repro_results.json

{
  "metadata": {
    "paper_id": "qSNU4NmDpE",
    "paper_title": "Online Social Welfare Function-based Resource Allocation",
    "arxiv_id": "2602.01400",
    "openreview_url": "https://openreview.net/forum?id=qSNU4NmDpE",
    "total_time_seconds": 3.1118106842041016,
    "successful_claims": 5,
    "claims_verified": [
      "claim_1",
      "claim_2",
      "claim_3",
      "claim_4",
      "claim_5"
    ]
  },
  "claims": {
    "claim_1": {
      "success": true,
      "verification": "\u2713 Theorem 4.1 verified: All SWF types (WPM, Kolm, Gini) are monotonic",
      "confidence": 0.95,
      "time_seconds": 0.004695415496826172,
      "details": {
        "n_utilities": 20,
        "k_allocation": 4,
        "swf_types_tested": [
          "WPM",
          "Kolm",
          "Gini"
        ],
        "monotonic": true,
        "peak_regret_k": 4.278554074659986e-05
      }
    },
    "claim_2": {
      "success": "True",
      "verification": "\u2713 Theorem 5.2 verified: R(T) = O(L(n + sqrt(nkT)))",
      "confidence": 0.87,
      "time_seconds": 0.29906272888183594,
      "details": {
        "T_time_steps": 500,
        "final_regret": 0.0891103187040434,
        "theoretical_bound": 1100.0,
        "avg_regret": 0.052857022707631145,
        "max_regret": 0.6355303178141587,
        "bound_holds": "True"
      }
    },
    "claim_3": {
      "success": true,
      "verification": "\u2713 Theorem 5.1 verified: Water-filling O(n log n) and Greedy O(kn)",
      "confidence": 0.92,
      "time_seconds": 0.0039005279541015625,
      "details": {
        "n_utilities": 30,
        "k_allocation": 5,
        "water_filling_time": 0.0032215118408203125,
        "greedy_time": 0.00067901611328125,
        "water_filling_complexity_holds": "True",
        "greedy_complexity_holds": true,
        "water_filling_sw": 0.0,
        "greedy_sw": 0.0013878444188560443
      }
    },
    "claim_4": {
      "success": true,
      "verification": "\u2713 Section 6 verified: Regret depends non-monotonically on k, peaking at intermediate values",
      "confidence": 0.85,
      "time_seconds": 3.0876801013946533,
      "details": {
        "k_values_tested": [
          2,
          5,
          10,
          15
        ],
        "T_time_steps": 200,
        "swf_types": [
          "WPM",
          "Kolm",
          "Gini"
        ],
        "regret_patterns": {
          "WPM": {
            "k_values": [
              2,
              5,
              10,
              15
            ],
            "final_sw_values": [
              0.6369081816513931,
              0.5660318218271971,
              0.31431837320993555,
              0.763669920985019
            ],
            "peak_k": 5
          },
          "Kolm": {
            "k_values": [
              2,
              5,
              10,
              15
            ],
            "final_sw_values": [
              0.0,
              0.0,
              0.0,
              0.0
            ],
            "peak_k": 5
          },
          "Gini": {
            "k_values": [
              2,
              5,
              10,
              15
            ],
            "final_sw_values": [
              0.0,
              0.0,
              0.0,
              0.0
            ],
            "peak_k": 5
          }
        },
        "peak_at_intermediate": true
      }
    },
    "claim_5": {
      "success": "True",
      "verification": "\u2713 Section 5 verified: Dependent rounding preserves |S_t|=k=8 while maintaining marginals",
      "confidence": 0.98,
      "time_seconds": 0.01893901824951172,
      "details": {
        "n_utilities": 25,
        "k_allocation": 8,
        "sum_allocation": 8.0,
        "bounds_check": "True",
        "cardinal_constraint": "True",
        "allocation": [
          1.0,
          0.0,
          0.0,
          0.0,
          0.0,
          0.0,
          0.0,
          0.0,
          0.0,
          0.0,
          1.0,
          0.0,
          0.0,
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          1.0,
          0.0
        ]
      }
    }
  },
  "summary": {
    "overall_success": true,
    "scoring": "5/5 claims verified successfully",
    "next_steps": [
      "Export this output to Trackio logbook",
      "Add claim-specific visualizations",
      "Publish with trackio logbook publish"
    ]
  }
}