{
  "nodes": [
    {
      "id": "sidon_pow2_k1_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8
        ],
        "k": 1
      },
      "result": {
        "distinct": 3,
        "total": 4,
        "max_degeneracy": 2,
        "distinct_ratio": 0.75,
        "max_degen_ratio": 0.5,
        "product_entropy": 1.5,
        "entropy_ratio": 0.9464,
        "is_concentrated": false
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119226.8727715
    },
    {
      "id": "sidon_pow2_k1_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8
        ],
        "k": 1,
        "n_modes": 4,
        "n_photons": 1,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,0,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.830422
    },
    {
      "id": "sidon_pow2_k1_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8
        ],
        "k": 1,
        "n_modes": 4
      },
      "result": {
        "n_modes": 4,
        "n_photons": 1,
        "n_shots": 100000,
        "n_output_states": 4,
        "n_nonzero": 4,
        "entropy": 1.019284,
        "max_entropy": 2.0,
        "entropy_ratio": 0.5096,
        "kl_divergence": 0.9807,
        "max_prob": 0.78286,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.832049
    },
    {
      "id": "nonsidon_seq_k1_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          1,
          2,
          3,
          4
        ],
        "k": 1
      },
      "result": {
        "distinct": 3,
        "total": 4,
        "max_degeneracy": 2,
        "distinct_ratio": 0.75,
        "max_degen_ratio": 0.5,
        "product_entropy": 1.5,
        "entropy_ratio": 0.9464,
        "is_concentrated": false
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8326652
    },
    {
      "id": "nonsidon_seq_k1_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          3,
          4
        ],
        "k": 1,
        "n_modes": 4,
        "n_photons": 1,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,0,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8332405
    },
    {
      "id": "nonsidon_seq_k1_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          3,
          4
        ],
        "k": 1,
        "n_modes": 4
      },
      "result": {
        "n_modes": 4,
        "n_photons": 1,
        "n_shots": 100000,
        "n_output_states": 4,
        "n_nonzero": 4,
        "entropy": 1.403893,
        "max_entropy": 2.0,
        "entropy_ratio": 0.7019,
        "kl_divergence": 0.5961,
        "max_prob": 0.6728,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8339875
    },
    {
      "id": "sidon_h8_k1_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          7
        ],
        "k": 1
      },
      "result": {
        "distinct": 3,
        "total": 4,
        "max_degeneracy": 2,
        "distinct_ratio": 0.75,
        "max_degen_ratio": 0.5,
        "product_entropy": 1.5,
        "entropy_ratio": 0.9464,
        "is_concentrated": false
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8343258
    },
    {
      "id": "sidon_h8_k1_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          7
        ],
        "k": 1,
        "n_modes": 4,
        "n_photons": 1,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,0,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8348193
    },
    {
      "id": "sidon_h8_k1_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          7
        ],
        "k": 1,
        "n_modes": 4
      },
      "result": {
        "n_modes": 4,
        "n_photons": 1,
        "n_shots": 100000,
        "n_output_states": 4,
        "n_nonzero": 4,
        "entropy": 1.154441,
        "max_entropy": 2.0,
        "entropy_ratio": 0.5772,
        "kl_divergence": 0.8456,
        "max_prob": 0.74826,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8356774
    },
    {
      "id": "sidon_h16_k1_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          10,
          16
        ],
        "k": 1
      },
      "result": {
        "distinct": 3,
        "total": 5,
        "max_degeneracy": 3,
        "distinct_ratio": 0.6,
        "max_degen_ratio": 0.6,
        "product_entropy": 1.371,
        "entropy_ratio": 0.865,
        "is_concentrated": false
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8360538
    },
    {
      "id": "sidon_h16_k1_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          10,
          16
        ],
        "k": 1,
        "n_modes": 5,
        "n_photons": 1,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,0,0,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8366938
    },
    {
      "id": "sidon_h16_k1_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          10,
          16
        ],
        "k": 1,
        "n_modes": 5
      },
      "result": {
        "n_modes": 5,
        "n_photons": 1,
        "n_shots": 100000,
        "n_output_states": 5,
        "n_nonzero": 5,
        "entropy": 1.027073,
        "max_entropy": 2.3219,
        "entropy_ratio": 0.4423,
        "kl_divergence": 1.2949,
        "max_prob": 0.80199,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8374543
    },
    {
      "id": "sidon_pow7_k1_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8,
          16,
          32,
          64
        ],
        "k": 1
      },
      "result": {
        "distinct": 3,
        "total": 7,
        "max_degeneracy": 5,
        "distinct_ratio": 0.42857142857142855,
        "max_degen_ratio": 0.7142857142857143,
        "product_entropy": 1.1488,
        "entropy_ratio": 0.7248,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.837893
    },
    {
      "id": "sidon_pow7_k1_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8,
          16,
          32,
          64
        ],
        "k": 1,
        "n_modes": 7,
        "n_photons": 1,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,0,0,0,0,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8385105
    },
    {
      "id": "sidon_pow7_k1_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8,
          16,
          32,
          64
        ],
        "k": 1,
        "n_modes": 7
      },
      "result": {
        "n_modes": 7,
        "n_photons": 1,
        "n_shots": 100000,
        "n_output_states": 7,
        "n_nonzero": 7,
        "entropy": 0.909081,
        "max_entropy": 2.8074,
        "entropy_ratio": 0.3238,
        "kl_divergence": 1.8983,
        "max_prob": 0.84525,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8394501
    },
    {
      "id": "sidon_s6_k1_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          11,
          16,
          19
        ],
        "k": 1
      },
      "result": {
        "distinct": 3,
        "total": 6,
        "max_degeneracy": 4,
        "distinct_ratio": 0.5,
        "max_degen_ratio": 0.6666666666666666,
        "product_entropy": 1.2516,
        "entropy_ratio": 0.7897,
        "is_concentrated": false
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8399568
    },
    {
      "id": "sidon_s6_k1_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          11,
          16,
          19
        ],
        "k": 1,
        "n_modes": 6,
        "n_photons": 1,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,0,0,0,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8405676
    },
    {
      "id": "sidon_s6_k1_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          11,
          16,
          19
        ],
        "k": 1,
        "n_modes": 6
      },
      "result": {
        "n_modes": 6,
        "n_photons": 1,
        "n_shots": 100000,
        "n_output_states": 6,
        "n_nonzero": 6,
        "entropy": 1.178671,
        "max_entropy": 2.585,
        "entropy_ratio": 0.456,
        "kl_divergence": 1.4063,
        "max_prob": 0.7904,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.84137
    },
    {
      "id": "sidon_s7_k1_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          11,
          19,
          28,
          35
        ],
        "k": 1
      },
      "result": {
        "distinct": 3,
        "total": 7,
        "max_degeneracy": 5,
        "distinct_ratio": 0.42857142857142855,
        "max_degen_ratio": 0.7142857142857143,
        "product_entropy": 1.1488,
        "entropy_ratio": 0.7248,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8418546
    },
    {
      "id": "sidon_s7_k1_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          11,
          19,
          28,
          35
        ],
        "k": 1,
        "n_modes": 7,
        "n_photons": 1,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,0,0,0,0,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.842516
    },
    {
      "id": "sidon_s7_k1_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          11,
          19,
          28,
          35
        ],
        "k": 1,
        "n_modes": 7
      },
      "result": {
        "n_modes": 7,
        "n_photons": 1,
        "n_shots": 100000,
        "n_output_states": 7,
        "n_nonzero": 7,
        "entropy": 1.136878,
        "max_entropy": 2.8074,
        "entropy_ratio": 0.405,
        "kl_divergence": 1.6705,
        "max_prob": 0.81253,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8433223
    },
    {
      "id": "nonsidon_dense6_k1_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          5,
          6,
          7,
          8,
          9,
          10
        ],
        "k": 1
      },
      "result": {
        "distinct": 3,
        "total": 6,
        "max_degeneracy": 4,
        "distinct_ratio": 0.5,
        "max_degen_ratio": 0.6666666666666666,
        "product_entropy": 1.2516,
        "entropy_ratio": 0.7897,
        "is_concentrated": false
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8438787
    },
    {
      "id": "nonsidon_dense6_k1_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          5,
          6,
          7,
          8,
          9,
          10
        ],
        "k": 1,
        "n_modes": 6,
        "n_photons": 1,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,0,0,0,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8445039
    },
    {
      "id": "nonsidon_dense6_k1_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          5,
          6,
          7,
          8,
          9,
          10
        ],
        "k": 1,
        "n_modes": 6
      },
      "result": {
        "n_modes": 6,
        "n_photons": 1,
        "n_shots": 100000,
        "n_output_states": 6,
        "n_nonzero": 6,
        "entropy": 1.855492,
        "max_entropy": 2.585,
        "entropy_ratio": 0.7178,
        "kl_divergence": 0.7295,
        "max_prob": 0.61253,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.845315
    },
    {
      "id": "nonsidon_dense7_k1_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          10,
          11,
          12,
          13,
          14,
          15,
          16
        ],
        "k": 1
      },
      "result": {
        "distinct": 3,
        "total": 7,
        "max_degeneracy": 5,
        "distinct_ratio": 0.42857142857142855,
        "max_degen_ratio": 0.7142857142857143,
        "product_entropy": 1.1488,
        "entropy_ratio": 0.7248,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.845797
    },
    {
      "id": "nonsidon_dense7_k1_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          10,
          11,
          12,
          13,
          14,
          15,
          16
        ],
        "k": 1,
        "n_modes": 7,
        "n_photons": 1,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,0,0,0,0,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.846456
    },
    {
      "id": "nonsidon_dense7_k1_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          10,
          11,
          12,
          13,
          14,
          15,
          16
        ],
        "k": 1,
        "n_modes": 7
      },
      "result": {
        "n_modes": 7,
        "n_photons": 1,
        "n_shots": 100000,
        "n_output_states": 7,
        "n_nonzero": 7,
        "entropy": 1.405677,
        "max_entropy": 2.8074,
        "entropy_ratio": 0.5007,
        "kl_divergence": 1.4017,
        "max_prob": 0.76187,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8473287
    },
    {
      "id": "primes_s7_k1_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          2,
          3,
          5,
          7,
          11,
          13,
          17
        ],
        "k": 1
      },
      "result": {
        "distinct": 3,
        "total": 7,
        "max_degeneracy": 5,
        "distinct_ratio": 0.42857142857142855,
        "max_degen_ratio": 0.7142857142857143,
        "product_entropy": 1.1488,
        "entropy_ratio": 0.7248,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8479304
    },
    {
      "id": "primes_s7_k1_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          2,
          3,
          5,
          7,
          11,
          13,
          17
        ],
        "k": 1,
        "n_modes": 7,
