{
  "analysis": "bad_luck_timing",
  "analysis_schema_version": 1,
  "analysis_source_sha256": "958863d31954575527bf0737172828ec09325221156d99aa4f7c9cda70646e82",
  "artifacts": {
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      "bytes": 95565,
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    "results.csv": {
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      "sha256": "71e9879ef49cec5b0f6b98d9cc00678afb05fad49700252e5a40d1a4d7abd376"
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  },
  "claim": "The lasting effect of one adverse terminal outcome depends jointly on its timing, the step-size rule, and the number of one-step TD backups between the outcome and the route choice.",
  "config": {
    "bad_rewards": [
      -5.0,
      -4.0
    ],
    "constant_alpha": 0.2,
    "depths": [
      1,
      3,
      6
    ],
    "epsilon_end": 0.01,
    "epsilon_start": 0.4,
    "good_reward": 1.0,
    "horizon": 200,
    "paired_seeds": 20000,
    "propagation_limit": 500000,
    "random_seed": 20260827,
    "safe_reward": 0.9
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  "event_rounds": [
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    4,
    8,
    12,
    16,
    20,
    24,
    28,
    32,
    36,
    39,
    40,
    44,
    48,
    50,
    52,
    56,
    60,
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    68,
    72,
    76,
    80,
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    92,
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    100,
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    160,
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    176,
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    196,
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  "exact_depth_one": [
    {
      "bad_reward": -5.0,
      "constant_alpha_recovery_visits": 12,
      "crossover_prior_good_traversals": 48,
      "paired_lock_probability_at_crossover": 0.47785,
      "sample_average_zero_history_recovery_visits": 60
    },
    {
      "bad_reward": -4.0,
      "constant_alpha_recovery_visits": 11,
      "crossover_prior_good_traversals": 39,
      "paired_lock_probability_at_crossover": 0.21445,
      "sample_average_zero_history_recovery_visits": 50
    }
  ],
  "full_return_comparator": "At every depth, a full-return update is algebraically identical to the reported depth-one exact calculation because it sends the terminal return directly to the start in the same episode.",
  "headline_main_setting": {
    "1": {
      "0": {
        "constant_alpha": 0.01325,
        "sample_average": 1.0
      },
      "100": {
        "constant_alpha": 0.99465,
        "sample_average": 0.0
      },
      "48": {
        "constant_alpha": 0.47785,
        "sample_average": 0.47785
      },
      "60": {
        "constant_alpha": 0.6864,
        "sample_average": 0.0
      }
    },
    "3": {
      "0": {
        "constant_alpha": 0.59985,
        "sample_average": 1.0
      },
      "100": {
        "constant_alpha": 1.0,
        "sample_average": 0.0
      },
      "48": {
        "constant_alpha": 0.99655,
        "sample_average": 0.0
      },
      "60": {
        "constant_alpha": 0.99975,
        "sample_average": 0.0
      }
    },
    "6": {
      "0": {
        "constant_alpha": 0.98985,
        "sample_average": 1.0
      },
      "100": {
        "constant_alpha": 1.0,
        "sample_average": 0.0
      },
      "48": {
        "constant_alpha": 1.0,
        "sample_average": 0.0
      },
      "60": {
        "constant_alpha": 1.0,
        "sample_average": 0.0
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    }
  },
  "intervention": "After n=tau forced successful risky-chain traversals, force risky once at round tau and replace only its terminal reward by b. Resume epsilon-greedy start choices with ordinary risky reward g. The paired control receives g.",
  "known_true_values": {
    "risky_route_at_every_depth": 1.0,
    "safe_route": 0.9
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  "limitations": [
    "The intervention conditions on an exact number of prior successful risky traversals.",
    "Rewards and transitions outside the intervention are deterministic.",
    "The safe value is known and fixed.",
    "The chain has no downstream decisions and uses discount one.",
    "The result does not establish behavior under traces, replay, function approximation, or deep RL.",
    "No novelty claim is made without a targeted literature review."
  ],
  "nearby_setting_at_analytic_crossover": {
    "bad_reward": -4.0,
    "by_depth": {
      "1": {
        "constant_alpha": 0.21445,
        "sample_average": 0.21445
      },
      "3": {
        "constant_alpha": 0.9561,
        "sample_average": 0.0
      },
      "6": {
        "constant_alpha": 0.9999,
        "sample_average": 0.0
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    },
    "event_round": 39
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  "runtime_seconds": 26.445150584040675,
  "status": "passed",
  "validation": {
    "all_propagation_windows_uncensored": true,
    "common_random_numbers": true,
    "depth_one_error_limit": 0.02,
    "max_absolute_depth_one_mc_error": 0.0051279345588824965
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