Computed synthetic examples for The Mathematics of Anthropology

All values below come from scripts/examples.py. People A-D are fictional.
Each batch contains distinct illustrative articles with identical toy coordinates; the count is not a claim that duplicate reporting is independent evidence.
Article representation example: xE1=(5,1,1.5), fixed mean=(1,1,1), V=R=I, D=(2,1,.5), so raw/named=(4,0,.5) and z=(2,0,1). The scales belong to a supplied fixed toy model; these articles do not fit the news basis.

backgrounds:
[
  [
    0.8,
    0.6,
    0.8
  ],
  [
    0.25,
    0.75,
    0.25
  ]
]

person_cell_counts:
[
  [
    15,
    5
  ],
  [
    10,
    10
  ],
  [
    5,
    5
  ],
  [
    5,
    5
  ]
]

person_cell_means:
[
  [
    [
      1.666666666667,
      0.333333333333,
      1.333333333333
    ],
    [
      1.0,
      -1.0,
      2.0
    ]
  ],
  [
    [
      2.0,
      0.0,
      1.0
    ],
    [
      1.0,
      2.0,
      0.0
    ]
  ],
  [
    [
      0.0,
      2.0,
      2.0
    ],
    [
      0.0,
      3.0,
      2.0
    ]
  ],
  [
    [
      -1.0,
      0.0,
      -2.0
    ],
    [
      -2.0,
      0.0,
      -1.0
    ]
  ]
]

person_cell_contrasts:
[
  [
    [
      0.866666666667,
      -0.266666666667,
      0.533333333333
    ],
    [
      0.75,
      -1.75,
      1.75
    ]
  ],
  [
    [
      1.2,
      -0.6,
      0.2
    ],
    [
      0.75,
      1.25,
      -0.25
    ]
  ],
  [
    [
      -0.8,
      1.4,
      1.2
    ],
    [
      -0.25,
      2.25,
      1.75
    ]
  ],
  [
    [
      -1.8,
      -0.6,
      -2.8
    ],
    [
      -2.25,
      -0.75,
      -1.25
    ]
  ]
]

person_residual_rows:
[
  [
    0.808333333333,
    -1.008333333333,
    1.141666666667
  ],
  [
    0.975,
    0.325,
    -0.025
  ],
  [
    -0.525,
    1.825,
    1.475
  ],
  [
    -2.025,
    -0.675,
    -2.025
  ]
]

article_weighted_contrasts_for_comparison:
[
  [
    0.8375,
    -0.6375,
    0.8375
  ],
  [
    0.975,
    0.325,
    -0.025
  ],
  [
    -0.525,
    1.825,
    1.475
  ],
  [
    -2.025,
    -0.675,
    -2.025
  ]
]

pre_normalization_norms:
[
  1.724396029532,
  1.028044259748,
  2.404552973008,
  2.94225678689
]

unit_profiles_B:
[
  [
    0.468763160834,
    -0.584745798566,
    0.662067557054
  ],
  [
    0.948402747017,
    0.316134249006,
    -0.024318019154
  ],
  [
    -0.218335801246,
    0.758976832903,
    0.613419632072
  ],
  [
    -0.688247201612,
    -0.229415733871,
    -0.688247201612
  ]
]

person_mean:
[
  0.127645726248,
  0.065237387368,
  0.14073049209
]

centered_profiles_H:
[
  [
    0.341117434586,
    -0.649983185934,
    0.521337064964
  ],
  [
    0.820757020769,
    0.250896861638,
    -0.165048511244
  ],
  [
    -0.345981527494,
    0.693739445535,
    0.472689139982
  ],
  [
    -0.81589292786,
    -0.294653121238,
    -0.828977693702
  ]
]

covariance:
[
  [
    0.393846919605,
    -0.003852717873,
    0.138796941187
  ],
  [
    -0.003852717873,
    0.263380564331,
    0.047978371712
  ],
  [
    0.138796941187,
    0.047978371712,
    0.30241809652
  ]
]

eigenvalues:
[
  0.497006828898,
  0.281673345829,
  0.180965405729
]

people_loadings_W:
[
  [
    0.796358235918,
    -0.35163608346
  ],
  [
    0.109041240633,
    0.883767477987
  ],
  [
    0.594914756857,
    0.308718495821
  ]
]

