{
 "study": "s8",
 "version": "1.1",
 "collected": "2026-09-26",
 "reanalyzed": "2026-09-28",
 "statistics": {
  "collected": "2026-09-26",
  "reanalyzed": "2026-09-28",
  "questions": 20,
  "answers": 300,
  "bootstrap": {
   "resamples": 2000,
   "seed": 20260926,
   "unit": "question"
  },
  "invalid_runs": [
   {
    "engine": "chatgpt",
    "question": "Who is the best divorce lawyer in Houston?",
    "run": 3,
    "chars": 172
   }
  ],
  "brand_vocabulary_note": "brands clustered per question over the 5 runs plus the study 17/18 answers to that question; version 1.0 clustered over runs only",
  "classes_definition": {
   "core": "named in every valid run (5 of 5)",
   "stable": "4 of 5",
   "intermittent": "2 or 3 of 5",
   "tail": "1 of 5"
  },
  "visibility": {
   "chatgpt": {
    "core": {
     "pct": 25.2,
     "ci95": [
      15.9,
      36.8
     ]
    },
    "stable": {
     "pct": 15.3,
     "ci95": [
      9.2,
      21.7
     ]
    },
    "intermittent": {
     "pct": 22.9,
     "ci95": [
      18.9,
      27.0
     ]
    },
    "tail": {
     "pct": 36.6,
     "ci95": [
      27.3,
      46.0
     ]
    },
    "brand_question_pairs": 262,
    "mean_visibility": 0.564,
    "hist_runs_named": {
     "1": 96,
     "2": 32,
     "3": 28,
     "4": 43,
     "5": 63
    }
   },
   "gemini": {
    "core": {
     "pct": 13.7,
     "ci95": [
      8.3,
      19.8
     ]
    },
    "stable": {
     "pct": 14.1,
     "ci95": [
      9.0,
      20.3
     ]
    },
    "intermittent": {
     "pct": 25.6,
     "ci95": [
      20.0,
      31.9
     ]
    },
    "tail": {
     "pct": 46.7,
     "ci95": [
      36.0,
      56.9
     ]
    },
    "brand_question_pairs": 227,
    "mean_visibility": 0.462,
    "hist_runs_named": {
     "1": 106,
     "2": 39,
     "3": 19,
     "4": 32,
     "5": 31
    }
   },
   "perplexity": {
    "core": {
     "pct": 40.9,
     "ci95": [
      35.0,
      47.8
     ]
    },
    "stable": {
     "pct": 14.8,
     "ci95": [
      9.3,
      20.6
     ]
    },
    "intermittent": {
     "pct": 28.6,
     "ci95": [
      22.3,
      34.6
     ]
    },
    "tail": {
     "pct": 15.8,
     "ci95": [
      10.6,
      21.0
     ]
    },
    "brand_question_pairs": 203,
    "mean_visibility": 0.701,
    "hist_runs_named": {
     "1": 32,
     "2": 29,
     "3": 29,
     "4": 30,
     "5": 83
    }
   }
  },
  "concentration": {
   "chatgpt": {
    "median_brands_per_run": 6.5,
    "median_distinct_5_runs": 11.0,
    "median_effective_brands": 9.5,
    "mean_effective_brands": 11.4,
    "mean_effective_brands_ci95": [
     9.1,
     13.8
    ],
    "mean_entropy_nats": 2.322,
    "median_core_size": 3.0,
    "median_core80_size": 5.0,
    "median_tail_size": 4.0,
    "effective_over_per_run_ratio": 1.759
   },
   "gemini": {
    "median_brands_per_run": 5.5,
    "median_distinct_5_runs": 10.5,
    "median_effective_brands": 9.2,
    "mean_effective_brands": 9.8,
    "mean_effective_brands_ci95": [
     8.3,
     11.4
    ],
    "mean_entropy_nats": 2.215,
    "median_core_size": 2.0,
