{
  "schema_version": "emnlp-protocol-routing-dataset-v1.0.0",
  "generated_utc": "2026-09-24T02:18:59.281412+00:00",
  "conventions": {
    "join_key_cross_solver": "problem_id",
    "join_key_within_setting": "source_problem_id",
    "setting_id_format": "<benchmark>__<condition>__<run_id>",
    "example_id_formula": "<setting_id>::sha1('<setting_id>:<source_problem_id>')[:12]",
    "oracle_order": [
      "baseline_llm",
      "single_agent",
      "per",
      "broadcast"
    ],
    "oracle_fallthrough_label": "none",
    "oracle_none_semantics": "retrospective router ACTION (abstain); all four observed executions failed. Not a fifth protocol.",
    "bootstrap": "2000 problem-level percentile resamples",
    "rate_units": "proportions unless the column name ends in _pct or _points"
  },
  "leakage_policy": {
    "rule": "No file with role 'feature' may contain gold answers, per-protocol correctness, or oracle labels.",
    "feature_files": [
      "data/confidence/postanswer_confidence_predictions.csv",
      "data/confidence/primary_omnimath_confidence_predictions.csv",
      "data/costs/omnimath_per_protocol_costs.csv",
      "data/probe_inputs.jsonl",
      "data/problems.csv",
      "data/splits/primary_omnimath_splits.csv",
      "data/splits/six_setting_splits.csv"
    ],
    "label_files": [
      "data/labels_for_scoring.csv",
      "data/matched_labels.csv",
      "data/router/six_setting_test_predictions.csv"
    ]
  },
  "tables": {
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      "format": "csv",
      "rows": 24,
      "role": "aggregate",
      "description": "Aggregate result table reproduced from the camera-ready ancillary directory (failure_and_protocol_value_targets.csv).",
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      "columns": [
        {
          "name": "setting_id",
          "type": "string"
        },
        {
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          "type": "string"
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        {
          "name": "setting",
          "type": "string"
        },
        {
          "name": "target",
          "type": "string"
        },
        {
          "name": "n_parseable",
          "type": "integer"
        },
        {
          "name": "positive_n",
          "type": "integer"
        },
        {
          "name": "prevalence",
          "type": "number"
        },
        {
          "name": "auroc",
          "type": "number"
        },
        {
          "name": "auprc",
          "type": "number",
          "precision": "approximately 2 decimals, not 4",
          "caveat": "Scores are heavily tied (integer confidences) and the original average-precision implementation did not handle ties, so a standard estimator will not match the published digits. AUROC is tie-invariant and reproduces exactly. See docs/provenance/auprc_tie_handling.md in the code repository."
        }
      ]
    },
    "data/aggregate/heldout_router_evaluation.csv": {
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      "rows": 6,
      "role": "aggregate",
      "description": "Aggregate result table reproduced from the camera-ready ancillary directory (heldout_router_evaluation.csv).",
      "bytes": 1164,
      "columns": [
        {
          "name": "setting_id",
          "type": "string"
        },
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          "type": "string"
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        {
          "name": "setting",
          "type": "string"
        },
        {
          "name": "n",
          "type": "integer"
        },
        {
          "name": "baseline_solve",
          "type": "number"
        },
        {
          "name": "router_solve",
          "type": "number"
        },
        {
          "name": "router_ci",
          "type": "string"
        },
        {
          "name": "oracle_solve",
          "type": "number"
        },
        {
          "name": "oracle_gap",
          "type": "number"
        },
        {
          "name": "oracle_label_macro_f1",
          "type": "number"
        },
        {
          "name": "route_baseline",
          "type": "number"
        },
        {
          "name": "route_single",
          "type": "number"
        },
        {
          "name": "route_per",
          "type": "number"
        },
        {
          "name": "route_broadcast",
          "type": "number"
        },
        {
          "name": "route_none",
          "type": "number"
        }
      ]
    },
    "data/aggregate/heldout_router_paired_differences.csv": {
      "format": "csv",
      "rows": 6,
      "role": "aggregate",
      "description": "Aggregate result table reproduced from the camera-ready ancillary directory (heldout_router_paired_differences.csv).",
      "bytes": 843,
      "columns": [
        {
          "name": "setting_id",
          "type": "string"
        },
        {
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          "type": "string"