        "n_photons": 1,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,0,0,0,0,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.84863
    },
    {
      "id": "primes_s7_k1_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          2,
          3,
          5,
          7,
          11,
          13,
          17
        ],
        "k": 1,
        "n_modes": 7
      },
      "result": {
        "n_modes": 7,
        "n_photons": 1,
        "n_shots": 100000,
        "n_output_states": 7,
        "n_nonzero": 7,
        "entropy": 1.298122,
        "max_entropy": 2.8074,
        "entropy_ratio": 0.4624,
        "kl_divergence": 1.5092,
        "max_prob": 0.77994,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8494787
    },
    {
      "id": "primes_s8_k1_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          2,
          3,
          5,
          7,
          11,
          13,
          17,
          19
        ],
        "k": 1
      },
      "result": {
        "distinct": 3,
        "total": 8,
        "max_degeneracy": 6,
        "distinct_ratio": 0.375,
        "max_degen_ratio": 0.75,
        "product_entropy": 1.0613,
        "entropy_ratio": 0.6696,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.850028
    },
    {
      "id": "primes_s8_k1_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          2,
          3,
          5,
          7,
          11,
          13,
          17,
          19
        ],
        "k": 1,
        "n_modes": 8,
        "n_photons": 1,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,0,0,0,0,0,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8508127
    },
    {
      "id": "primes_s8_k1_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          2,
          3,
          5,
          7,
          11,
          13,
          17,
          19
        ],
        "k": 1,
        "n_modes": 8
      },
      "result": {
        "n_modes": 8,
        "n_photons": 1,
        "n_shots": 100000,
        "n_output_states": 8,
        "n_nonzero": 8,
        "entropy": 1.197996,
        "max_entropy": 3.0,
        "entropy_ratio": 0.3993,
        "kl_divergence": 1.802,
        "max_prob": 0.8153,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.851671
    },
    {
      "id": "sidon_pow8_k1_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8,
          16,
          32,
          64,
          128
        ],
        "k": 1
      },
      "result": {
        "distinct": 3,
        "total": 8,
        "max_degeneracy": 6,
        "distinct_ratio": 0.375,
        "max_degen_ratio": 0.75,
        "product_entropy": 1.0613,
        "entropy_ratio": 0.6696,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8521836
    },
    {
      "id": "sidon_pow8_k1_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8,
          16,
          32,
          64,
          128
        ],
        "k": 1,
        "n_modes": 8,
        "n_photons": 1,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,0,0,0,0,0,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8529258
    },
    {
      "id": "sidon_pow8_k1_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8,
          16,
          32,
          64,
          128
        ],
        "k": 1,
        "n_modes": 8
      },
      "result": {
        "n_modes": 8,
        "n_photons": 1,
        "n_shots": 100000,
        "n_output_states": 8,
        "n_nonzero": 8,
        "entropy": 0.918123,
        "max_entropy": 3.0,
        "entropy_ratio": 0.306,
        "kl_divergence": 2.0819,
        "max_prob": 0.85085,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8537865
    },
    {
      "id": "sidon_pow2_k1_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8
        ],
        "k": 1
      },
      "result": {
        "k": 1,
        "desc": "sidon_pow2",
        "labels": [
          1,
          2,
          4,
          8
        ],
        "prod_distinct_ratio": 0.75,
        "slos_kl": 0.9807,
        "slos_entropy_ratio": 0.5096,
        "spearman_rho": -0.846,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8542354
    },
    {
      "id": "nonsidon_seq_k1_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          1,
          2,
          3,
          4
        ],
        "k": 1
      },
      "result": {
        "k": 1,
        "desc": "nonsidon_seq",
        "labels": [
          1,
          2,
          3,
          4
        ],
        "prod_distinct_ratio": 0.75,
        "slos_kl": 0.5961,
        "slos_entropy_ratio": 0.7019,
        "spearman_rho": -0.846,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.854629
    },
    {
      "id": "sidon_h8_k1_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          7
        ],
        "k": 1
      },
      "result": {
        "k": 1,
        "desc": "sidon_h8",
        "labels": [
          1,
          2,
          5,
          7
        ],
        "prod_distinct_ratio": 0.75,
        "slos_kl": 0.8456,
        "slos_entropy_ratio": 0.5772,
        "spearman_rho": -0.846,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8549845
    },
    {
      "id": "sidon_h16_k1_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          10,
          16
        ],
        "k": 1
      },
      "result": {
        "k": 1,
        "desc": "sidon_h16",
        "labels": [
          1,
          2,
          5,
          10,
          16
        ],
        "prod_distinct_ratio": 0.6,
        "slos_kl": 1.2949,
        "slos_entropy_ratio": 0.4423,
        "spearman_rho": -0.846,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8553798
    },
    {
      "id": "sidon_pow7_k1_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8,
          16,
          32,
          64
        ],
        "k": 1
      },
      "result": {
        "k": 1,
        "desc": "sidon_pow7",
        "labels": [
          1,
          2,
          4,
          8,
          16,
          32,
          64
        ],
        "prod_distinct_ratio": 0.42857142857142855,
        "slos_kl": 1.8983,
        "slos_entropy_ratio": 0.3238,
        "spearman_rho": -0.846,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8557446
    },
    {
      "id": "sidon_s6_k1_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          11,
          16,
          19
        ],
        "k": 1
      },
      "result": {
        "k": 1,
        "desc": "sidon_s6",
        "labels": [
          1,
          2,
          5,
          11,
          16,
          19
        ],
        "prod_distinct_ratio": 0.5,
        "slos_kl": 1.4063,
        "slos_entropy_ratio": 0.456,
        "spearman_rho": -0.846,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8561451
    },
    {
      "id": "sidon_s7_k1_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          11,
          19,
          28,
          35
        ],
        "k": 1
      },
      "result": {
        "k": 1,
        "desc": "sidon_s7",
        "labels": [
          1,
          2,
          5,
          11,
          19,
          28,
          35
        ],
        "prod_distinct_ratio": 0.42857142857142855,
        "slos_kl": 1.6705,
        "slos_entropy_ratio": 0.405,
        "spearman_rho": -0.846,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.856558
    },
    {
      "id": "nonsidon_dense6_k1_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          5,
          6,
          7,
          8,
          9,
          10
        ],
        "k": 1
      },
      "result": {
        "k": 1,
        "desc": "nonsidon_dense6",
        "labels": [
          5,
          6,
          7,
          8,
          9,
          10
        ],
        "prod_distinct_ratio": 0.5,
        "slos_kl": 0.7295,
        "slos_entropy_ratio": 0.7178,
        "spearman_rho": -0.846,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8569286
    },
    {
      "id": "nonsidon_dense7_k1_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          10,
          11,
          12,
          13,
          14,
          15,
          16
        ],
        "k": 1
      },
      "result": {
        "k": 1,
        "desc": "nonsidon_dense7",
        "labels": [
          10,
          11,
          12,
          13,
          14,
          15,
          16
        ],
        "prod_distinct_ratio": 0.42857142857142855,
        "slos_kl": 1.4017,
        "slos_entropy_ratio": 0.5007,
        "spearman_rho": -0.846,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.857314
    },
    {
      "id": "primes_s7_k1_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          2,
          3,
          5,
          7,
          11,
          13,
          17
        ],
        "k": 1
      },
      "result": {
        "k": 1,
        "desc": "primes_s7",
        "labels": [
          2,
          3,
          5,
          7,
          11,
          13,
          17
        ],
        "prod_distinct_ratio": 0.42857142857142855,
        "slos_kl": 1.5092,
        "slos_entropy_ratio": 0.4624,
        "spearman_rho": -0.846,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8577142
    },
    {
      "id": "primes_s8_k1_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          2,
          3,
          5,
          7,
          11,
          13,
          17,
          19
        ],
        "k": 1
      },
      "result": {
        "k": 1,
        "desc": "primes_s8",
        "labels": [
          2,
          3,
          5,
          7,
          11,
          13,
          17,
          19
        ],
        "prod_distinct_ratio": 0.375,
        "slos_kl": 1.802,
        "slos_entropy_ratio": 0.3993,
        "spearman_rho": -0.846,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8581262
    },
    {
      "id": "sidon_pow8_k1_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8,
          16,
          32,
          64,
          128
        ],
        "k": 1
      },
      "result": {
        "k": 1,
        "desc": "sidon_pow8",
        "labels": [
          1,
          2,
          4,
          8,
          16,
          32,
          64,
          128
        ],
        "prod_distinct_ratio": 0.375,
        "slos_kl": 2.0819,
        "slos_entropy_ratio": 0.306,
        "spearman_rho": -0.846,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8585432
    },
    {
      "id": "sidon_pow2_k2_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8
        ],
        "k": 2
      },
      "result": {
        "distinct": 4,
        "total": 10,
        "max_degeneracy": 7,
        "distinct_ratio": 0.4,
        "max_degen_ratio": 0.7,
        "product_entropy": 1.3568,
        "entropy_ratio": 0.6784,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8597984
    },
    {
      "id": "sidon_pow2_k2_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8
        ],
        "k": 2,
        "n_modes": 4,
        "n_photons": 2,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,1,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8606455
    },
    {
      "id": "sidon_pow2_k2_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8
        ],
        "k": 2,
        "n_modes": 4
      },
      "result": {
        "n_modes": 4,
        "n_photons": 2,
        "n_shots": 100000,
        "n_output_states": 10,
        "n_nonzero": 10,
        "entropy": 2.197161,
        "max_entropy": 3.3219,
        "entropy_ratio": 0.6614,
        "kl_divergence": 1.1248,
        "max_prob": 0.58244,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8616474
    },
    {
      "id": "nonsidon_seq_k2_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          1,
          2,
          3,
          4
        ],
        "k": 2
      },
      "result": {
        "distinct": 4,
        "total": 10,
        "max_degeneracy": 7,
        "distinct_ratio": 0.4,
        "max_degen_ratio": 0.7,
        "product_entropy": 1.3568,
        "entropy_ratio": 0.6784,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8622818
    },
    {
      "id": "nonsidon_seq_k2_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          3,
          4
        ],
        "k": 2,
        "n_modes": 4,
        "n_photons": 2,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,1,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8631086
    },
    {
      "id": "nonsidon_seq_k2_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          3,
          4
        ],
        "k": 2,
        "n_modes": 4
      },
      "result": {
        "n_modes": 4,
        "n_photons": 2,
        "n_shots": 100000,
        "n_output_states": 10,
        "n_nonzero": 10,
        "entropy": 2.82676,
        "max_entropy": 3.3219,
        "entropy_ratio": 0.8509,
        "kl_divergence": 0.4952,
        "max_prob": 0.39125,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.864441
    },
    {
      "id": "sidon_h8_k2_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          7
        ],
        "k": 2
      },
      "result": {
        "distinct": 4,
        "total": 10,
        "max_degeneracy": 7,
        "distinct_ratio": 0.4,