people_scores:
[
  [
    0.510927818707,
    -0.533436805153
  ],
  [
    0.582784923304,
    -0.11782682574
  ],
  [
    0.081330715703,
    0.880691829724
  ],
  [
    -1.175043457714,
    -0.229428198831
  ]
]

reconstructed_centered_profiles:
[
  [
    0.594457205324,
    -0.415721896729,
    0.139276690935
  ],
  [
    0.505537736972,
    -0.040583925564,
    0.310332030538
  ],
  [
    -0.244914640456,
    0.78719519938,
    0.320270699912
  ],
  [
    -0.85508030184,
    -0.330889377087,
    -0.769879421384
  ]
]

discarded_profiles:
[
  [
    -0.253339770738,
    -0.234261289205,
    0.382060374029
  ],
  [
    0.315219283797,
    0.291480787202,
    -0.475380541782
  ],
  [
    -0.101066887038,
    -0.093455753846,
    0.15241844007
  ],
  [
    0.03918737398,
    0.036236255848,
    -0.059098272317
  ]
]

discarded_squared_norms:
[
  0.265029520461,
  0.41031090569,
  0.042179874456,
  0.006341322308
]

centered_squared_norms:
[
  0.810631581481,
  0.763832333385,
  0.824412658715,
  1.439705748243
]

individual_retained_energy_fraction:
[
  0.673057987727,
  0.462825953083,
  0.948836454644,
  0.995595403911
]

population_variance_retained:
0.811424749497

cosine_pairs:
[
  {
    "people": [
      "A",
      "B"
    ],
    "full_centered_cosine": 0.039205113954,
    "retained_cosine": 0.821101689712
  },
  {
    "people": [
      "A",
      "C"
    ],
    "full_centered_cosine": -0.394509684234,
    "retained_cosine": -0.655511814382
  },
  {
    "people": [
      "A",
      "D"
    ],
    "full_centered_cosine": -0.480391968477,
    "retained_cosine": -0.540493701618
  },
  {
    "people": [
      "B",
      "C"
    ],
    "full_centered_cosine": -0.236818894647,
    "retained_cosine": -0.107195950758
  },
  {
    "people": [
      "B",
      "D"
    ],
    "full_centered_cosine": -0.5785995472,
    "retained_cosine": -0.924026563924
  },
  {
    "people": [
      "C",
      "D"
    ],
    "full_centered_cosine": -0.288196793617,
    "retained_cosine": -0.281073359354
  }
]

query:
{
  "centered_news_direction": [
    1.0,
    0.0,
    0.0
  ],
  "people_coordinates": [
    0.796358235918,
    -0.35163608346
  ],
  "returned_news_direction": [
    0.757834375106,
    -0.223928644616,
    0.36520870353
  ],
  "discarded": [
    0.242165624894,
    0.223928644616,
    -0.36520870353
  ]
}

Checkpoint answers:
{
  "unique_vs_associations": "45 unique articles; 60 person-article associations. E1 and L3 are shared.",
  "A_cell_weights": "One-half each; article weighting would assign three-quarters to E and one-quarter to L.",
  "PCA_shape": "H is 4x3; covariance 3x3; W 3x2; scores 4x2; W transpose 2x3.",
  "zero_recent_profile": "Unsupported recent coverage is missing, not a zero vector.",
  "ontology_probabilities": "1.3 and -0.3 are linear scores, not probabilities; training fit cannot establish calibration."
}

