{
  "all_gates_pass": true,
  "arxiv_id": "2604.20098v1",
  "claims": [
    "Differentiable Coherent Factuality (DCF) achieves up to a 141% improvement in claim retention over frequency-based baselines on the MATH dataset at reliability level \u03b1=0.03 (1.76 vs. 0.73 claims retained) (Section 4.3).",
    "DCF achieves up to a 61% improvement in claim retention over frequency-based baselines on the FELM dataset at \u03b1=0.01 (Section 4.3).",
    "Theorem 3.1 (Calibration Convergence) shows that as temperature parameters approach their limits, DCF's soft nonconformity scores converge to the hard Coherent Factuality algorithm's scores, recovering its conformal quantile properties (Theorem 3.1).",
    "Theorem 3.2 (Prediction Convergence) shows DCF's soft retention probabilities converge to the original Coherent Factuality prediction set, preserving test-time coverage guarantees (Theorem 3.2).",
    "DCF's soft relaxations achieve 90-100% agreement with hard Coherent Factuality predictions across \u03b1\u2208[0.01, 0.10], validating the smooth approximation (Section 4.2).",
    "DCF jointly relaxes claim scoring together with logical-ancestor coherence enforcement and constrained argmax selection, rather than treating these graph operations independently (Section 3.2-3.4)."
  ],
  "gates": [
    {
      "detail": "literal source marker '\\\\label{thm:calibration}'",
      "name": "source_theorem_calibration",
      "passed": true
    },
    {
      "detail": "literal source marker '\\\\label{thm:prediction}'",
      "name": "source_theorem_prediction",
      "passed": true
    },
    {
      "detail": "literal source marker '\\\\label{eqn:softkeep}'",
      "name": "source_soft_filter",
      "passed": true
    },
    {
      "detail": "literal source marker '\\\\label{eqn:ancestor_coherence}'",
      "name": "source_ancestor_coherence",
      "passed": true
    },
    {
      "detail": "literal source marker 'w_{\\\\tau}^{\\\\text{cal}}'",
      "name": "source_soft_supremum",
      "passed": true
    },
    {
      "detail": "literal source marker '\\\\label{eqn: w_tau unnorm}'",
      "name": "source_gated_argmax",
      "passed": true
    },
    {
      "detail": "literal source marker 'three \\\\emph{coupled} discrete operations'",
      "name": "source_joint_cascade",
      "passed": true
    },
    {
      "detail": "literal source marker '\\\\text{SoftQuantile}'",
      "name": "source_quantile_scope",
      "passed": true
    },
    {
      "detail": "literal source marker '1.76 & 0.73 & +141.1'",
      "name": "source_math_table",
      "passed": true
    },
    {
      "detail": "literal source marker '17.9 & 11.1 & +61.3'",
      "name": "source_felm_table",
      "passed": true
    },
    {
      "detail": "literal source marker '6923 &  12 & 1416 & 6249 & 90.2\\\\%'",
      "name": "source_agreement_table",
      "passed": true
    },
    {
      "detail": "141.095890410959%",
      "name": "math_relative_improvement",
      "passed": true
    },
    {
      "detail": "rounded=141.1%",
      "name": "math_rounding",
      "passed": true
    },
    {
      "detail": "coverage=96.55%, target=97.00%, miss=0.45pp",
      "name": "math_target_near_miss",
      "passed": true
    },
    {
      "detail": "61.261261261261%",
      "name": "felm_relative_improvement",
      "passed": true
    },
    {
      "detail": "rounded=61.3%",
      "name": "felm_rounding",
      "passed": true
    },
    {
      "detail": "coverage=99.15%, target=99.00%",
      "name": "felm_target_met",
      "passed": true
    },
    {
      "detail": "all eight rows total 14,600 predictions",
      "name": "agreement_row_totals",
      "passed": true
    },
    {
      "detail": "recomputed=[100.0, 99.79452054794521, 93.82191780821918, 93.9041095890411, 95.3972602739726, 91.5068493150685, 90.21917808219177, 92.82191780821918]",
      "name": "agreement_recomputed",
      "passed": true
    },
    {
      "detail": "minimum=90.2%",
      "name": "agreement_minimum",
      "passed": true
    },
    {
      "detail": "maximum=100.0%",
      "name": "agreement_maximum",
      "passed": true
    },
    {
      "detail": "registered 90-100% interval contains all rows",
      "name": "agreement_claim_range",
      "passed": true
    },
    {
      "detail": "U_0.3=['ancestor']",
      "name": "hard_ancestor_filter",
      "passed": true
    },
    {
      "detail": "invalid thresholds=[0.5, 0.7, 0.9]",
      "name": "hard_false_claim_boundary",
      "passed": true
    },
    {
      "detail": "nu=0.3",
      "name": "hard_nonconformity",
      "passed": true
    },
    {
      "detail": "soft=0.300000000000, hard=0.3",
      "name": "calibration_single_limit",
      "passed": true
    },
    {
      "detail": "last two=[0.2999999998689819, 0.29999999999999993]",
      "name": "calibration_final_stability",
      "passed": true
    },
    {
      "detail": "V_0.5=1.0",
      "name": "calibration_invalid_threshold_penalty",
      "passed": true
    },
    {
      "detail": "tau*=0.5",
      "name": "hard_prediction_threshold",
      "passed": true
    },
    {
      "detail": "U_filtered=['ancestor', 'child']",
      "name": "hard_prediction_set",
      "passed": true
    },
    {
      "detail": "modal=0.5",
      "name": "prediction_modal_threshold",
      "passed": true
    },
    {
      "detail": "soft retained=['ancestor', 'child']",
      "name": "prediction_set_convergence",
      "passed": true
    },
    {
      "detail": "q={'ancestor': 0.9999967953382292, 'child': 0.9982082429080843, 'isolated': 5.138975898152613e-131}",
      "name": "prediction_probability_separation",
      "passed": true
    },
    {
      "detail": "independent child=1.000000000000, ancestor-aware child=9.358e-14",
      "name": "ancestor_destructive_control",
      "passed": true
    },
    {
      "detail": "Theorem 3.1 proves nonconformity-score convergence; quantile recovery is a separate source statement",
      "name": "quantile_scope_disclosed",
      "passed": true
    },
    {
      "detail": "all coupled components occur in the source",
      "name": "joint_relaxation_components",
      "passed": true
    }
  ],
  "paper_id": "XfndtVLIub",
  "passed": 36,
  "total": 36
}