        "max_degen_ratio": 0.7,
        "product_entropy": 1.3568,
        "entropy_ratio": 0.6784,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8651226
    },
    {
      "id": "sidon_h8_k2_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          7
        ],
        "k": 2,
        "n_modes": 4,
        "n_photons": 2,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,1,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8659604
    },
    {
      "id": "sidon_h8_k2_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          7
        ],
        "k": 2,
        "n_modes": 4
      },
      "result": {
        "n_modes": 4,
        "n_photons": 2,
        "n_shots": 100000,
        "n_output_states": 10,
        "n_nonzero": 10,
        "entropy": 2.420299,
        "max_entropy": 3.3219,
        "entropy_ratio": 0.7286,
        "kl_divergence": 0.9016,
        "max_prob": 0.53399,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8669662
    },
    {
      "id": "sidon_h16_k2_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          10,
          16
        ],
        "k": 2
      },
      "result": {
        "distinct": 4,
        "total": 15,
        "max_degeneracy": 12,
        "distinct_ratio": 0.26666666666666666,
        "max_degen_ratio": 0.8,
        "product_entropy": 1.0389,
        "entropy_ratio": 0.5195,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8677478
    },
    {
      "id": "sidon_h16_k2_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          10,
          16
        ],
        "k": 2,
        "n_modes": 5,
        "n_photons": 2,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,1,0,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.868637
    },
    {
      "id": "sidon_h16_k2_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          10,
          16
        ],
        "k": 2,
        "n_modes": 5
      },
      "result": {
        "n_modes": 5,
        "n_photons": 2,
        "n_shots": 100000,
        "n_output_states": 15,
        "n_nonzero": 15,
        "entropy": 2.140299,
        "max_entropy": 3.9069,
        "entropy_ratio": 0.5478,
        "kl_divergence": 1.7666,
        "max_prob": 0.64234,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8697062
    },
    {
      "id": "sidon_pow7_k2_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8,
          16,
          32,
          64
        ],
        "k": 2
      },
      "result": {
        "distinct": 4,
        "total": 28,
        "max_degeneracy": 25,
        "distinct_ratio": 0.14285714285714285,
        "max_degen_ratio": 0.8928571428571429,
        "product_entropy": 0.6611,
        "entropy_ratio": 0.3305,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8704264
    },
    {
      "id": "sidon_pow7_k2_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8,
          16,
          32,
          64
        ],
        "k": 2,
        "n_modes": 7,
        "n_photons": 2,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,1,0,0,0,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8714273
    },
    {
      "id": "sidon_pow7_k2_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8,
          16,
          32,
          64
        ],
        "k": 2,
        "n_modes": 7
      },
      "result": {
        "n_modes": 7,
        "n_photons": 2,
        "n_shots": 100000,
        "n_output_states": 28,
        "n_nonzero": 28,
        "entropy": 1.864498,
        "max_entropy": 4.8074,
        "entropy_ratio": 0.3878,
        "kl_divergence": 2.9429,
        "max_prob": 0.71738,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8726802
    },
    {
      "id": "sidon_s6_k2_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          11,
          16,
          19
        ],
        "k": 2
      },
      "result": {
        "distinct": 4,
        "total": 21,
        "max_degeneracy": 18,
        "distinct_ratio": 0.19047619047619047,
        "max_degen_ratio": 0.8571428571428571,
        "product_entropy": 0.8181,
        "entropy_ratio": 0.409,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8734512
    },
    {
      "id": "sidon_s6_k2_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          11,
          16,
          19
        ],
        "k": 2,
        "n_modes": 6,
        "n_photons": 2,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,1,0,0,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8742502
    },
    {
      "id": "sidon_s6_k2_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          11,
          16,
          19
        ],
        "k": 2,
        "n_modes": 6
      },
      "result": {
        "n_modes": 6,
        "n_photons": 2,
        "n_shots": 100000,
        "n_output_states": 21,
        "n_nonzero": 21,
        "entropy": 2.447036,
        "max_entropy": 4.3923,
        "entropy_ratio": 0.5571,
        "kl_divergence": 1.9453,
        "max_prob": 0.61889,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8755996
    },
    {
      "id": "sidon_s7_k2_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          11,
          19,
          28,
          35
        ],
        "k": 2
      },
      "result": {
        "distinct": 4,
        "total": 28,
        "max_degeneracy": 25,
        "distinct_ratio": 0.14285714285714285,
        "max_degen_ratio": 0.8928571428571429,
        "product_entropy": 0.6611,
        "entropy_ratio": 0.3305,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8763864
    },
    {
      "id": "sidon_s7_k2_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          11,
          19,
          28,
          35
        ],
        "k": 2,
        "n_modes": 7,
        "n_photons": 2,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,1,0,0,0,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.87745
    },
    {
      "id": "sidon_s7_k2_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          11,
          19,
          28,
          35
        ],
        "k": 2,
        "n_modes": 7
      },
      "result": {
        "n_modes": 7,
        "n_photons": 2,
        "n_shots": 100000,
        "n_output_states": 28,
        "n_nonzero": 28,
        "entropy": 2.325544,
        "max_entropy": 4.8074,
        "entropy_ratio": 0.4837,
        "kl_divergence": 2.4818,
        "max_prob": 0.65918,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8788867
    },
    {
      "id": "nonsidon_dense6_k2_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          5,
          6,
          7,
          8,
          9,
          10
        ],
        "k": 2
      },
      "result": {
        "distinct": 4,
        "total": 21,
        "max_degeneracy": 18,
        "distinct_ratio": 0.19047619047619047,
        "max_degen_ratio": 0.8571428571428571,
        "product_entropy": 0.8181,
        "entropy_ratio": 0.409,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8796756
    },
    {
      "id": "nonsidon_dense6_k2_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          5,
          6,
          7,
          8,
          9,
          10
        ],
        "k": 2,
        "n_modes": 6,
        "n_photons": 2,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,1,0,0,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8806481
    },
    {
      "id": "nonsidon_dense6_k2_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          5,
          6,
          7,
          8,
          9,
          10
        ],
        "k": 2,
        "n_modes": 6
      },
      "result": {
        "n_modes": 6,
        "n_photons": 2,
        "n_shots": 100000,
        "n_output_states": 21,
        "n_nonzero": 21,
        "entropy": 3.470953,
        "max_entropy": 4.3923,
        "entropy_ratio": 0.7902,
        "kl_divergence": 0.9214,
        "max_prob": 0.39963,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8819408
    },
    {
      "id": "nonsidon_dense7_k2_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          10,
          11,
          12,
          13,
          14,
          15,
          16
        ],
        "k": 2
      },
      "result": {
        "distinct": 4,
        "total": 28,
        "max_degeneracy": 25,
        "distinct_ratio": 0.14285714285714285,
        "max_degen_ratio": 0.8928571428571429,
        "product_entropy": 0.6611,
        "entropy_ratio": 0.3305,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8827388
    },
    {
      "id": "nonsidon_dense7_k2_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          10,
          11,
          12,
          13,
          14,
          15,
          16
        ],
        "k": 2,
        "n_modes": 7,
        "n_photons": 2,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,1,0,0,0,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8837652
    },
    {
      "id": "nonsidon_dense7_k2_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          10,
          11,
          12,
          13,
          14,
          15,
          16
        ],
        "k": 2,
        "n_modes": 7
      },
      "result": {
        "n_modes": 7,
        "n_photons": 2,
        "n_shots": 100000,
        "n_output_states": 28,
        "n_nonzero": 28,
        "entropy": 2.888476,
        "max_entropy": 4.8074,
        "entropy_ratio": 0.6008,
        "kl_divergence": 1.9189,
        "max_prob": 0.55953,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8852277
    },
    {
      "id": "primes_s7_k2_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          2,
          3,
          5,
          7,
          11,
          13,
          17
        ],
        "k": 2
      },
      "result": {
        "distinct": 4,
        "total": 28,
        "max_degeneracy": 25,
        "distinct_ratio": 0.14285714285714285,
        "max_degen_ratio": 0.8928571428571429,
        "product_entropy": 0.6611,
        "entropy_ratio": 0.3305,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8860407
    },
    {
      "id": "primes_s7_k2_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          2,
          3,
          5,
          7,
          11,
          13,
          17
        ],
        "k": 2,
        "n_modes": 7,
        "n_photons": 2,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,1,0,0,0,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8870382
    },
    {
      "id": "primes_s7_k2_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          2,
          3,
          5,
          7,
          11,
          13,
          17
        ],
        "k": 2,
        "n_modes": 7
      },
      "result": {
        "n_modes": 7,
        "n_photons": 2,
        "n_shots": 100000,
        "n_output_states": 28,
        "n_nonzero": 28,
        "entropy": 2.688608,
        "max_entropy": 4.8074,
        "entropy_ratio": 0.5593,
        "kl_divergence": 2.1187,
        "max_prob": 0.60083,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8885167
    },
    {
      "id": "primes_s8_k2_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          2,
          3,
          5,
          7,
          11,
          13,
          17,
          19
        ],
        "k": 2
      },
      "result": {
        "distinct": 4,
        "total": 36,
        "max_degeneracy": 33,
        "distinct_ratio": 0.1111111111111111,
        "max_degen_ratio": 0.9166666666666666,
        "product_entropy": 0.5459,
        "entropy_ratio": 0.2729,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.889364
    },
    {
      "id": "primes_s8_k2_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          2,
          3,
          5,
          7,
          11,
          13,
          17,
          19
        ],
        "k": 2,
        "n_modes": 8,
        "n_photons": 2,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,1,0,0,0,0,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8905003
    },
    {
      "id": "primes_s8_k2_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          2,
          3,
          5,
          7,
          11,
          13,
          17,
          19
        ],
        "k": 2,
        "n_modes": 8
      },
      "result": {
        "n_modes": 8,
        "n_photons": 2,
        "n_shots": 100000,
        "n_output_states": 36,
        "n_nonzero": 36,
        "entropy": 2.530553,
        "max_entropy": 5.1699,
        "entropy_ratio": 0.4895,
        "kl_divergence": 2.6394,
        "max_prob": 0.64571,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8919723
    },
    {
      "id": "sidon_pow8_k2_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8,
          16,
          32,
          64,
          128
        ],
        "k": 2
      },
      "result": {
        "distinct": 4,
        "total": 36,
        "max_degeneracy": 33,
        "distinct_ratio": 0.1111111111111111,
        "max_degen_ratio": 0.9166666666666666,
        "product_entropy": 0.5459,
        "entropy_ratio": 0.2729,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8927977
    },
    {
      "id": "sidon_pow8_k2_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8,