    "median_core80_size": 3.0,
    "median_tail_size": 4.0,
    "effective_over_per_run_ratio": 2.007
   },
   "perplexity": {
    "median_brands_per_run": 6.8,
    "median_distinct_5_runs": 9.5,
    "median_effective_brands": 8.6,
    "mean_effective_brands": 9.1,
    "mean_effective_brands_ci95": [
     7.7,
     10.7
    ],
    "mean_entropy_nats": 2.14,
    "median_core_size": 4.0,
    "median_core80_size": 6.0,
    "median_tail_size": 1.0,
    "effective_over_per_run_ratio": 1.269
   }
  },
  "run_pairs": 596,
  "profile": {
   "chatgpt": {
    "brand_jaccard": {
     "mean": 0.545,
     "ci95": [
      0.45,
      0.639
     ]
    },
    "rbo": {
     "mean": 0.595,
     "ci95": [
      0.5,
      0.683
     ]
    },
    "kendall_shared": {
     "mean": 0.635,
     "ci95": [
      0.523,
      0.741
     ]
    },
    "top3_jaccard": {
     "mean": 0.556,
     "ci95": [
      0.437,
      0.676
     ]
    },
    "domain_jaccard": {
     "mean": 0.475,
     "ci95": [
      0.375,
      0.578
     ]
    },
    "url_jaccard": {
     "mean": 0.363,
     "ci95": [
      0.273,
      0.455
     ]
    },
    "word_jaccard": {
     "mean": 0.412,
     "ci95": [
      0.386,
      0.438
     ]
    },
    "text_similarity": {
     "mean": 0.799,
     "ci95": [
      0.766,
      0.832
     ]
    },
    "same_first_pair_pct": 53.8,
    "kendall_pairs_with_3plus_shared": 150,
    "identical_text_pairs": 0
   },
   "gemini": {
    "brand_jaccard": {
     "mean": 0.42,
     "ci95": [
      0.337,
      0.498
     ]
    },
    "rbo": {
     "mean": 0.472,
     "ci95": [
      0.386,
      0.553
     ]
    },
    "kendall_shared": {
     "mean": 0.439,
     "ci95": [
      0.295,
      0.587
     ]
    },
    "top3_jaccard": {
     "mean": 0.363,
     "ci95": [
      0.288,
      0.445
     ]
    },
    "domain_jaccard": {
     "mean": 0.326,
     "ci95": [
      0.224,
      0.442
     ]
    },
    "url_jaccard": {
     "mean": 0.221,
     "ci95": [
      0.146,
      0.304
     ]
    },
    "word_jaccard": {
     "mean": 0.311,
     "ci95": [
      0.288,
      0.334
     ]
    },
    "text_similarity": {
     "mean": 0.82,
     "ci95": [
      0.786,
      0.852
     ]
    },
    "same_first_pair_pct": 43.0,
    "kendall_pairs_with_3plus_shared": 127,
    "identical_text_pairs": 0
   },
   "perplexity": {
    "brand_jaccard": {
     "mean": 0.68,
     "ci95": [
      0.637,
      0.723
     ]
    },
    "rbo": {
     "mean": 0.757,
     "ci95": [
      0.722,
      0.79
     ]
    },
    "kendall_shared": {
     "mean": 0.681,
     "ci95": [
      0.601,
      0.754
     ]
    },
    "top3_jaccard": {
     "mean": 0.713,
     "ci95": [
      0.64,
      0.787
     ]
    },
    "domain_jaccard": {
     "mean": 0.987,
     "ci95": [
      0.973,
      0.998
     ]
    },
    "url_jaccard": {
     "mean": 0.98,
     "ci95": [
      0.965,
      0.994
     ]
    },
    "word_jaccard": {
     "mean": 0.449,
     "ci95": [
      0.434,
      0.464
     ]
    },
    "text_similarity": {
     "mean": 0.888,