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        {
          "name": "setting",
          "type": "string"
        },
        {
          "name": "n",
          "type": "integer"
        },
        {
          "name": "router_minus_tier_majority_points",
          "type": "number"
        },
        {
          "name": "router_minus_tier_majority_ci_points",
          "type": "string"
        },
        {
          "name": "router_minus_baseline_points",
          "type": "number"
        },
        {
          "name": "router_minus_baseline_ci_points",
          "type": "string"
        }
      ]
    },
    "data/aggregate/main_routing_heldout.csv": {
      "format": "csv",
      "rows": 6,
      "role": "aggregate",
      "description": "Aggregate result table reproduced from the camera-ready ancillary directory (main_routing_heldout.csv).",
      "bytes": 623,
      "columns": [
        {
          "name": "class",
          "type": "string"
        },
        {
          "name": "policy",
          "type": "string"
        },
        {
          "name": "n",
          "type": "integer"
        },
        {
          "name": "solve_pct",
          "type": "number"
        },
        {
          "name": "solve_ci",
          "type": "string"
        },
        {
          "name": "avg_tokens_k",
          "type": "number"
        },
        {
          "name": "avg_tokens_ci",
          "type": "string"
        },
        {
          "name": "excess_tokens_k",
          "type": "number"
        },
        {
          "name": "excess_tokens_ci",
          "type": "string"
        }
      ]
    },
    "data/aggregate/matched_protocol_coverage.csv": {
      "format": "csv",
      "rows": 10,
      "role": "aggregate",
      "description": "Aggregate result table reproduced from the camera-ready ancillary directory (matched_protocol_coverage.csv).",
      "bytes": 1096,
      "columns": [
        {
          "name": "setting_id",
          "type": "string"
        },
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          "type": "string"
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        {
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          "type": "string"
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        {
          "name": "n",
          "type": "integer"
        },
        {
          "name": "baseline_pct",
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        {
          "name": "single_pct",
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        },
        {
          "name": "per_pct",
          "type": "number"
        },
        {
          "name": "broadcast_pct",
          "type": "number"
        },
        {
          "name": "oracle_pct",
          "type": "number"
        }
      ]
    },
    "data/aggregate/oracle_label_distribution.csv": {
      "format": "csv",
      "rows": 10,
      "role": "aggregate",
      "description": "Aggregate result table reproduced from the camera-ready ancillary directory (oracle_label_distribution.csv).",
      "bytes": 1076,
      "columns": [
        {
          "name": "setting_id",
          "type": "string"
        },
        {
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          "type": "string"
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        {
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          "type": "integer"
        },
        {
          "name": "baseline_pct",
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        {
          "name": "single_pct",
          "type": "number"
        },
        {
          "name": "per_pct",
          "type": "number"
        },
        {
          "name": "broadcast_pct",
          "type": "number"
        },
        {
          "name": "none_pct",
          "type": "number"
        }
      ]
    },
    "data/aggregate/per_broadcast_bootstrap_conditional.csv": {
      "format": "csv",
      "rows": 24,
      "role": "aggregate",
      "description": "Aggregate result table reproduced from the camera-ready ancillary directory (per_broadcast_bootstrap_conditional.csv).",
      "bytes": 6449,
      "columns": [
        {
          "name": "display_name",
          "type": "string"
        },
        {
          "name": "setting_id",
          "type": "string"
        },
        {
          "name": "subset",
          "type": "string"
        },
        {
          "name": "n",
          "type": "integer"
        },
        {
          "name": "PER_solve_rate",
          "type": "number"
        },
        {
          "name": "Broadcast_solve_rate",
          "type": "number"
        },
        {
          "name": "Broadcast_minus_PER",
          "type": "number"
        },
        {
          "name": "Broadcast_minus_PER_CI",
          "type": "string"
        },
        {
          "name": "PER_only_count",
          "type": "integer"
        },
        {
          "name": "PER_only_rate",
          "type": "number"
        },
        {
          "name": "Broadcast_only_count",
          "type": "integer"
        },