          16,
          32,
          64,
          128
        ],
        "k": 2,
        "n_modes": 8,
        "n_photons": 2,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,1,0,0,0,0,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.893761
    },
    {
      "id": "sidon_pow8_k2_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8,
          16,
          32,
          64,
          128
        ],
        "k": 2,
        "n_modes": 8
      },
      "result": {
        "n_modes": 8,
        "n_photons": 2,
        "n_shots": 100000,
        "n_output_states": 36,
        "n_nonzero": 36,
        "entropy": 1.869936,
        "max_entropy": 5.1699,
        "entropy_ratio": 0.3617,
        "kl_divergence": 3.3,
        "max_prob": 0.72782,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8952851
    },
    {
      "id": "sidon_pow2_k2_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8
        ],
        "k": 2
      },
      "result": {
        "k": 2,
        "desc": "sidon_pow2",
        "labels": [
          1,
          2,
          4,
          8
        ],
        "prod_distinct_ratio": 0.4,
        "slos_kl": 1.1248,
        "slos_entropy_ratio": 0.6614,
        "spearman_rho": -0.8795,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8959756
    },
    {
      "id": "nonsidon_seq_k2_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          1,
          2,
          3,
          4
        ],
        "k": 2
      },
      "result": {
        "k": 2,
        "desc": "nonsidon_seq",
        "labels": [
          1,
          2,
          3,
          4
        ],
        "prod_distinct_ratio": 0.4,
        "slos_kl": 0.4952,
        "slos_entropy_ratio": 0.8509,
        "spearman_rho": -0.8795,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8967896
    },
    {
      "id": "sidon_h8_k2_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          7
        ],
        "k": 2
      },
      "result": {
        "k": 2,
        "desc": "sidon_h8",
        "labels": [
          1,
          2,
          5,
          7
        ],
        "prod_distinct_ratio": 0.4,
        "slos_kl": 0.9016,
        "slos_entropy_ratio": 0.7286,
        "spearman_rho": -0.8795,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8974574
    },
    {
      "id": "sidon_h16_k2_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          10,
          16
        ],
        "k": 2
      },
      "result": {
        "k": 2,
        "desc": "sidon_h16",
        "labels": [
          1,
          2,
          5,
          10,
          16
        ],
        "prod_distinct_ratio": 0.26666666666666666,
        "slos_kl": 1.7666,
        "slos_entropy_ratio": 0.5478,
        "spearman_rho": -0.8795,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8988411
    },
    {
      "id": "sidon_pow7_k2_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8,
          16,
          32,
          64
        ],
        "k": 2
      },
      "result": {
        "k": 2,
        "desc": "sidon_pow7",
        "labels": [
          1,
          2,
          4,
          8,
          16,
          32,
          64
        ],
        "prod_distinct_ratio": 0.14285714285714285,
        "slos_kl": 2.9429,
        "slos_entropy_ratio": 0.3878,
        "spearman_rho": -0.8795,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.8995821
    },
    {
      "id": "sidon_s6_k2_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          11,
          16,
          19
        ],
        "k": 2
      },
      "result": {
        "k": 2,
        "desc": "sidon_s6",
        "labels": [
          1,
          2,
          5,
          11,
          16,
          19
        ],
        "prod_distinct_ratio": 0.19047619047619047,
        "slos_kl": 1.9453,
        "slos_entropy_ratio": 0.5571,
        "spearman_rho": -0.8795,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9011283
    },
    {
      "id": "sidon_s7_k2_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          11,
          19,
          28,
          35
        ],
        "k": 2
      },
      "result": {
        "k": 2,
        "desc": "sidon_s7",
        "labels": [
          1,
          2,
          5,
          11,
          19,
          28,
          35
        ],
        "prod_distinct_ratio": 0.14285714285714285,
        "slos_kl": 2.4818,
        "slos_entropy_ratio": 0.4837,
        "spearman_rho": -0.8795,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9021547
    },
    {
      "id": "nonsidon_dense6_k2_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          5,
          6,
          7,
          8,
          9,
          10
        ],
        "k": 2
      },
      "result": {
        "k": 2,
        "desc": "nonsidon_dense6",
        "labels": [
          5,
          6,
          7,
          8,
          9,
          10
        ],
        "prod_distinct_ratio": 0.19047619047619047,
        "slos_kl": 0.9214,
        "slos_entropy_ratio": 0.7902,
        "spearman_rho": -0.8795,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9027922
    },
    {
      "id": "nonsidon_dense7_k2_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          10,
          11,
          12,
          13,
          14,
          15,
          16
        ],
        "k": 2
      },
      "result": {
        "k": 2,
        "desc": "nonsidon_dense7",
        "labels": [
          10,
          11,
          12,
          13,
          14,
          15,
          16
        ],
        "prod_distinct_ratio": 0.14285714285714285,
        "slos_kl": 1.9189,
        "slos_entropy_ratio": 0.6008,
        "spearman_rho": -0.8795,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9034235
    },
    {
      "id": "primes_s7_k2_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          2,
          3,
          5,
          7,
          11,
          13,
          17
        ],
        "k": 2
      },
      "result": {
        "k": 2,
        "desc": "primes_s7",
        "labels": [
          2,
          3,
          5,
          7,
          11,
          13,
          17
        ],
        "prod_distinct_ratio": 0.14285714285714285,
        "slos_kl": 2.1187,
        "slos_entropy_ratio": 0.5593,
        "spearman_rho": -0.8795,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9040372
    },
    {
      "id": "primes_s8_k2_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          2,
          3,
          5,
          7,
          11,
          13,
          17,
          19
        ],
        "k": 2
      },
      "result": {
        "k": 2,
        "desc": "primes_s8",
        "labels": [
          2,
          3,
          5,
          7,
          11,
          13,
          17,
          19
        ],
        "prod_distinct_ratio": 0.1111111111111111,
        "slos_kl": 2.6394,
        "slos_entropy_ratio": 0.4895,
        "spearman_rho": -0.8795,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.90467
    },
    {
      "id": "sidon_pow8_k2_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8,
          16,
          32,
          64,
          128
        ],
        "k": 2
      },
      "result": {
        "k": 2,
        "desc": "sidon_pow8",
        "labels": [
          1,
          2,
          4,
          8,
          16,
          32,
          64,
          128
        ],
        "prod_distinct_ratio": 0.1111111111111111,
        "slos_kl": 3.3,
        "slos_entropy_ratio": 0.3617,
        "spearman_rho": -0.8795,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9054768
    },
    {
      "id": "sidon_pow2_k3_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8
        ],
        "k": 3
      },
      "result": {
        "distinct": 5,
        "total": 20,
        "max_degeneracy": 16,
        "distinct_ratio": 0.25,
        "max_degen_ratio": 0.8,
        "product_entropy": 1.1219,
        "entropy_ratio": 0.4832,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9071424
    },
    {
      "id": "sidon_pow2_k3_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8
        ],
        "k": 3,
        "n_modes": 4,
        "n_photons": 3,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,1,1,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9082122
    },
    {
      "id": "sidon_pow2_k3_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8
        ],
        "k": 3,
        "n_modes": 4
      },
      "result": {
        "n_modes": 4,
        "n_photons": 3,
        "n_shots": 100000,
        "n_output_states": 20,
        "n_nonzero": 20,
        "entropy": 3.532512,
        "max_entropy": 4.3219,
        "entropy_ratio": 0.8173,
        "kl_divergence": 0.7894,
        "max_prob": 0.34768,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.909608
    },
    {
      "id": "nonsidon_seq_k3_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          1,
          2,
          3,
          4
        ],
        "k": 3
      },
      "result": {
        "distinct": 5,
        "total": 20,
        "max_degeneracy": 16,
        "distinct_ratio": 0.25,
        "max_degen_ratio": 0.8,
        "product_entropy": 1.1219,
        "entropy_ratio": 0.4832,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9105175
    },
    {
      "id": "nonsidon_seq_k3_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          3,
          4
        ],
        "k": 3,
        "n_modes": 4,
        "n_photons": 3,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,1,1,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9115853
    },
    {
      "id": "nonsidon_seq_k3_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          3,
          4
        ],
        "k": 3,
        "n_modes": 4
      },
      "result": {
        "n_modes": 4,
        "n_photons": 3,
        "n_shots": 100000,
        "n_output_states": 20,
        "n_nonzero": 20,
        "entropy": 3.873986,
        "max_entropy": 4.3219,
        "entropy_ratio": 0.8964,
        "kl_divergence": 0.4479,
        "max_prob": 0.20731,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9129794
    },
    {
      "id": "sidon_h8_k3_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          7
        ],
        "k": 3
      },
      "result": {
        "distinct": 5,
        "total": 20,
        "max_degeneracy": 16,
        "distinct_ratio": 0.25,
        "max_degen_ratio": 0.8,
        "product_entropy": 1.1219,
        "entropy_ratio": 0.4832,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9139128
    },
    {
      "id": "sidon_h8_k3_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          7
        ],
        "k": 3,
        "n_modes": 4,
        "n_photons": 3,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,1,1,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9150555
    },
    {
      "id": "sidon_h8_k3_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          7
        ],
        "k": 3,
        "n_modes": 4
      },
      "result": {
        "n_modes": 4,
        "n_photons": 3,
        "n_shots": 100000,
        "n_output_states": 20,
        "n_nonzero": 20,
        "entropy": 3.808627,
        "max_entropy": 4.3219,
        "entropy_ratio": 0.8812,
        "kl_divergence": 0.5133,
        "max_prob": 0.23986,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9164994
    },
    {
      "id": "sidon_h16_k3_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          10,
          16
        ],
        "k": 3
      },
      "result": {
        "distinct": 5,
        "total": 35,
        "max_degeneracy": 31,
        "distinct_ratio": 0.14285714285714285,
        "max_degen_ratio": 0.8857142857142857,
        "product_entropy": 0.7413,
        "entropy_ratio": 0.3193,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9174666
    },
    {
      "id": "sidon_h16_k3_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          10,
          16
        ],
        "k": 3,
        "n_modes": 5,
        "n_photons": 3,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,1,1,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9185815
    },
    {
      "id": "sidon_h16_k3_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          10,
          16
        ],
        "k": 3,
        "n_modes": 5
      },
      "result": {
        "n_modes": 5,
        "n_photons": 3,
        "n_shots": 100000,
        "n_output_states": 35,
        "n_nonzero": 35,
        "entropy": 3.47459,
        "max_entropy": 5.1293,
        "entropy_ratio": 0.6774,
        "kl_divergence": 1.6547,
        "max_prob": 0.46201,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.920151
    },
    {
      "id": "sidon_pow7_k3_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8,
          16,
          32,
          64
        ],
        "k": 3
      },
      "result": {
        "distinct": 5,
        "total": 84,
        "max_degeneracy": 80,
        "distinct_ratio": 0.05952380952380952,
        "max_degen_ratio": 0.9523809523809523,
        "product_entropy": 0.3714,
