{
  "schema_version": 1,
  "status": "Independent density-matrix and formula checks for browser analytic models; not empirical data",
  "werner": {
    "singlet": "(|01>-|10>)/sqrt(2)",
    "thresholds": {
      "separable_through_p": 0.3333333333333333,
      "CHSH_violates_strictly_above_p": 0.7071067811865475
    },
    "threshold_semantics": "Both inequalities are strict; equality is separable at 1/3 and CHSH-saturating at 1/sqrt(2). Classify from p rather than rounded labels.",
    "settings": "a0=z,a1=x,b0=(z+x)/sqrt(2),b1=(z-x)/sqrt(2); signed combination E00+E01+E10-E11 is negative",
    "CHSH_scope": "Nondegenerate spin measurements; no claim about every Bell scenario.",
    "presets": [
      {
        "p": 0.0,
        "CHSH_absolute": 0.0,
        "negativity": 0.0,
        "mutual_information_bits": 0.0,
        "partial_transpose_eigenvalues": [
          0.25,
          0.25,
          0.25,
          0.25
        ]
      },
      {
        "p": 0.3333333333333333,
        "CHSH_absolute": 0.9428090415820634,
        "negativity": 0.0,
        "mutual_information_bits": 0.20751874963942196,
        "partial_transpose_eigenvalues": [
          0.0,
          0.3333333333333333,
          0.3333333333333333,
          0.3333333333333333
        ]
      },
      {
        "p": 0.5,
        "CHSH_absolute": 1.4142135623730951,
        "negativity": 0.125,
        "mutual_information_bits": 0.45120505930460153,
        "partial_transpose_eigenvalues": [
          -0.125,
          0.375,
          0.375,
          0.375
        ]
      },
      {
        "p": 0.7071067811865475,
        "CHSH_absolute": 2.0,
        "negativity": 0.2803300858899106,
        "mutual_information_bits": 0.8922671059485869,
        "partial_transpose_eigenvalues": [
          -0.2803300858899106,
          0.42677669529663687,
          0.42677669529663687,
          0.42677669529663687
        ]
      },
      {
        "p": 0.85,
        "CHSH_absolute": 2.4041630560342617,
        "negativity": 0.38749999999999996,
        "mutual_information_bits": 1.314280755004173,
        "partial_transpose_eigenvalues": [
          -0.38749999999999996,
          0.4625,
          0.4625,
          0.4625
        ]
      },
      {
        "p": 1.0,
        "CHSH_absolute": 2.8284271247461903,
        "negativity": 0.5,
        "mutual_information_bits": 2.0,
        "partial_transpose_eigenvalues": [
          -0.5,
          0.5,
          0.5,
          0.5
        ]
      }
    ],
    "validation": {
      "partial_transpose_spectrum": {
        "passed": true,
        "max_absolute_error": 2.220446049250313e-16,
        "tolerance": 1e-11
      },
      "local_marginals": {
        "passed": true,
        "max_absolute_error": 1.1102230246251565e-16,
        "tolerance": 1e-11
      },
      "CHSH": {
        "passed": true,
        "max_absolute_error": 1.3322676295501878e-15,
        "tolerance": 1e-11
      },
      "negativity": {
        "passed": true,
        "max_absolute_error": 2.220446049250313e-16,
        "tolerance": 1e-11
      },
      "joint_distribution": {
        "passed": true,
        "max_absolute_error": 1.6653345369377348e-16,
        "tolerance": 1e-11
      }
    }
  },
  "AdS3_two_intervals": {
    "assumptions": "Vacuum on infinite line, equal intervals, static semiclassical AdS3, leading classical RT contribution, cutoff much smaller than gap and interval.",
    "units": "Entropies in nats; table uses length=1, cutoff=0.0001, central charge=30.",
    "transition_gap_over_length": 0.41421356237309515,
    "transition_cross_ratio": 0.5,
    "formula": "3 I(A:B)/c = max(0, ln[1/(r(2+r))]), r=d/ell",
    "presets": [
      {
        "gap_over_length": 0.1,
        "cross_ratio": 0.8264462809917354,
        "three_MI_over_c": 1.5606477482646683,
        "S_disconnected": 184.2068074395237,
        "S_connected": 168.60032995687698
      },
      {
        "gap_over_length": 0.25,
        "cross_ratio": 0.64,
        "three_MI_over_c": 0.5753641449035618,
        "S_disconnected": 184.2068074395237,
        "S_connected": 178.45316599048803
      },
      {
        "gap_over_length": 0.41421356237309515,
        "cross_ratio": 0.4999999999999999,
        "three_MI_over_c": 0.0,
        "S_disconnected": 184.2068074395237,
        "S_connected": 184.2068074395237
      },
      {
        "gap_over_length": 0.5,
        "cross_ratio": 0.4444444444444444,
        "three_MI_over_c": 0.0,
        "S_disconnected": 184.2068074395237,
        "S_connected": 186.43824295266575
      },
      {
        "gap_over_length": 1.0,
        "cross_ratio": 0.25,
        "three_MI_over_c": 0.0,
        "S_disconnected": 184.2068074395237,
        "S_connected": 195.19293032620476
      }
    ],
    "validation": {
      "equivalent_formulas": {
        "passed": true,
        "max_absolute_error": 3.6637359812630166e-15,
        "tolerance": 1e-11
      },
      "scale_invariance": {
        "passed": true,
        "max_absolute_error": 0.0,
        "tolerance": 1e-11
      }
    },
    "limitations": "Connected entanglement wedge is not a traversable signal route. Zero leading-order mutual information need not be exact at finite c."
  }
}