{
  "arxiv_id": "2510.23476",
  "claims": [
    {
      "assessment": "verified",
      "claim": 1,
      "literal_claim": "The optimal collaborative prediction set C*(x) has a two-threshold form: it augments the human-proposed set H(x) with labels whose score exceeds threshold a*, and prunes labels within H(x) whose score exceeds threshold b* (Theorem 2.1, Section 2).",
      "result": {
        "exhaustive_instances": 64,
        "inclusion_rule_disambiguation": "The paper uses nonconformity s=1-p and includes s<=threshold; equivalently it includes posterior p>=1-threshold. Outside-H passing a augments, while inside-H failing b is pruned.",
        "one_threshold_suboptimal_instances": 20,
        "policies_enumerated": 32768,
        "two_threshold_zero_gap_instances": 64
      }
    },
    {
      "assessment": "verified",
      "claim": 2,
      "literal_claim": "The counterfactual harm principle requires P(Y not in C(X) | Y in H(X)) < epsilon, i.e., the AI must not remove correct labels the human already proposed (Section 1).",
      "result": {
        "epsilon": "1/5",
        "event_computed": "Y not in C(X), conditioned on Y in H(X)",
        "exact_counterfactual_harm": "2950/39211",
        "prune_all_control_harm": "1/1"
      }
    },
    {
      "assessment": "verified",
      "claim": 3,
      "literal_claim": "The complementarity principle requires P(Y in C(X) | Y not in H(X)) >= 1-delta, i.e., the AI must recover correct labels the human missed (Section 1).",
      "result": {
        "delta": "1/4",
        "event_computed": "Y in C(X), conditioned on Y not in H(X)",
        "exact_complementarity": "17851/23308",
        "no_augmentation_control_complementarity": "0/1"
      }
    },
    {
      "assessment": "verified",
      "claim": 4,
      "literal_claim": "The offline calibration procedure gives distribution-free finite-sample coverage guarantees whose bounds depend on the sizes of the calibration sets used to fit a* and b* (Proposition 4.1, Section 4.1).",
      "result": {
        "all_lower_bounds_hold": true,
        "all_strict_upper_bounds_hold": true,
        "exact_rank_cases": 766,
        "floor_quantile_control_violations": 3,
        "group_size_settings": 14
      }
    },
    {
      "assessment": "verified",
      "claim": 5,
      "literal_claim": "The CUP-Online algorithm updates thresholds a_t and b_t via stochastic approximation steps (a_{t+1}=a_t+eta(1{s(x_t,y_t)>a_t}-delta), and analogously for b_t) to track target error rates under arbitrary distribution shift, including shifts caused by humans adapting their behavior to the AI (Section 4.2, Proposition 4.2).",
      "result": {
        "all_claimed_bounds_hold": true,
        "all_exact_telescopes": true,
        "correct_update_rounds": 76000,
        "correct_update_trajectories": 16,
        "delta": "1/5",
        "empirical_log_deviation_slope": -1.0459650194247514,
        "epsilon": "1/10",
        "eta": "1/5",
        "rate_horizons": [
          1000,
          2000,
          4000,
          12000
        ],
        "rate_repetitions_per_horizon": 8,
        "sign_flipped_control_bound_violations": 2
      }
    }
  ],
  "execution": {
    "deterministic": true,
    "exact_rational_arithmetic": true,
    "nearby_proxy_used": false,
    "peer_artifacts_used": false,
    "source_only_verdicts": false
  },
  "paper_id": "FzP6XZGG4d",
  "schema": "icml-native-reproduction-v1"
}