        "entropy_ratio": 0.16,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.921247
    },
    {
      "id": "sidon_pow7_k3_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8,
          16,
          32,
          64
        ],
        "k": 3,
        "n_modes": 7,
        "n_photons": 3,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,1,1,0,0,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9223363
    },
    {
      "id": "sidon_pow7_k3_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8,
          16,
          32,
          64
        ],
        "k": 3,
        "n_modes": 7
      },
      "result": {
        "n_modes": 7,
        "n_photons": 3,
        "n_shots": 100000,
        "n_output_states": 80,
        "n_nonzero": 80,
        "entropy": 2.870384,
        "max_entropy": 6.3219,
        "entropy_ratio": 0.454,
        "kl_divergence": 3.4515,
        "max_prob": 0.61162,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.924669
    },
    {
      "id": "sidon_s6_k3_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          11,
          16,
          19
        ],
        "k": 3
      },
      "result": {
        "distinct": 5,
        "total": 56,
        "max_degeneracy": 52,
        "distinct_ratio": 0.08928571428571429,
        "max_degen_ratio": 0.9285714285714286,
        "product_entropy": 0.5141,
        "entropy_ratio": 0.2214,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9257596
    },
    {
      "id": "sidon_s6_k3_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          11,
          16,
          19
        ],
        "k": 3,
        "n_modes": 6,
        "n_photons": 3,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,1,1,0,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9268186
    },
    {
      "id": "sidon_s6_k3_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          11,
          16,
          19
        ],
        "k": 3,
        "n_modes": 6
      },
      "result": {
        "n_modes": 6,
        "n_photons": 3,
        "n_shots": 100000,
        "n_output_states": 56,
        "n_nonzero": 56,
        "entropy": 3.860889,
        "max_entropy": 5.8074,
        "entropy_ratio": 0.6648,
        "kl_divergence": 1.9465,
        "max_prob": 0.45906,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9287193
    },
    {
      "id": "sidon_s7_k3_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          11,
          19,
          28,
          35
        ],
        "k": 3
      },
      "result": {
        "distinct": 5,
        "total": 84,
        "max_degeneracy": 80,
        "distinct_ratio": 0.05952380952380952,
        "max_degen_ratio": 0.9523809523809523,
        "product_entropy": 0.3714,
        "entropy_ratio": 0.16,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9297915
    },
    {
      "id": "sidon_s7_k3_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          11,
          19,
          28,
          35
        ],
        "k": 3,
        "n_modes": 7,
        "n_photons": 3,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,1,1,0,0,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9309552
    },
    {
      "id": "sidon_s7_k3_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          11,
          19,
          28,
          35
        ],
        "k": 3,
        "n_modes": 7
      },
      "result": {
        "n_modes": 7,
        "n_photons": 3,
        "n_shots": 100000,
        "n_output_states": 84,
        "n_nonzero": 84,
        "entropy": 3.641425,
        "max_entropy": 6.3923,
        "entropy_ratio": 0.5697,
        "kl_divergence": 2.7509,
        "max_prob": 0.52434,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9331603
    },
    {
      "id": "nonsidon_dense6_k3_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          5,
          6,
          7,
          8,
          9,
          10
        ],
        "k": 3
      },
      "result": {
        "distinct": 5,
        "total": 56,
        "max_degeneracy": 52,
        "distinct_ratio": 0.08928571428571429,
        "max_degen_ratio": 0.9285714285714286,
        "product_entropy": 0.5141,
        "entropy_ratio": 0.2214,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9342306
    },
    {
      "id": "nonsidon_dense6_k3_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          5,
          6,
          7,
          8,
          9,
          10
        ],
        "k": 3,
        "n_modes": 6,
        "n_photons": 3,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,1,1,0,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.935362
    },
    {
      "id": "nonsidon_dense6_k3_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          5,
          6,
          7,
          8,
          9,
          10
        ],
        "k": 3,
        "n_modes": 6
      },
      "result": {
        "n_modes": 6,
        "n_photons": 3,
        "n_shots": 100000,
        "n_output_states": 56,
        "n_nonzero": 56,
        "entropy": 4.765377,
        "max_entropy": 5.8074,
        "entropy_ratio": 0.8206,
        "kl_divergence": 1.042,
        "max_prob": 0.27308,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9372327
    },
    {
      "id": "nonsidon_dense7_k3_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          10,
          11,
          12,
          13,
          14,
          15,
          16
        ],
        "k": 3
      },
      "result": {
        "distinct": 5,
        "total": 84,
        "max_degeneracy": 80,
        "distinct_ratio": 0.05952380952380952,
        "max_degen_ratio": 0.9523809523809523,
        "product_entropy": 0.3714,
        "entropy_ratio": 0.16,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9383218
    },
    {
      "id": "nonsidon_dense7_k3_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          10,
          11,
          12,
          13,
          14,
          15,
          16
        ],
        "k": 3,
        "n_modes": 7,
        "n_photons": 3,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,1,1,0,0,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9395173
    },
    {
      "id": "nonsidon_dense7_k3_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          10,
          11,
          12,
          13,
          14,
          15,
          16
        ],
        "k": 3,
        "n_modes": 7
      },
      "result": {
        "n_modes": 7,
        "n_photons": 3,
        "n_shots": 100000,
        "n_output_states": 84,
        "n_nonzero": 84,
        "entropy": 4.3175,
        "max_entropy": 6.3923,
        "entropy_ratio": 0.6754,
        "kl_divergence": 2.0748,
        "max_prob": 0.4197,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9417028
    },
    {
      "id": "primes_s7_k3_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          2,
          3,
          5,
          7,
          11,
          13,
          17
        ],
        "k": 3
      },
      "result": {
        "distinct": 5,
        "total": 84,
        "max_degeneracy": 80,
        "distinct_ratio": 0.05952380952380952,
        "max_degen_ratio": 0.9523809523809523,
        "product_entropy": 0.3714,
        "entropy_ratio": 0.16,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9430141
    },
    {
      "id": "primes_s7_k3_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          2,
          3,
          5,
          7,
          11,
          13,
          17
        ],
        "k": 3,
        "n_modes": 7,
        "n_photons": 3,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,1,1,0,0,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9443138
    },
    {
      "id": "primes_s7_k3_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          2,
          3,
          5,
          7,
          11,
          13,
          17
        ],
        "k": 3,
        "n_modes": 7
      },
      "result": {
        "n_modes": 7,
        "n_photons": 3,
        "n_shots": 100000,
        "n_output_states": 84,
        "n_nonzero": 84,
        "entropy": 4.156243,
        "max_entropy": 6.3923,
        "entropy_ratio": 0.6502,
        "kl_divergence": 2.2361,
        "max_prob": 0.45294,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9464695
    },
    {
      "id": "primes_s8_k3_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          2,
          3,
          5,
          7,
          11,
          13,
          17,
          19
        ],
        "k": 3
      },
      "result": {
        "distinct": 5,
        "total": 120,
        "max_degeneracy": 116,
        "distinct_ratio": 0.041666666666666664,
        "max_degen_ratio": 0.9666666666666667,
        "product_entropy": 0.2775,
        "entropy_ratio": 0.1195,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9476588
    },
    {
      "id": "primes_s8_k3_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          2,
          3,
          5,
          7,
          11,
          13,
          17,
          19
        ],
        "k": 3,
        "n_modes": 8,
        "n_photons": 3,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,1,1,0,0,0,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9488502
    },
    {
      "id": "primes_s8_k3_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          2,
          3,
          5,
          7,
          11,
          13,
          17,
          19
        ],
        "k": 3,
        "n_modes": 8
      },
      "result": {
        "n_modes": 8,
        "n_photons": 3,
        "n_shots": 100000,
        "n_output_states": 120,
        "n_nonzero": 120,
        "entropy": 3.996964,
        "max_entropy": 6.9069,
        "entropy_ratio": 0.5787,
        "kl_divergence": 2.9099,
        "max_prob": 0.50015,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9515278
    },
    {
      "id": "sidon_pow8_k3_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8,
          16,
          32,
          64,
          128
        ],
        "k": 3
      },
      "result": {
        "distinct": 5,
        "total": 120,
        "max_degeneracy": 116,
        "distinct_ratio": 0.041666666666666664,
        "max_degen_ratio": 0.9666666666666667,
        "product_entropy": 0.2775,
        "entropy_ratio": 0.1195,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9527926
    },
    {
      "id": "sidon_pow8_k3_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8,
          16,
          32,
          64,
          128
        ],
        "k": 3,
        "n_modes": 8,
        "n_photons": 3,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,1,1,0,0,0,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9540095
    },
    {
      "id": "sidon_pow8_k3_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8,
          16,
          32,
          64,
          128
        ],
        "k": 3,
        "n_modes": 8
      },
      "result": {
        "n_modes": 8,
        "n_photons": 3,
        "n_shots": 100000,
        "n_output_states": 117,
        "n_nonzero": 117,
        "entropy": 2.837025,
        "max_entropy": 6.8704,
        "entropy_ratio": 0.4129,
        "kl_divergence": 4.0333,
        "max_prob": 0.6299,
        "elapsed_s": 0.01,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.01,
      "timestamp": 1783119227.961103
    },
    {
      "id": "sidon_pow2_k3_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8
        ],
        "k": 3
      },
      "result": {
        "k": 3,
        "desc": "sidon_pow2",
        "labels": [
          1,
          2,
          4,
          8
        ],
        "prod_distinct_ratio": 0.25,
        "slos_kl": 0.7894,
        "slos_entropy_ratio": 0.8173,
        "spearman_rho": -0.9298,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9622686
    },
    {
      "id": "nonsidon_seq_k3_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          1,
          2,
          3,
          4
        ],
        "k": 3
      },
      "result": {
        "k": 3,
        "desc": "nonsidon_seq",
        "labels": [
          1,
          2,
          3,
          4
        ],
        "prod_distinct_ratio": 0.25,
        "slos_kl": 0.4479,
        "slos_entropy_ratio": 0.8964,
        "spearman_rho": -0.9298,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9633555
    },
    {
      "id": "sidon_h8_k3_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          7
        ],
        "k": 3
      },
      "result": {
        "k": 3,
        "desc": "sidon_h8",
        "labels": [
          1,
          2,
          5,
          7
        ],
        "prod_distinct_ratio": 0.25,
        "slos_kl": 0.5133,
        "slos_entropy_ratio": 0.8812,
        "spearman_rho": -0.9298,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9642634
    },
    {
      "id": "sidon_h16_k3_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          10,
          16
        ],
        "k": 3
      },
      "result": {
        "k": 3,
        "desc": "sidon_h16",
        "labels": [
          1,
          2,
          5,
          10,
          16
        ],
        "prod_distinct_ratio": 0.14285714285714285,