     "ci95": [
      0.879,
      0.898
     ]
    },
    "same_first_pair_pct": 78.0,
    "kendall_pairs_with_3plus_shared": 186,
    "identical_text_pairs": 0
   }
  },
  "volatility_profile": {
   "chatgpt": {
    "membership": 0.455,
    "order_rbo": 0.405,
    "order_among_shared_kendall": 0.182,
    "first_pick": 0.462,
    "top3": 0.444,
    "source_domains": 0.525,
    "source_urls": 0.637,
    "wording": 0.588
   },
   "gemini": {
    "membership": 0.58,
    "order_rbo": 0.528,
    "order_among_shared_kendall": 0.28,
    "first_pick": 0.57,
    "top3": 0.637,
    "source_domains": 0.674,
    "source_urls": 0.779,
    "wording": 0.689
   },
   "perplexity": {
    "membership": 0.32,
    "order_rbo": 0.243,
    "order_among_shared_kendall": 0.159,
    "first_pick": 0.22,
    "top3": 0.287,
    "source_domains": 0.013,
    "source_urls": 0.02,
    "wording": 0.551
   }
  },
  "engine_differences": {
   "chatgpt-gemini_brand_jaccard": {
    "diff": 0.125,
    "ci95": [
     0.013,
     0.233
    ]
   },
   "chatgpt-perplexity_brand_jaccard": {
    "diff": -0.135,
    "ci95": [
     -0.247,
     -0.034
    ]
   },
   "gemini-perplexity_brand_jaccard": {
    "diff": -0.26,
    "ci95": [
     -0.359,
     -0.168
    ]
   }
  },
  "decision": {
   "chatgpt": {
    "mean_modal_first_share": 0.718,
    "mean_modal_first_share_pct": 71.8,
    "mean_modal_first_share_ci95": [
     0.63,
     0.807
    ],
    "first_pick_changed_pct": 80.0,
    "same_top3_set_all_runs_pct": 15.0,
    "questions_with_a_brand_top3_in_every_run_pct": 60.0,
    "core_brands": 66,
    "core_brands_rank_moved_pct": 86.4,
    "core_brands_always_top3_pct": 34.8
   },
   "gemini": {
    "mean_modal_first_share": 0.63,
    "mean_modal_first_share_pct": 63.0,
    "mean_modal_first_share_ci95": [
     0.53,
     0.74
    ],
    "first_pick_changed_pct": 85.0,
    "same_top3_set_all_runs_pct": 0.0,
    "questions_with_a_brand_top3_in_every_run_pct": 40.0,
    "core_brands": 31,
    "core_brands_rank_moved_pct": 87.1,
    "core_brands_always_top3_pct": 25.8
   },
   "perplexity": {
    "mean_modal_first_share": 0.87,
    "mean_modal_first_share_pct": 87.0,
    "mean_modal_first_share_ci95": [
     0.78,
     0.94
    ],
    "first_pick_changed_pct": 40.0,
    "same_top3_set_all_runs_pct": 15.0,
    "questions_with_a_brand_top3_in_every_run_pct": 90.0,
    "core_brands": 83,
    "core_brands_rank_moved_pct": 72.3,
    "core_brands_always_top3_pct": 42.2
   }
  },
  "coupling": {
   "pooled_between": {
    "slope_per_0.1": 0.025,
    "ci95": [
     0.005,
     0.048
    ],
    "model": "brand overlap ~ domain overlap + engine"
   },
   "within_question": {
    "slope_per_0.1": 0.03,
    "ci95": [
     0.017,
     0.043
    ],
    "model": "question x engine fixed effects"
   },
   "chatgpt": {
    "pairs": 190,
    "within_question_slope_per_0.1": 0.027,
    "ci95": [
     0.009,
     0.044
    ],
    "pearson_r": 0.357,
    "sd_domain_jaccard": 0.306,
    "pairs_identical_domains": 26,
    "brand_jaccard_when_domains_identical": 0.725,