        {
          "name": "Broadcast_only_rate",
          "type": "number"
        },
        {
          "name": "both_count",
          "type": "integer"
        },
        {
          "name": "both_rate",
          "type": "number"
        },
        {
          "name": "neither_count",
          "type": "integer"
        },
        {
          "name": "neither_rate",
          "type": "number"
        }
      ]
    },
    "data/aggregate/per_broadcast_interaction.csv": {
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      "rows": 6,
      "role": "aggregate",
      "description": "Aggregate result table reproduced from the camera-ready ancillary directory (per_broadcast_interaction.csv).",
      "bytes": 1073,
      "columns": [
        {
          "name": "setting_id",
          "type": "string"
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        {
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          "type": "string"
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        {
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          "type": "integer"
        },
        {
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          "type": "number"
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        {
          "name": "broadcast_solve_pct",
          "type": "number"
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        {
          "name": "broadcast_minus_per_points",
          "type": "number"
        },
        {
          "name": "broadcast_minus_per_ci_points",
          "type": "string"
        },
        {
          "name": "per_only_count",
          "type": "integer"
        },
        {
          "name": "per_only_pct",
          "type": "number"
        },
        {
          "name": "broadcast_only_count",
          "type": "integer"
        },
        {
          "name": "broadcast_only_pct",
          "type": "number"
        },
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          "name": "both_count",
          "type": "integer"
        },
        {
          "name": "both_pct",
          "type": "number"
        },
        {
          "name": "neither_count",
          "type": "integer"
        },
        {
          "name": "neither_pct",
          "type": "number"
        }
      ]
    },
    "data/aggregate/postanswer_confidence.csv": {
      "format": "csv",
      "rows": 6,
      "role": "aggregate",
      "description": "Aggregate result table reproduced from the camera-ready ancillary directory (postanswer_confidence.csv).",
      "bytes": 1216,
      "columns": [
        {
          "name": "setting_id",
          "type": "string"
        },
        {
          "name": "solver",
          "type": "string"
        },
        {
          "name": "setting",
          "type": "string"
        },
        {
          "name": "n_total",
          "type": "integer"
        },
        {
          "name": "n_parseable",
          "type": "integer"
        },
        {
          "name": "parse_rate",
          "type": "number"
        },
        {
          "name": "failure_auroc",
          "type": "number"
        },
        {
          "name": "failure_auroc_ci",
          "type": "string"
        },
        {
          "name": "ece",
          "type": "number"
        },
        {
          "name": "ece_ci",
          "type": "string"
        },
        {
          "name": "brier",
          "type": "number"
        },
        {
          "name": "brier_ci",
          "type": "string"
        },
        {
          "name": "mean_conf_correct",
          "type": "number"
        },
        {
          "name": "mean_conf_wrong",
          "type": "number"
        }
      ]
    },
    "data/confidence/failure_and_protocol_value_targets.csv": {
      "format": "csv",
      "rows": 24,
      "role": "aggregate",
      "description": "The failure score scored against four increasingly protocol-specific targets. The paper's central negative result.",
      "bytes": 4253,
      "columns": [
        {
          "name": "display_name",
          "type": "string"
        },
        {
          "name": "setting_id",
          "type": "string"
        },
        {
          "name": "target",
          "type": "string"
        },
        {
          "name": "n_parseable",
          "type": "integer"
        },
        {
          "name": "positive_n",
          "type": "integer"
        },
        {
          "name": "prevalence",
          "type": "number"
        },
        {
          "name": "AUROC_using_failure_score",
          "type": "number"
        },
        {
          "name": "AUPRC_using_failure_score",
          "type": "number",
          "precision": "approximately 2 decimals, not 4",
          "caveat": "Scores are heavily tied (integer confidences) and the original average-precision implementation did not handle ties, so a standard estimator will not match the published digits. AUROC is tie-invariant and reproduces exactly. See docs/provenance/auprc_tie_handling.md in the code repository."