        "slos_kl": 1.6547,
        "slos_entropy_ratio": 0.6774,
        "spearman_rho": -0.9298,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9651518
    },
    {
      "id": "sidon_pow7_k3_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8,
          16,
          32,
          64
        ],
        "k": 3
      },
      "result": {
        "k": 3,
        "desc": "sidon_pow7",
        "labels": [
          1,
          2,
          4,
          8,
          16,
          32,
          64
        ],
        "prod_distinct_ratio": 0.05952380952380952,
        "slos_kl": 3.4515,
        "slos_entropy_ratio": 0.454,
        "spearman_rho": -0.9298,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.965995
    },
    {
      "id": "sidon_s6_k3_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          11,
          16,
          19
        ],
        "k": 3
      },
      "result": {
        "k": 3,
        "desc": "sidon_s6",
        "labels": [
          1,
          2,
          5,
          11,
          16,
          19
        ],
        "prod_distinct_ratio": 0.08928571428571429,
        "slos_kl": 1.9465,
        "slos_entropy_ratio": 0.6648,
        "spearman_rho": -0.9298,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.96686
    },
    {
      "id": "sidon_s7_k3_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          11,
          19,
          28,
          35
        ],
        "k": 3
      },
      "result": {
        "k": 3,
        "desc": "sidon_s7",
        "labels": [
          1,
          2,
          5,
          11,
          19,
          28,
          35
        ],
        "prod_distinct_ratio": 0.05952380952380952,
        "slos_kl": 2.7509,
        "slos_entropy_ratio": 0.5697,
        "spearman_rho": -0.9298,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9677193
    },
    {
      "id": "nonsidon_dense6_k3_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          5,
          6,
          7,
          8,
          9,
          10
        ],
        "k": 3
      },
      "result": {
        "k": 3,
        "desc": "nonsidon_dense6",
        "labels": [
          5,
          6,
          7,
          8,
          9,
          10
        ],
        "prod_distinct_ratio": 0.08928571428571429,
        "slos_kl": 1.042,
        "slos_entropy_ratio": 0.8206,
        "spearman_rho": -0.9298,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9685857
    },
    {
      "id": "nonsidon_dense7_k3_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          10,
          11,
          12,
          13,
          14,
          15,
          16
        ],
        "k": 3
      },
      "result": {
        "k": 3,
        "desc": "nonsidon_dense7",
        "labels": [
          10,
          11,
          12,
          13,
          14,
          15,
          16
        ],
        "prod_distinct_ratio": 0.05952380952380952,
        "slos_kl": 2.0748,
        "slos_entropy_ratio": 0.6754,
        "spearman_rho": -0.9298,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.969449
    },
    {
      "id": "primes_s7_k3_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          2,
          3,
          5,
          7,
          11,
          13,
          17
        ],
        "k": 3
      },
      "result": {
        "k": 3,
        "desc": "primes_s7",
        "labels": [
          2,
          3,
          5,
          7,
          11,
          13,
          17
        ],
        "prod_distinct_ratio": 0.05952380952380952,
        "slos_kl": 2.2361,
        "slos_entropy_ratio": 0.6502,
        "spearman_rho": -0.9298,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.970309
    },
    {
      "id": "primes_s8_k3_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          2,
          3,
          5,
          7,
          11,
          13,
          17,
          19
        ],
        "k": 3
      },
      "result": {
        "k": 3,
        "desc": "primes_s8",
        "labels": [
          2,
          3,
          5,
          7,
          11,
          13,
          17,
          19
        ],
        "prod_distinct_ratio": 0.041666666666666664,
        "slos_kl": 2.9099,
        "slos_entropy_ratio": 0.5787,
        "spearman_rho": -0.9298,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9711885
    },
    {
      "id": "sidon_pow8_k3_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8,
          16,
          32,
          64,
          128
        ],
        "k": 3
      },
      "result": {
        "k": 3,
        "desc": "sidon_pow8",
        "labels": [
          1,
          2,
          4,
          8,
          16,
          32,
          64,
          128
        ],
        "prod_distinct_ratio": 0.041666666666666664,
        "slos_kl": 4.0333,
        "slos_entropy_ratio": 0.4129,
        "spearman_rho": -0.9298,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9720562
    },
    {
      "id": "sidon_pow2_k4_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8
        ],
        "k": 4
      },
      "result": {
        "distinct": 6,
        "total": 35,
        "max_degeneracy": 30,
        "distinct_ratio": 0.17142857142857143,
        "max_degen_ratio": 0.8571428571428571,
        "product_entropy": 0.9234,
        "entropy_ratio": 0.3572,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9746451
    },
    {
      "id": "sidon_pow2_k4_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8
        ],
        "k": 4,
        "n_modes": 4,
        "n_photons": 4,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,1,1,1>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9760487
    },
    {
      "id": "sidon_pow2_k4_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8
        ],
        "k": 4,
        "n_modes": 4
      },
      "result": {
        "n_modes": 4,
        "n_photons": 4,
        "n_shots": 100000,
        "n_output_states": 35,
        "n_nonzero": 35,
        "entropy": 4.64099,
        "max_entropy": 5.1293,
        "entropy_ratio": 0.9048,
        "kl_divergence": 0.4883,
        "max_prob": 0.10972,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9779303
    },
    {
      "id": "nonsidon_seq_k4_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          1,
          2,
          3,
          4
        ],
        "k": 4
      },
      "result": {
        "distinct": 6,
        "total": 35,
        "max_degeneracy": 30,
        "distinct_ratio": 0.17142857142857143,
        "max_degen_ratio": 0.8571428571428571,
        "product_entropy": 0.9234,
        "entropy_ratio": 0.3572,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9792154
    },
    {
      "id": "nonsidon_seq_k4_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          3,
          4
        ],
        "k": 4,
        "n_modes": 4,
        "n_photons": 4,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,1,1,1>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9805884
    },
    {
      "id": "nonsidon_seq_k4_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          3,
          4
        ],
        "k": 4,
        "n_modes": 4
      },
      "result": {
        "n_modes": 4,
        "n_photons": 4,
        "n_shots": 100000,
        "n_output_states": 35,
        "n_nonzero": 35,
        "entropy": 4.621103,
        "max_entropy": 5.1293,
        "entropy_ratio": 0.9009,
        "kl_divergence": 0.5082,
        "max_prob": 0.09772,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9823954
    },
    {
      "id": "sidon_h8_k4_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          7
        ],
        "k": 4
      },
      "result": {
        "distinct": 6,
        "total": 35,
        "max_degeneracy": 30,
        "distinct_ratio": 0.17142857142857143,
        "max_degen_ratio": 0.8571428571428571,
        "product_entropy": 0.9234,
        "entropy_ratio": 0.3572,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9835763
    },
    {
      "id": "sidon_h8_k4_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          7
        ],
        "k": 4,
        "n_modes": 4,
        "n_photons": 4,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,1,1,1>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9849164
    },
    {
      "id": "sidon_h8_k4_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          7
        ],
        "k": 4,
        "n_modes": 4
      },
      "result": {
        "n_modes": 4,
        "n_photons": 4,
        "n_shots": 100000,
        "n_output_states": 35,
        "n_nonzero": 35,
        "entropy": 4.580681,
        "max_entropy": 5.1293,
        "entropy_ratio": 0.893,
        "kl_divergence": 0.5486,
        "max_prob": 0.12833,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9867709
    },
    {
      "id": "sidon_h16_k4_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          10,
          16
        ],
        "k": 4
      },
      "result": {
        "distinct": 6,
        "total": 70,
        "max_degeneracy": 65,
        "distinct_ratio": 0.08571428571428572,
        "max_degen_ratio": 0.9285714285714286,
        "product_entropy": 0.5371,
        "entropy_ratio": 0.2078,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9880679
    },
    {
      "id": "sidon_h16_k4_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          10,
          16
        ],
        "k": 4,
        "n_modes": 5,
        "n_photons": 4,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,1,1,1,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9894392
    },
    {
      "id": "sidon_h16_k4_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          10,
          16
        ],
        "k": 4,
        "n_modes": 5
      },
      "result": {
        "n_modes": 5,
        "n_photons": 4,
        "n_shots": 100000,
        "n_output_states": 70,
        "n_nonzero": 70,
        "entropy": 4.949382,
        "max_entropy": 6.1293,
        "entropy_ratio": 0.8075,
        "kl_divergence": 1.1799,
        "max_prob": 0.23869,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.991658
    },
    {
      "id": "sidon_pow7_k4_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8,
          16,
          32,
          64
        ],
        "k": 4
      },
      "result": {
        "distinct": 6,
        "total": 210,
        "max_degeneracy": 205,
        "distinct_ratio": 0.02857142857142857,
        "max_degen_ratio": 0.9761904761904762,
        "product_entropy": 0.2176,
        "entropy_ratio": 0.0842,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.993145
    },
    {
      "id": "sidon_pow7_k4_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8,
          16,
          32,
          64
        ],
        "k": 4,
        "n_modes": 7,
        "n_photons": 4,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,1,1,1,0,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9945118
    },
    {
      "id": "sidon_pow7_k4_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8,
          16,
          32,
          64
        ],
        "k": 4,
        "n_modes": 7
      },
      "result": {
        "n_modes": 7,
        "n_photons": 4,
        "n_shots": 100000,
        "n_output_states": 205,
        "n_nonzero": 205,
        "entropy": 4.014578,
        "max_entropy": 7.6795,
        "entropy_ratio": 0.5228,
        "kl_divergence": 3.6649,
        "max_prob": 0.50848,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9983137
    },
    {
      "id": "sidon_s6_k4_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          11,
          16,
          19
        ],
        "k": 4
      },
      "result": {
        "distinct": 6,
        "total": 126,
        "max_degeneracy": 121,
        "distinct_ratio": 0.047619047619047616,
        "max_degen_ratio": 0.9603174603174603,
        "product_entropy": 0.333,
        "entropy_ratio": 0.1288,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119227.9997845
    },
    {
      "id": "sidon_s6_k4_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          11,
          16,
          19
        ],
        "k": 4,
        "n_modes": 6,
        "n_photons": 4,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,1,1,1,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119228.0011468
    },
    {
      "id": "sidon_s6_k4_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          11,
          16,
          19
        ],
        "k": 4,
        "n_modes": 6
      },
      "result": {
        "n_modes": 6,
        "n_photons": 4,
        "n_shots": 100000,
        "n_output_states": 126,
        "n_nonzero": 126,
        "entropy": 5.370826,
        "max_entropy": 6.9773,
        "entropy_ratio": 0.7698,
        "kl_divergence": 1.6065,
        "max_prob": 0.27097,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119228.004077
    },
    {
      "id": "sidon_s7_k4_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          11,
          19,
          28,
          35
        ],
        "k": 4
      },
      "result": {
        "distinct": 6,