    "pairs_identical_urls": 9,
    "brand_jaccard_when_urls_identical": 0.898,
    "brand_changed_when_urls_identical_pct": 44.4,
    "first_changed_when_urls_identical_pct": 44.4
   },
   "gemini": {
    "pairs": 190,
    "within_question_slope_per_0.1": 0.032,
    "ci95": [
     0.019,
     0.047
    ],
    "pearson_r": 0.228,
    "sd_domain_jaccard": 0.331,
    "pairs_identical_domains": 22,
    "brand_jaccard_when_domains_identical": 0.374,
    "pairs_identical_urls": 4,
    "brand_jaccard_when_urls_identical": 0.598,
    "brand_changed_when_urls_identical_pct": 100.0,
    "first_changed_when_urls_identical_pct": 75.0
   },
   "perplexity": {
    "pairs": 200,
    "within_question_slope_per_0.1": 0.091,
    "ci95": [
     -0.061,
     0.173
    ],
    "pearson_r": -0.039,
    "sd_domain_jaccard": 0.037,
    "pairs_identical_domains": 175,
    "brand_jaccard_when_domains_identical": 0.676,
    "pairs_identical_urls": 166,
    "brand_jaccard_when_urls_identical": 0.675,
    "brand_changed_when_urls_identical_pct": 91.6,
    "first_changed_when_urls_identical_pct": 21.1
   },
   "wording_vs_brands_pearson": {
    "chatgpt": 0.521,
    "gemini": 0.643,
    "perplexity": 0.464
   }
  },
  "by_question_type": {
   "chatgpt": {
    "local_n": 7,
    "local_mean_jaccard": 0.539,
    "national_n": 13,
    "national_mean_jaccard": 0.523,
    "pearson_brands_per_run_vs_jaccard": 0.355
   },
   "gemini": {
    "local_n": 7,
    "local_mean_jaccard": 0.343,
    "national_n": 13,
    "national_mean_jaccard": 0.46,
    "pearson_brands_per_run_vs_jaccard": 0.573
   },
   "perplexity": {
    "local_n": 7,
    "local_mean_jaccard": 0.662,
    "national_n": 13,
    "national_mean_jaccard": 0.691,
    "pearson_brands_per_run_vs_jaccard": -0.431
   }
  },
  "by_industry_mean_jaccard_all_engines": {
   "B2B software and technology": {
    "n_question_engine": 9,
    "mean": 0.708
   },
   "Financial services and insurance": {
    "n_question_engine": 9,
    "mean": 0.57
   },
   "Franchises and multi-location brands": {
    "n_question_engine": 6,
    "mean": 0.434
   },
   "Healthcare and dental": {
    "n_question_engine": 6,
    "mean": 0.509
   },
   "Home and local services": {
    "n_question_engine": 6,
    "mean": 0.523
   },
   "Hospitality and travel": {
    "n_question_engine": 9,
    "mean": 0.512
   },
   "Legal and professional services": {
    "n_question_engine": 6,
    "mean": 0.589
   },
   "Retail and ecommerce": {
    "n_question_engine": 9,
    "mean": 0.458
   }
  },
  "stability_variance_split_pct": {
   "question": 30.0,
   "engine": 25.5,
   "question_x_engine_residual": 44.5,
   "note": "sum of squares of mean run-to-run brand overlap per question and engine (20 x 3 cells)"
  },
  "question_mean_jaccard_range": [
   0.299,
   0.747
  ],
  "cross_engine_question_stability_pearson": {
   "chatgpt-gemini": 0.301,
   "chatgpt-perplexity": -0.065,
   "gemini-perplexity": -0.076
  },
  "conditions": {
   "rewording": {
    "questions": 5,
    "engines": [
     "chatgpt",
     "gemini",
     "perplexity"