        }
      ]
    },
    "data/confidence/postanswer_confidence_predictions.csv": {
      "format": "csv",
      "rows": 12928,
      "role": "feature",
      "description": "POST-ANSWER, pre-collaboration probe (probe_type=post_answer_pre_collaboration), all 6 analysed settings. Sees the problem, allowed metadata and the model's own Baseline final answer; never the gold answer, correctness, oracle label or any protocol outcome. Reproduces the paper's headline failure-risk numbers. JOIN ON example_id, never on problem_uid_run.",
      "bytes": 2921875,
      "columns": [
        {
          "name": "setting_id",
          "type": "string"
        },
        {
          "name": "problem_id",
          "type": "string"
        },
        {
          "name": "example_id",
          "type": "string"
        },
        {
          "name": "problem_uid_run",
          "type": "string"
        },
        {
          "name": "probe_type",
          "type": "string"
        },
        {
          "name": "prober_model",
          "type": "string"
        },
        {
          "name": "run_id",
          "type": "string"
        },
        {
          "name": "parse_ok",
          "type": "boolean"
        },
        {
          "name": "confidence",
          "type": "number",
          "unit": "percent",
          "scale": "0-100 integer, NOT 0-1",
          "description": "P(the Baseline final answer is correct), integer percent 0-100."
        },
        {
          "name": "confidence_norm",
          "type": "number",
          "unit": "proportion",
          "scale": "0-1",
          "description": "The same value as `confidence`, rescaled to 0-1."
        },
        {
          "name": "repair_attempts",
          "type": "integer"
        },
        {
          "name": "parse_error",
          "type": "string"
        }
      ]
    },
    "data/confidence/primary_omnimath_confidence_predictions.csv": {
      "format": "csv",
      "rows": 839,
      "role": "feature",
      "description": "PRE-ANSWER q1 probe (probe_type=pre_answer_q1) on the primary OmniMath split. Sees the problem only, before any solving. Feature side: no correctness, no oracle label.",
      "bytes": 144860,
      "columns": [
        {
          "name": "problem_id",
          "type": "string"
        },
        {
          "name": "legacy_tier_id",
          "type": "string"
        },
        {
          "name": "split",
          "type": "string",
          "enum": [
            "train",
            "dev",
            "test"
          ]
        },
        {
          "name": "probe_type",
          "type": "string"
        },
        {
          "name": "probe_run",
          "type": "string"
        },
        {
          "name": "prober_model",
          "type": "string"
        },
        {
          "name": "probe_question_id",
          "type": "string"
        },
        {
          "name": "prompt_version",
          "type": "string"
        },
        {
          "name": "confidence_probability",
          "type": "number",
          "unit": "percent",
          "scale": "0-100 integer, NOT 0-1",
          "observed_min": 7.0,
          "observed_max": 99.0,
          "observed_distinct": 41,
          "nullable": true,
          "null_meaning": "the probe produced no parseable confidence (used_fallback=true, status=fallback_after_failure); 222 of 839 rows are null",
          "null_handling": "the documented confidence gate treats a null as ESCALATE. Threshold 70 means 70 percent. Reading the column as a 0-1 probability, or treating nulls as 'stay', silently yields a wrong solve rate (60.76% and 73.76% respectively, against the published 78.0%).",
          "description": "P(the model solves this problem in one pass), integer percent 0-100. Empty when unparseable."