        "total": 210,
        "max_degeneracy": 205,
        "distinct_ratio": 0.02857142857142857,
        "max_degen_ratio": 0.9761904761904762,
        "product_entropy": 0.2176,
        "entropy_ratio": 0.0842,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119228.0055747
    },
    {
      "id": "sidon_s7_k4_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          11,
          19,
          28,
          35
        ],
        "k": 4,
        "n_modes": 7,
        "n_photons": 4,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,1,1,1,0,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119228.0069768
    },
    {
      "id": "sidon_s7_k4_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          11,
          19,
          28,
          35
        ],
        "k": 4,
        "n_modes": 7
      },
      "result": {
        "n_modes": 7,
        "n_photons": 4,
        "n_shots": 100000,
        "n_output_states": 210,
        "n_nonzero": 210,
        "entropy": 5.100881,
        "max_entropy": 7.7142,
        "entropy_ratio": 0.6612,
        "kl_divergence": 2.6134,
        "max_prob": 0.38876,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119228.010712
    },
    {
      "id": "nonsidon_dense6_k4_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          5,
          6,
          7,
          8,
          9,
          10
        ],
        "k": 4
      },
      "result": {
        "distinct": 6,
        "total": 126,
        "max_degeneracy": 121,
        "distinct_ratio": 0.047619047619047616,
        "max_degen_ratio": 0.9603174603174603,
        "product_entropy": 0.333,
        "entropy_ratio": 0.1288,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119228.012155
    },
    {
      "id": "nonsidon_dense6_k4_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          5,
          6,
          7,
          8,
          9,
          10
        ],
        "k": 4,
        "n_modes": 6,
        "n_photons": 4,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,1,1,1,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119228.0138614
    },
    {
      "id": "nonsidon_dense6_k4_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          5,
          6,
          7,
          8,
          9,
          10
        ],
        "k": 4,
        "n_modes": 6
      },
      "result": {
        "n_modes": 6,
        "n_photons": 4,
        "n_shots": 100000,
        "n_output_states": 126,
        "n_nonzero": 126,
        "entropy": 5.877634,
        "max_entropy": 6.9773,
        "entropy_ratio": 0.8424,
        "kl_divergence": 1.0996,
        "max_prob": 0.19064,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119228.0167286
    },
    {
      "id": "nonsidon_dense7_k4_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          10,
          11,
          12,
          13,
          14,
          15,
          16
        ],
        "k": 4
      },
      "result": {
        "distinct": 6,
        "total": 210,
        "max_degeneracy": 205,
        "distinct_ratio": 0.02857142857142857,
        "max_degen_ratio": 0.9761904761904762,
        "product_entropy": 0.2176,
        "entropy_ratio": 0.0842,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119228.018246
    },
    {
      "id": "nonsidon_dense7_k4_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          10,
          11,
          12,
          13,
          14,
          15,
          16
        ],
        "k": 4,
        "n_modes": 7,
        "n_photons": 4,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,1,1,1,0,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119228.0197258
    },
    {
      "id": "nonsidon_dense7_k4_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          10,
          11,
          12,
          13,
          14,
          15,
          16
        ],
        "k": 4,
        "n_modes": 7
      },
      "result": {
        "n_modes": 7,
        "n_photons": 4,
        "n_shots": 100000,
        "n_output_states": 210,
        "n_nonzero": 210,
        "entropy": 5.669085,
        "max_entropy": 7.7142,
        "entropy_ratio": 0.7349,
        "kl_divergence": 2.0452,
        "max_prob": 0.31966,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119228.023684
    },
    {
      "id": "primes_s7_k4_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          2,
          3,
          5,
          7,
          11,
          13,
          17
        ],
        "k": 4
      },
      "result": {
        "distinct": 6,
        "total": 210,
        "max_degeneracy": 205,
        "distinct_ratio": 0.02857142857142857,
        "max_degen_ratio": 0.9761904761904762,
        "product_entropy": 0.2176,
        "entropy_ratio": 0.0842,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119228.0253265
    },
    {
      "id": "primes_s7_k4_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          2,
          3,
          5,
          7,
          11,
          13,
          17
        ],
        "k": 4,
        "n_modes": 7,
        "n_photons": 4,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,1,1,1,0,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119228.0267866
    },
    {
      "id": "primes_s7_k4_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          2,
          3,
          5,
          7,
          11,
          13,
          17
        ],
        "k": 4,
        "n_modes": 7
      },
      "result": {
        "n_modes": 7,
        "n_photons": 4,
        "n_shots": 100000,
        "n_output_states": 210,
        "n_nonzero": 210,
        "entropy": 5.59635,
        "max_entropy": 7.7142,
        "entropy_ratio": 0.7255,
        "kl_divergence": 2.1179,
        "max_prob": 0.32744,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119228.030754
    },
    {
      "id": "primes_s8_k4_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          2,
          3,
          5,
          7,
          11,
          13,
          17,
          19
        ],
        "k": 4
      },
      "result": {
        "distinct": 6,
        "total": 330,
        "max_degeneracy": 325,
        "distinct_ratio": 0.01818181818181818,
        "max_degen_ratio": 0.9848484848484849,
        "product_entropy": 0.1485,
        "entropy_ratio": 0.0574,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119228.0325181
    },
    {
      "id": "primes_s8_k4_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          2,
          3,
          5,
          7,
          11,
          13,
          17,
          19
        ],
        "k": 4,
        "n_modes": 8,
        "n_photons": 4,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,1,1,1,0,0,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119228.0339906
    },
    {
      "id": "primes_s8_k4_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          2,
          3,
          5,
          7,
          11,
          13,
          17,
          19
        ],
        "k": 4,
        "n_modes": 8
      },
      "result": {
        "n_modes": 8,
        "n_photons": 4,
        "n_shots": 100000,
        "n_output_states": 330,
        "n_nonzero": 330,
        "entropy": 5.488591,
        "max_entropy": 8.3663,
        "entropy_ratio": 0.656,
        "kl_divergence": 2.8777,
        "max_prob": 0.38094,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119228.039467
    },
    {
      "id": "sidon_pow8_k4_products",
      "type": "eigenvalue_products",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8,
          16,
          32,
          64,
          128
        ],
        "k": 4
      },
      "result": {
        "distinct": 6,
        "total": 330,
        "max_degeneracy": 325,
        "distinct_ratio": 0.01818181818181818,
        "max_degen_ratio": 0.9848484848484849,
        "product_entropy": 0.1485,
        "entropy_ratio": 0.0574,
        "is_concentrated": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119228.0413115
    },
    {
      "id": "sidon_pow8_k4_slos_circuit",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8,
          16,
          32,
          64,
          128
        ],
        "k": 4,
        "n_modes": 8,
        "n_photons": 4,
        "cloud": false
      },
      "result": {
        "circuit_built": true,
        "input_state": "|1,1,1,1,0,0,0,0>"
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119228.0428355
    },
    {
      "id": "sidon_pow8_k4_slos",
      "type": "slos",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8,
          16,
          32,
          64,
          128
        ],
        "k": 4,
        "n_modes": 8
      },
      "result": {
        "n_modes": 8,
        "n_photons": 4,
        "n_shots": 100000,
        "n_output_states": 302,
        "n_nonzero": 302,
        "entropy": 3.886943,
        "max_entropy": 8.2384,
        "entropy_ratio": 0.4718,
        "kl_divergence": 4.3515,
        "max_prob": 0.54008,
        "elapsed_s": 0.0,
        "cloud": false,
        "n_shots_actual": 100000
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119228.048183
    },
    {
      "id": "sidon_pow2_k4_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8
        ],
        "k": 4
      },
      "result": {
        "k": 4,
        "desc": "sidon_pow2",
        "labels": [
          1,
          2,
          4,
          8
        ],
        "prod_distinct_ratio": 0.17142857142857143,
        "slos_kl": 0.4883,
        "slos_entropy_ratio": 0.9048,
        "spearman_rho": -0.9298,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119228.0495384
    },
    {
      "id": "nonsidon_seq_k4_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          1,
          2,
          3,
          4
        ],
        "k": 4
      },
      "result": {
        "k": 4,
        "desc": "nonsidon_seq",
        "labels": [
          1,
          2,
          3,
          4
        ],
        "prod_distinct_ratio": 0.17142857142857143,
        "slos_kl": 0.5082,
        "slos_entropy_ratio": 0.9009,
        "spearman_rho": -0.9298,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119228.0507195
    },
    {
      "id": "sidon_h8_k4_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          7
        ],
        "k": 4
      },
      "result": {
        "k": 4,
        "desc": "sidon_h8",
        "labels": [
          1,
          2,
          5,
          7
        ],
        "prod_distinct_ratio": 0.17142857142857143,
        "slos_kl": 0.5486,
        "slos_entropy_ratio": 0.893,
        "spearman_rho": -0.9298,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119228.0518818
    },
    {
      "id": "sidon_h16_k4_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          10,
          16
        ],
        "k": 4
      },
      "result": {
        "k": 4,
        "desc": "sidon_h16",
        "labels": [
          1,
          2,
          5,
          10,
          16
        ],
        "prod_distinct_ratio": 0.08571428571428572,
        "slos_kl": 1.1799,
        "slos_entropy_ratio": 0.8075,
        "spearman_rho": -0.9298,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119228.053007
    },
    {
      "id": "sidon_pow7_k4_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8,
          16,
          32,
          64
        ],
        "k": 4
      },
      "result": {
        "k": 4,
        "desc": "sidon_pow7",
        "labels": [
          1,
          2,
          4,
          8,
          16,
          32,
          64
        ],
        "prod_distinct_ratio": 0.02857142857142857,
        "slos_kl": 3.6649,
        "slos_entropy_ratio": 0.5228,
        "spearman_rho": -0.9298,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119228.0541127
    },
    {
      "id": "sidon_s6_k4_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          11,
          16,
          19
        ],
        "k": 4
      },
      "result": {
        "k": 4,
        "desc": "sidon_s6",
        "labels": [
          1,
          2,
          5,
          11,
          16,
          19
        ],
        "prod_distinct_ratio": 0.047619047619047616,
        "slos_kl": 1.6065,
        "slos_entropy_ratio": 0.7698,
        "spearman_rho": -0.9298,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119228.0552475
    },
    {
      "id": "sidon_s7_k4_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          1,
          2,
          5,
          11,
          19,
          28,
          35
        ],
        "k": 4
      },
      "result": {
        "k": 4,
        "desc": "sidon_s7",
        "labels": [
          1,
          2,
          5,
          11,
          19,
          28,
          35
        ],
        "prod_distinct_ratio": 0.02857142857142857,
        "slos_kl": 2.6134,
        "slos_entropy_ratio": 0.6612,
        "spearman_rho": -0.9298,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119228.056396
    },
    {
      "id": "nonsidon_dense6_k4_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          5,
          6,
          7,
          8,
          9,