Side examples:
{
  "rotation_scaling": {
    "raw_covariance": [
      [
        4.0,
        0.0
      ],
      [
        0.0,
        1.0
      ]
    ],
    "R": [
      [
        0.707106781187,
        -0.707106781187
      ],
      [
        0.707106781187,
        0.707106781187
      ]
    ],
    "named_covariance": [
      [
        2.5,
        -1.5
      ],
      [
        -1.5,
        2.5
      ]
    ],
    "named_marginal_sd": [
      1.581138830084,
      1.581138830084
    ],
    "standardized_covariance": [
      [
        1.0,
        -0.6
      ],
      [
        -0.6,
        1.0
      ]
    ],
    "c": [
      2.0,
      0.0
    ],
    "y": [
      1.414213562373,
      -1.414213562373
    ],
    "z": [
      0.894427191,
      -0.894427191
    ],
    "scale_first_then_rotate": [
      0.707106781187,
      -0.707106781187
    ],
    "raw_energy": 4.0,
    "rotated_energy": 4.0,
    "standardized_energy": 1.6
  },
  "time_mixture": {
    "scope": "Hypothetical windows hold A's cell contrasts fixed while their counts change.",
    "counts": [
      [
        90,
        10
      ],
      [
        10,
        90
      ]
    ],
    "cell_contrasts": [
      [
        0.866666666667,
        -0.266666666667,
        0.533333333333
      ],
      [
        0.75,
        -1.75,
        1.75
      ]
    ],
    "article_weighted_residuals": [
      [
        0.855,
        -0.415,
        0.655
      ],
      [
        0.761666666667,
        -1.601666666667,
        1.628333333333
      ]
    ],
    "cell_balanced_residuals": [
      [
        0.808333333333,
        -1.008333333333,
        1.141666666667
      ],
      [
        0.808333333333,
        -1.008333333333,
        1.141666666667
      ]
    ],
    "article_weighted_people_scores": [
      [
        0.695803414366,
        -0.45925245545
      ],
      [
        0.389245961709,
        -0.546576736901
      ]
    ],
    "cell_balanced_people_scores": [
      [
        0.510927818707,
        -0.533436805153
      ],
      [
        0.510927818707,
        -0.533436805153
      ]
    ],
    "apparent_people_distance_article_weighted": 0.318752257891,
    "cell_balanced_people_distance": 0.0,
    "gate_four_articles": {
      "retained_cells": [
        "Source E / 2010s"
      ],
      "residual": [
        0.866666666667,
        -0.266666666667,
        0.533333333333
      ]
    },
    "gate_five_articles": {
      "retained_cells": [
        "Source E / 2010s",
        "Source L / 2020s"
      ],
      "residual": [
        0.808333333333,
        -1.008333333333,
        1.141666666667
      ]
    }
  },
  "attention": {
    "source_totals": [
      100,
      1000
    ],
    "person_attributed_scores": [
      10,
      0
    ],
    "source_shares": [
      0.1,
      0
    ],
    "active_source_mean": 0.05,
    "pooled_share_for_comparison": 0.009090909091,
    "article_ids": [
      "E1",
      "E2",
      "L1"
    ],
    "absolute_axis_coordinates": [
      2,
      1,
      1
    ],
    "edition_attention_shares": [
      0.01,
      0.1,
      0.04
    ],
    "topic_times_attention": [
      0.02,
      0.1,
      0.04
    ],
    "independent_two_article_example": {
      "article_ids": [
        "X",
        "Y"
      ],
      "absolute_axis_coordinates": [
        2,
        0.5
      ],
      "edition_attention_shares": [
        0.01,
        0.1
      ],
      "topic_times_attention": [
        0.02,
        0.05
      ],
      "topic_order": [
        "X",
        "Y"
      ],
      "combined_order": [
        "Y",
        "X"
      ]
    }
  },
  "ontology_ridge": {
    "scope": "Separate fictional 2-coordinate example; labels are stipulated, never measured.",
    "article_coordinates": [
      [
        -1.0,
        -1.0
      ],
      [
        -1.0,
        1.0
      ],
      [
        1.0,
        -1.0
      ],
      [
        1.0,
        1.0
      ]
    ],
    "reviewed_targets": [
      [
        0.0,
        0.0
      ],
      [
        0.0,
        1.0
      ],
      [
        1.0,
        0.0
      ],
      [
        1.0,
        1.0
      ]
    ],
    "rho": 1.0,
    "slopes": [
      [
        0.4,
        0.0
      ],
      [
        0.0,
        0.4
      ]
    ],
    "unpenalized_intercept": [
      0.5,
      0.5
    ],
    "training_scores": [
      [
        0.1,
        0.1
      ],
      [
        0.1,
        0.9
      ],
      [
        0.9,
        0.1
      ],
      [
        0.9,
        0.9
      ]
    ],
    "extrapolating_query": [
      2.0,
      -2.0
    ],
    "query_scores": [
      1.3,
      -0.3
    ],
    "calibration_status": "No held-out probability calibration or validation on people profiles."
  }
}
