{
  "environment": {
    "torch": "2.13.0",
    "device": "CPU",
    "scope": "mechanism and arithmetic only; not model accuracy or GPU benchmark"
  },
  "position_cases": [
    {
      "shape": [
        2,
        3,
        4
      ],
      "tokens": 24,
      "position_span": 12,
      "range": [
        7,
        18
      ],
      "next_text": 19,
      "matches_paper_with_permutation": true,
      "half_time_dim_received": 2,
      "half_time_dim_effective": 0
    },
    {
      "shape": [
        16,
        8,
        8
      ],
      "tokens": 1024,
      "position_span": 240,
      "range": [
        7,
        246
      ],
      "next_text": 247,
      "matches_paper_with_permutation": true,
      "half_time_dim_received": 2,
      "half_time_dim_effective": 0
    },
    {
      "shape": [
        1,
        1,
        5
      ],
      "tokens": 5,
      "position_span": 5,
      "range": [
        7,
        11
      ],
      "next_text": 12,
      "matches_paper_with_permutation": true,
      "half_time_dim_received": 2,
      "half_time_dim_effective": 0
    },
    {
      "shape": [
        2,
        4,
        1
      ],
      "tokens": 8,
      "position_span": 8,
      "range": [
        7,
        14
      ],
      "next_text": 15,
      "matches_paper_with_permutation": true,
      "half_time_dim_received": 2,
      "half_time_dim_effective": 0
    },
    {
      "shape": [
        1,
        1,
        1
      ],
      "tokens": 1,
      "position_span": 1,
      "range": [
        7,
        7
      ],
      "next_text": 8,
      "matches_paper_with_permutation": true,
      "half_time_dim_received": 2,
      "half_time_dim_effective": 0
    }
  ],
  "rotation_relative_identity_error": 8.881784197001252e-16,
  "single_frequency_nonmonotonic_counterexample": {
    "cos_pi": -1.0,
    "cos_2pi": 1.0
  },
  "table_means": {
    "Vicuna7B": {
      "baseline_mean": 43.346666666666664,
      "vrope_mean": 44.48333333333333,
      "mean_gain": 1.1366666666666656,
      "declining_task_indices": [
        3
      ]
    },
    "Qwen2_1.5B": {
      "baseline_mean": 48.89833333333333,
      "vrope_mean": 49.96333333333333,
      "mean_gain": 1.0649999999999988,
      "declining_task_indices": [
        2
      ]
    },
    "Qwen2_7B": {
      "baseline_mean": 54.921666666666674,
      "vrope_mean": 56.345000000000006,
      "mean_gain": 1.4233333333333344,
      "declining_task_indices": []
    },
    "Qwen3_8B_Table9": {
      "baseline_mean": 61.92166666666666,
      "vrope_mean": 62.395,
      "mean_gain": 0.4733333333333339,
      "declining_task_indices": [
        2
      ]
    }
  },
  "retrieval_gain_pp": 32.19,
  "retrieval_gain_relative_percent": 58.69803063457329,
  "text_to_video_ratio_vrope_vs_3d": 7.2265625
}