {
                "modification": "(add an additional fallback solution generation step before ensembling results)",
                "score": 0.6999999999999998
            }
        },
        "failure": {}
    },
    "7": {
        "score": 0.7200000000000001,
        "success": {
            "4": {
                "modification": "modify: encapsulated the fallback generation in a function to better manage complexity and reuse code",
                "score": 0.8
            },
            "6": {
                "modification": "(add a feedback loop for fallback solution testing and integrate self-consistency for selection)",
                "score": 0.8
            },
            "7": {
                "modification": "(modify: added an additional unique fallback generation step before testing the solutions to increase robustness)",
                "score": 0.9
            },
            "2": {
                "modification": "(modify: added a secondary fallback solution generation step before ensemble to enhance solution robustness)",
                "score": 0.85
            }
        },
        "failure": {
            "9": {
                "modification": "(add a new operator to provide an alternative solution approach)",
                "score": 0.7200000000000001
            },
            "12": {
                "modification": "modify: enhanced fallback solutions by adding a fourth fallback generation step before ensemble",
                "score": 0.6733333333333333
            },
            "10": {
                "modification": "add additional validation step before considering fallback solutions",
                "score": 0.6933333333333334
            },
            "14": {
                "modification": "modify: integrated a secondary validation step before fallback generation to enhance solution quality",
                "score": 0.7133333333333333
            }
        }
    },
    "9": {
        "score": 0.7200000000000001,
        "success": {
            "3": {
                "modification": "Modified the fallback solution selection mechanism to prioritize quality over quantity",
                "score": 0.8
            },
            "5": {
                "modification": "Modified the approach for retrieving valid fallback solutions to include a maximum validity check for fallback solutions. This aims to ensure that not only are unique solutions retrieved, but they also meet a certain quality standard. The condition for valid fallback solutions now checks if a solution passes an additional verification step before being returned.",
                "score": 0.8
            },
            "1": {
                "modification": "Added a timeout mechanism for testing fallback solutions",
                "score": 0.9
            }
        },
        "failure": {
            "11": {
                "modification": "modify: Added a retry mechanism for testing fallback solutions to enhance robustness.",
                "score": 0.6933333333333334
            }
        }
    },
    "8": {
        "score": 0.7000000000000001,
        "success": {},
        "failure": {
            "13": {
                "modification": "modify the retrieval mechanism for testing unique fallback solutions",
                "score": 0.6866666666666666
            }
        }
    }
}