        },
        {
          "name": "status",
          "type": "string"
        },
        {
          "name": "used_fallback",
          "type": "boolean"
        },
        {
          "name": "attempts",
          "type": "integer"
        },
        {
          "name": "probe_prompt_tokens",
          "type": "number"
        },
        {
          "name": "probe_completion_tokens",
          "type": "number"
        },
        {
          "name": "probe_total_tokens",
          "type": "number"
        }
      ]
    },
    "data/confidence/six_setting_confidence_metrics.csv": {
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      "rows": 6,
      "role": "aggregate",
      "description": "Post-answer failure-risk metrics: parse rate, AUROC, ECE, Brier, with bootstrap CIs.",
      "bytes": 1317,
      "columns": [
        {
          "name": "display_name",
          "type": "string"
        },
        {
          "name": "setting_id",
          "type": "string"
        },
        {
          "name": "model",
          "type": "string",
          "enum": [
            "gpt_oss_120b",
            "gemma_4_31b"
          ]
        },
        {
          "name": "domain",
          "type": "string",
          "enum": [
            "math",
            "science",
            "biology"
          ]
        },
        {
          "name": "n",
          "type": "integer"
        },
        {
          "name": "parse_rate",
          "type": "number"
        },
        {
          "name": "AUROC_failure",
          "type": "number"
        },
        {
          "name": "AUROC_CI",
          "type": "string"
        },
        {
          "name": "ECE",
          "type": "number"
        },
        {
          "name": "ECE_CI",
          "type": "string"
        },
        {
          "name": "Brier",
          "type": "number"
        },
        {
          "name": "Brier_CI",
          "type": "string"
        },
        {
          "name": "mean_conf_correct",
          "type": "number"
        },
        {
          "name": "mean_conf_wrong",
          "type": "number"
        }
      ]
    },
    "data/costs/omnimath_per_protocol_costs.csv": {
      "format": "csv",
      "rows": 4155,
      "role": "feature",
      "description": "Per-problem protocol-level token totals and model-call counts, summed over every model call (the paper's cost accounting). Covers ONE of the ten settings (omnimath2 gpt-oss-120b), 4155 of its 4181 problems; 26 omitted as unidentifiable through duplicate-text groups. Feature side: no correctness, no oracle label.",
      "bytes": 395362,
      "columns": [
        {
          "name": "setting_id",
          "type": "string"
        },
        {
          "name": "problem_id",
          "type": "string"
        },
        {
          "name": "baseline_total_tokens",
          "type": "integer"
        },
        {
          "name": "single_total_tokens",
          "type": "integer"
        },
        {
          "name": "per_total_tokens",
          "type": "integer"
        },
        {
          "name": "broadcast_total_tokens",
          "type": "integer"
        },
        {
          "name": "baseline_model_calls",
          "type": "integer"
        },
        {
          "name": "single_model_calls",
          "type": "integer"
        },
        {
          "name": "per_model_calls",
          "type": "integer"
        },
        {
          "name": "broadcast_model_calls",
          "type": "integer"
        }
      ]
    },
    "data/labels_for_scoring.csv": {
      "format": "csv",
      "rows": 12928,
      "role": "label",
      "description": "Outcome labels for the 6 settings with router and confidence analyses. Join to probe_inputs.jsonl on example_id.",
      "bytes": 2919126,
      "columns": [
        {
          "name": "example_id",
          "type": "string"
        },
        {
          "name": "setting_id",
          "type": "string"
        },
        {
          "name": "benchmark_id",
          "type": "string",
          "enum": [
            "omnimath2",
            "jeebench",
            "scibench",
            "labbench"
          ]
        },
        {
          "name": "slice_id",
          "type": "string"
        },
        {
          "name": "run_id",
          "type": "string"
        },
        {
          "name": "model",
          "type": "string",
          "enum": [
            "gpt_oss_120b",
            "gemma_4_31b"
          ]
        },
        {
          "name": "domain",
          "type": "string",
          "enum": [
            "math",
            "science",
            "biology"
          ]
        },
        {
          "name": "problem_id",
          "type": "string"
        },
        {
          "name": "source_problem_id",
          "type": "string"
        },
        {
          "name": "baseline_correct",
          "type": "integer",
          "enum": [
            0,
            1
          ]
        },
        {
          "name": "single_correct",
          "type": "integer",
          "enum": [
            0,
            1
          ]
        },
        {
          "name": "per_correct",
          "type": "integer",
          "enum": [
            0,
            1
          ]
        },
        {
          "name": "broadcast_correct",
          "type": "integer",
          "enum": [
            0,
            1
          ]
        },
        {
          "name": "oracle_label",
          "type": "string",
          "enum": [
            "baseline_llm",
            "single_agent",
            "per",
            "broadcast",
            "none"
          ]
        },
        {
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