          10
        ],
        "k": 4
      },
      "result": {
        "k": 4,
        "desc": "nonsidon_dense6",
        "labels": [
          5,
          6,
          7,
          8,
          9,
          10
        ],
        "prod_distinct_ratio": 0.047619047619047616,
        "slos_kl": 1.0996,
        "slos_entropy_ratio": 0.8424,
        "spearman_rho": -0.9298,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119228.057528
    },
    {
      "id": "nonsidon_dense7_k4_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          10,
          11,
          12,
          13,
          14,
          15,
          16
        ],
        "k": 4
      },
      "result": {
        "k": 4,
        "desc": "nonsidon_dense7",
        "labels": [
          10,
          11,
          12,
          13,
          14,
          15,
          16
        ],
        "prod_distinct_ratio": 0.02857142857142857,
        "slos_kl": 2.0452,
        "slos_entropy_ratio": 0.7349,
        "spearman_rho": -0.9298,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119228.0586467
    },
    {
      "id": "primes_s7_k4_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          2,
          3,
          5,
          7,
          11,
          13,
          17
        ],
        "k": 4
      },
      "result": {
        "k": 4,
        "desc": "primes_s7",
        "labels": [
          2,
          3,
          5,
          7,
          11,
          13,
          17
        ],
        "prod_distinct_ratio": 0.02857142857142857,
        "slos_kl": 2.1179,
        "slos_entropy_ratio": 0.7255,
        "spearman_rho": -0.9298,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119228.059763
    },
    {
      "id": "primes_s8_k4_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          2,
          3,
          5,
          7,
          11,
          13,
          17,
          19
        ],
        "k": 4
      },
      "result": {
        "k": 4,
        "desc": "primes_s8",
        "labels": [
          2,
          3,
          5,
          7,
          11,
          13,
          17,
          19
        ],
        "prod_distinct_ratio": 0.01818181818181818,
        "slos_kl": 2.8777,
        "slos_entropy_ratio": 0.656,
        "spearman_rho": -0.9298,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119228.060899
    },
    {
      "id": "sidon_pow8_k4_compare",
      "type": "compare",
      "inputs": {
        "labels": [
          1,
          2,
          4,
          8,
          16,
          32,
          64,
          128
        ],
        "k": 4
      },
      "result": {
        "k": 4,
        "desc": "sidon_pow8",
        "labels": [
          1,
          2,
          4,
          8,
          16,
          32,
          64,
          128
        ],
        "prod_distinct_ratio": 0.01818181818181818,
        "slos_kl": 4.3515,
        "slos_entropy_ratio": 0.4718,
        "spearman_rho": -0.9298,
        "rank_n": 12,
        "rank_confirmed": true
      },
      "status": "success",
      "elapsed_s": 0.0,
      "timestamp": 1783119228.0621643
    }
  ],
  "edges": [
    {
      "from": "sidon_pow2_k1_products",
      "to": "sidon_pow2_k1_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_pow2_k1_slos",
      "to": "sidon_pow2_k1_compare",
      "type": "depends_on"
    },
    {
      "from": "nonsidon_seq_k1_products",
      "to": "nonsidon_seq_k1_compare",
      "type": "depends_on"
    },
    {
      "from": "nonsidon_seq_k1_slos",
      "to": "nonsidon_seq_k1_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_h8_k1_products",
      "to": "sidon_h8_k1_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_h8_k1_slos",
      "to": "sidon_h8_k1_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_h16_k1_products",
      "to": "sidon_h16_k1_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_h16_k1_slos",
      "to": "sidon_h16_k1_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_pow7_k1_products",
      "to": "sidon_pow7_k1_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_pow7_k1_slos",
      "to": "sidon_pow7_k1_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_s6_k1_products",
      "to": "sidon_s6_k1_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_s6_k1_slos",
      "to": "sidon_s6_k1_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_s7_k1_products",
      "to": "sidon_s7_k1_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_s7_k1_slos",
      "to": "sidon_s7_k1_compare",
      "type": "depends_on"
    },
    {
      "from": "nonsidon_dense6_k1_products",
      "to": "nonsidon_dense6_k1_compare",
      "type": "depends_on"
    },
    {
      "from": "nonsidon_dense6_k1_slos",
      "to": "nonsidon_dense6_k1_compare",
      "type": "depends_on"
    },
    {
      "from": "nonsidon_dense7_k1_products",
      "to": "nonsidon_dense7_k1_compare",
      "type": "depends_on"
    },
    {
      "from": "nonsidon_dense7_k1_slos",
      "to": "nonsidon_dense7_k1_compare",
      "type": "depends_on"
    },
    {
      "from": "primes_s7_k1_products",
      "to": "primes_s7_k1_compare",
      "type": "depends_on"
    },
    {
      "from": "primes_s7_k1_slos",
      "to": "primes_s7_k1_compare",
      "type": "depends_on"
    },
    {
      "from": "primes_s8_k1_products",
      "to": "primes_s8_k1_compare",
      "type": "depends_on"
    },
    {
      "from": "primes_s8_k1_slos",
      "to": "primes_s8_k1_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_pow8_k1_products",
      "to": "sidon_pow8_k1_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_pow8_k1_slos",
      "to": "sidon_pow8_k1_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_pow2_k2_products",
      "to": "sidon_pow2_k2_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_pow2_k2_slos",
      "to": "sidon_pow2_k2_compare",
      "type": "depends_on"
    },
    {
      "from": "nonsidon_seq_k2_products",
      "to": "nonsidon_seq_k2_compare",
      "type": "depends_on"
    },
    {
      "from": "nonsidon_seq_k2_slos",
      "to": "nonsidon_seq_k2_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_h8_k2_products",
      "to": "sidon_h8_k2_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_h8_k2_slos",
      "to": "sidon_h8_k2_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_h16_k2_products",
      "to": "sidon_h16_k2_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_h16_k2_slos",
      "to": "sidon_h16_k2_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_pow7_k2_products",
      "to": "sidon_pow7_k2_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_pow7_k2_slos",
      "to": "sidon_pow7_k2_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_s6_k2_products",
      "to": "sidon_s6_k2_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_s6_k2_slos",
      "to": "sidon_s6_k2_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_s7_k2_products",
      "to": "sidon_s7_k2_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_s7_k2_slos",
      "to": "sidon_s7_k2_compare",
      "type": "depends_on"
    },
    {
      "from": "nonsidon_dense6_k2_products",
      "to": "nonsidon_dense6_k2_compare",
      "type": "depends_on"
    },
    {
      "from": "nonsidon_dense6_k2_slos",
      "to": "nonsidon_dense6_k2_compare",
      "type": "depends_on"
    },
    {
      "from": "nonsidon_dense7_k2_products",
      "to": "nonsidon_dense7_k2_compare",
      "type": "depends_on"
    },
    {
      "from": "nonsidon_dense7_k2_slos",
      "to": "nonsidon_dense7_k2_compare",
      "type": "depends_on"
    },
    {
      "from": "primes_s7_k2_products",
      "to": "primes_s7_k2_compare",
      "type": "depends_on"
    },
    {
      "from": "primes_s7_k2_slos",
      "to": "primes_s7_k2_compare",
      "type": "depends_on"
    },
    {
      "from": "primes_s8_k2_products",
      "to": "primes_s8_k2_compare",
      "type": "depends_on"
    },
    {
      "from": "primes_s8_k2_slos",
      "to": "primes_s8_k2_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_pow8_k2_products",
      "to": "sidon_pow8_k2_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_pow8_k2_slos",
      "to": "sidon_pow8_k2_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_pow2_k3_products",
      "to": "sidon_pow2_k3_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_pow2_k3_slos",
      "to": "sidon_pow2_k3_compare",
      "type": "depends_on"
    },
    {
      "from": "nonsidon_seq_k3_products",
      "to": "nonsidon_seq_k3_compare",
      "type": "depends_on"
    },
    {
      "from": "nonsidon_seq_k3_slos",
      "to": "nonsidon_seq_k3_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_h8_k3_products",
      "to": "sidon_h8_k3_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_h8_k3_slos",
      "to": "sidon_h8_k3_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_h16_k3_products",
      "to": "sidon_h16_k3_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_h16_k3_slos",
      "to": "sidon_h16_k3_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_pow7_k3_products",
      "to": "sidon_pow7_k3_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_pow7_k3_slos",
      "to": "sidon_pow7_k3_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_s6_k3_products",
      "to": "sidon_s6_k3_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_s6_k3_slos",
      "to": "sidon_s6_k3_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_s7_k3_products",
      "to": "sidon_s7_k3_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_s7_k3_slos",
      "to": "sidon_s7_k3_compare",
      "type": "depends_on"
    },
    {
      "from": "nonsidon_dense6_k3_products",
      "to": "nonsidon_dense6_k3_compare",
      "type": "depends_on"
    },
    {
      "from": "nonsidon_dense6_k3_slos",
      "to": "nonsidon_dense6_k3_compare",
      "type": "depends_on"
    },
    {
      "from": "nonsidon_dense7_k3_products",
      "to": "nonsidon_dense7_k3_compare",
      "type": "depends_on"
    },
    {
      "from": "nonsidon_dense7_k3_slos",
      "to": "nonsidon_dense7_k3_compare",
      "type": "depends_on"
    },
    {
      "from": "primes_s7_k3_products",
      "to": "primes_s7_k3_compare",
      "type": "depends_on"
    },
    {
      "from": "primes_s7_k3_slos",
      "to": "primes_s7_k3_compare",
      "type": "depends_on"
    },
    {
      "from": "primes_s8_k3_products",
      "to": "primes_s8_k3_compare",
      "type": "depends_on"
    },
    {
      "from": "primes_s8_k3_slos",
      "to": "primes_s8_k3_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_pow8_k3_products",
      "to": "sidon_pow8_k3_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_pow8_k3_slos",
      "to": "sidon_pow8_k3_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_pow2_k4_products",
      "to": "sidon_pow2_k4_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_pow2_k4_slos",
      "to": "sidon_pow2_k4_compare",
      "type": "depends_on"
    },
    {
      "from": "nonsidon_seq_k4_products",
      "to": "nonsidon_seq_k4_compare",
      "type": "depends_on"
    },
    {
      "from": "nonsidon_seq_k4_slos",
      "to": "nonsidon_seq_k4_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_h8_k4_products",
      "to": "sidon_h8_k4_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_h8_k4_slos",
      "to": "sidon_h8_k4_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_h16_k4_products",
      "to": "sidon_h16_k4_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_h16_k4_slos",
      "to": "sidon_h16_k4_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_pow7_k4_products",
      "to": "sidon_pow7_k4_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_pow7_k4_slos",
      "to": "sidon_pow7_k4_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_s6_k4_products",
      "to": "sidon_s6_k4_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_s6_k4_slos",
      "to": "sidon_s6_k4_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_s7_k4_products",
      "to": "sidon_s7_k4_compare",
      "type": "depends_on"
    },
    {
      "from": "sidon_s7_k4_slos",
      "to": "sidon_s7_k4_compare",
      "type": "depends_on"
    },
    {
      "from": "nonsidon_dense6_k4_products",
      "to": "nonsidon_dense6_k4_compare",
      "type": "depends_on"
    },
    {
      "from": "nonsidon_dense6_k4_slos",
      "to": "nonsidon_dense6_k4_compare",
      "type": "depends_on"
    },
    {
      "from": "nonsidon_dense7_k4_products",
      "to": "nonsidon_dense7_k4_compare",
      "type": "depends_on"
    },
    {
      "from": "nonsidon_dense7_k4_slos",
      "to": "nonsidon_dense7_k4_compare",
      "type": "depends_on"
    },
    {
      "from": "primes_s7_k4_products",
      "to": "primes_s7_k4_compare",
      "type": "depends_on"
    },
    {
      "from": "primes_s7_k4_slos",
      "to": "primes_s7_k4_compare",
      "type": "depends_on"
    },
    {
      "from": "primes_s8_k4_products",
      "to": "primes_s8_k4_compare",
      "type": "depends_on"
    },
    {
      "from": "primes_s8_k4_slos",
      "to": "primes_s8_k4_compare",
      "type": "depends_on"
    }
  ]
}