    ],
    "chatgpt": {
     "n": 5,
     "repeat_jaccard": 0.694,
     "other_vs_runs_jaccard": 0.431,
     "extra_change": 0.264,
     "repeat_same_first_pct": 62.0,
     "other_same_first_pct": 12.0
    },
    "gemini": {
     "n": 5,
     "repeat_jaccard": 0.453,
     "other_vs_runs_jaccard": 0.298,
     "extra_change": 0.154,
     "repeat_same_first_pct": 26.0,
     "other_same_first_pct": 17.3
    },
    "perplexity": {
     "n": 5,
     "repeat_jaccard": 0.663,
     "other_vs_runs_jaccard": 0.462,
     "extra_change": 0.201,
     "repeat_same_first_pct": 76.0,
     "other_same_first_pct": 53.3
    }
   },
   "country": {
    "questions": 10,
    "engines": [
     "chatgpt",
     "gemini"
    ],
    "chatgpt": {
     "n": 10,
     "repeat_jaccard": 0.588,
     "other_vs_runs_jaccard": 0.398,
     "extra_change": 0.19,
     "repeat_same_first_pct": 72.2,
     "other_same_first_pct": 32.0
    },
    "gemini": {
     "n": 10,
     "repeat_jaccard": 0.453,
     "other_vs_runs_jaccard": 0.363,
     "extra_change": 0.09,
     "repeat_same_first_pct": 29.0,
     "other_same_first_pct": 35.3
    }
   },
   "us_separate_batch_vs_runs": {
    "chatgpt": {
     "jaccard": 0.477,
     "n": 10
    },
    "gemini": {
     "jaccard": 0.491,
     "n": 10
    }
   }
  },
  "ladder": {
   "chatgpt": {
    "country_questions": {
     "questions": 10,
     "same_batch_repeat": 0.588,
     "same_question_hours_later": 0.477,
     "changed_condition_hours_later": 0.398,
     "time_step": 0.11,
     "condition_step": 0.08
    },
    "rewording_questions": {
     "questions": 5,
     "same_batch_repeat": 0.694,
     "same_question_hours_later": 0.455,
     "changed_condition_hours_later": 0.431,
     "time_step": 0.239,
     "condition_step": 0.025
    }
   },
   "gemini": {
    "country_questions": {
     "questions": 10,
     "same_batch_repeat": 0.453,
     "same_question_hours_later": 0.491,
     "changed_condition_hours_later": 0.363,
     "time_step": -0.038,
     "condition_step": 0.128
    },
    "rewording_questions": {
     "questions": 5,
     "same_batch_repeat": 0.453,
     "same_question_hours_later": 0.466,
     "changed_condition_hours_later": 0.298,
     "time_step": -0.013,
     "condition_step": 0.168
    }
   },
   "hours_after_runs_median": 4.4
  },
  "single_run": {
   "chatgpt": {
    "one_run_shows_pct_of_5run_brands": 57.8,
    "one_run_shows_pct_ci95": [
     50.0,
     65.2
    ],
    "of_brands_missing_from_a_run_share_named_in_3plus_runs_pct": 16.3,
    "brand_pairs_reversed_by_one_run_pct": 4.2,
    "brand_pair_run_comparisons": 4330,
    "new_brands_by_run_number": {
     "1": 7.388,
     "2": 2.263,
     "3": 1.419,
     "4": 1.128,
     "5": 0.958
    }
   },
   "gemini": {
    "one_run_shows_pct_of_5run_brands": 48.4,
    "one_run_shows_pct_ci95": [
     41.7,
     55.3
    ],
    "of_brands_missing_from_a_run_share_named_in_3plus_runs_pct": 15.8,
    "brand_pairs_reversed_by_one_run_pct": 6.1,
    "brand_pair_run_comparisons": 2420,
    "new_brands_by_run_number": {
     "1": 5.24,
     "2": 2.25,
     "3": 1.545,
     "4": 1.255,
     "5": 1.06
    }
   },
   "perplexity": {
    "one_run_shows_pct_of_5run_brands": 72.2,
    "one_run_shows_pct_ci95": [
     68.7,
     75.4
    ],
    "of_brands_missing_from_a_run_share_named_in_3plus_runs_pct": 27.5,
    "brand_pairs_reversed_by_one_run_pct": 2.0,
    "brand_pair_run_comparisons": 2815,
    "new_brands_by_run_number": {
     "1": 7.12,
     "2": 1.49,
     "3": 0.755,
     "4": 0.465,
     "5": 0.32
    }
   }
  },
  "sampling": {
   "wilson_95_at_5_runs": {
    "0/5": [
     0,
     0.434
    ],
    "1/5": [
     0.036,
     0.624
    ],
    "2/5": [
     0.118,
     0.769
    ],
    "3/5": [
     0.231,
     0.882
    ],
    "4/5": [
     0.376,
     0.964
    ],
    "5/5": [
     0.566,
     1
    ]
   },
   "wilson_95_at_5_runs_pct": {
    "0/5": [
     0,
     43.4
    ],
    "1/5": [
     3.6,
     62.4
    ],
    "2/5": [
     11.8,
     76.9
    ],
    "3/5": [
     23.1,
     88.2
    ],
    "4/5": [
     37.6,
     96.4
    ],
    "5/5": [
     56.6,
     100
    ]
   },
   "runs_for_half_width_10pts_at_p50": 97,
   "runs_for_half_width_10pts_at_p80": 62,
   "runs_for_half_width_20pts_at_p50": 25,
   "note": "normal approximation n = 1.96^2 p(1-p) / h^2; assumes independent runs, which runs minutes apart may not be",
   "median_wilson_width_this_data": 0.588
  },
  "time_span": {
   "chatgpt": {
    "median_minutes": 11.3,
    "max_minutes": 16.0
   },
   "gemini": {
    "median_minutes": 11.1,
    "max_minutes": 15.5
   },
   "perplexity": {
    "median_minutes": 11.2,
    "max_minutes": 15.5
   }
  }
 },
 "version_1_0_statistics": {
  "s8_n_prompts": 20,
  "s8": {
   "chatgpt": {
    "prompts_complete": 20,
    "mean_pairwise_brand_jaccard": 0.53,
    "brands_in_all5_runs_pct": 23.7,
    "brands_in_only1_run_pct": 37.8,
    "same_first_brand_all5_pct": 20.0,
    "median_distinct_brands_over_5_runs": 11.5,
    "median_brands_per_run": 6.0,
    "mean_pairwise_source_domain_jaccard": 0.466
   },
   "gemini": {
    "prompts_complete": 20,
    "mean_pairwise_brand_jaccard": 0.421,
    "brands_in_all5_runs_pct": 13.6,
    "brands_in_only1_run_pct": 44.9,
    "same_first_brand_all5_pct": 15.0,
    "median_distinct_brands_over_5_runs": 10.0,
    "median_brands_per_run": 5.0,
    "mean_pairwise_source_domain_jaccard": 0.326
   },
   "perplexity": {
    "prompts_complete": 20,
    "mean_pairwise_brand_jaccard": 0.682,
    "brands_in_all5_runs_pct": 41.2,
    "brands_in_only1_run_pct": 16.1,
    "same_first_brand_all5_pct": 60.0,
    "median_distinct_brands_over_5_runs": 8.5,
    "median_brands_per_run": 7.0,
    "mean_pairwise_source_domain_jaccard": 0.987
   }
  },
  "s8_time_span": {
   "chatgpt": {
    "median_span_minutes": 11.3,
    "max_span_minutes": 16.0
   },
   "gemini": {
    "median_span_minutes": 11.1,
    "max_span_minutes": 15.5
   },
   "perplexity": {
    "median_span_minutes": 11.2,
    "max_span_minutes": 15.5
   }
  },
  "s8_identical_answer_pairs": {
   "pairs_compared": 600,
   "identical": 0
  }
 }
}