{
  "titre": "Test n° 2 : symétrie cubique des rayons cosmiques les plus énergétiques (Auger)",
  "date": "2026-09-28",
  "prediction": "Beane, Davoudi, Savage, arXiv:1210.1847 : brisure de la symétrie de rotation reflétant la grille, dans les directions des rayons cosmiques les plus énergétiques",
  "donnees": {
    "source": "Pierre Auger Collaboration, ApJS 264, 50 (2023), arXiv:2211.16020 ; Auger Open Data release 3, DOI 10.5281/zenodo.10488964, CC BY-SA 4.0",
    "fichier": "donnees/auger_catalogSD.csv",
    "sha256": "dc94ee0da5a20dc6d3897b8dde23d28d4f283a4fd94d2264e4dbe5cc02911b6b",
    "n_evenements": 100,
    "energie_min_EeV": 78.0,
    "energie_max_EeV": 166.0,
    "periode": "2004-01-01 / 2020-12-31",
    "ecartes_etalonnage": [
      "PAO060329",
      "PAO071111",
      "PAO080703a",
      "PAO080703b",
      "PAO090322",
      "PAO110527",
      "PAO110627",
      "PAO140131",
      "PAO150912"
    ]
  },
  "methode": {
    "exposition": "Sommers 2001, latitude -35.2°, zénith <= 80.0°",
    "latitude_deg": -35.2,
    "zenith_max_deg": 80.0,
    "declinaison_max_visible_deg": 44.8,
    "fraction_du_ciel_visible": 0.8523171049817972,
    "angle_axe_diagonale_deg": 54.735610317245346,
    "fonction_l4": "Q(Rn) = somme (R n)_k^4",
    "fonction_l6": "somme (R n)_k^6 + -1.363636 somme (R n)_k^4",
    "fonction_l6_alpha": -1.3636363636363655,
    "orientations": 20000,
    "ciels_isotropes": 20000,
    "ciels_par_amplitude": 1000,
    "graine": 20260928,
    "test_principal": "l = 4, Z4 = max_R |T4(R)|"
  },
  "resultats": {
    "Z4_observe": 3.014108440585914,
    "p_valeur_l4": 0.19984000799960003,
    "Z6_observe": 2.7278244876704716,
    "p_valeur_l6": 0.5244237788110594,
    "Z46_observe": 11.717910473748312,
    "p_valeur_l4_l6": 0.3466326683665817,
    "seuils_Z4_isotrope": {
      "0.5": 2.463659812286664,
      "0.95": 3.5650454328727124,
      "0.99": 4.074012689037251,
      "0.999": 4.663377804025682
    },
    "meilleure_orientation_T4": 3.014108440585914,
    "meilleure_orientation_matrice": [
      [
        0.426197,
        -0.622662,
        -0.656238
      ],
      [
        0.207429,
        -0.638828,
        0.740859
      ],
      [
        -0.880528,
        -0.451875,
        -0.143108
      ]
    ],
    "Q_moyen_observe": 0.6499151975834333,
    "Q_moyen_attendu_isotrope": 0.5976836018133992,
    "ecart_relatif_Q": 0.0873900431793027
  },
  "limite_superieure_95": {
    "definition": "densité relative 1 + eps (5 Q - 3) / 2 ; eps = excès relatif le long des axes de la grille (eps < 0 : le long des diagonales)",
    "epsilon_axes_max": 0.9551724137931035,
    "epsilon_diagonales_max": 0.9157894736842105,
    "exces_axes_max": 0.9551724137931035,
    "exces_diagonales_max": 0.6105263157894736,
    "convention": "orientation de la grille tirée au hasard pour chaque ciel simulé : limite moyenne sur les orientations",
    "par_orientation_fixe": [
      {
        "indice": 8821,
        "ecart_type_Q_expo": 0.17311682638656503,
        "epsilon_axes_max": 1.0357142857142856,
        "epsilon_diagonales_max": 0.9162790697674419
      },
      {
        "indice": 1214,
        "ecart_type_Q_expo": 0.17342103328007705,
        "epsilon_axes_max": 0.9720930232558139,
        "epsilon_diagonales_max": 0.8733333333333332
      },
      {
        "indice": 4920,
        "ecart_type_Q_expo": 0.1734216854856925,
        "epsilon_axes_max": 0.9487179487179487,
        "epsilon_diagonales_max": 0.917391304347826
      },
      {
        "indice": 19342,
        "ecart_type_Q_expo": 0.17359917645704612,
        "epsilon_axes_max": 0.937142857142857,
        "epsilon_diagonales_max": 0.9121951219512194
      },
      {
        "indice": 19931,
        "ecart_type_Q_expo": 0.17674390930969613,
        "epsilon_axes_max": 0.9772727272727272,
        "epsilon_diagonales_max": 0.888235294117647
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      {
        "indice": 11134,
        "ecart_type_Q_expo": 0.17471500427606745,
        "epsilon_axes_max": 0.9722222222222221,
        "epsilon_diagonales_max": 0.8719999999999999
      },
      {
        "indice": 15802,
        "ecart_type_Q_expo": 0.1736304065822434,
        "epsilon_axes_max": 0.9349999999999999,
        "epsilon_diagonales_max": 0.9199999999999999
      },
      {
        "indice": 558,
        "ecart_type_Q_expo": 0.17546285126093275,
        "epsilon_axes_max": 0.9333333333333331,
        "epsilon_diagonales_max": 0.9255813953488372
      },
      {
        "indice": 15960,
        "ecart_type_Q_expo": 0.17652981418586786,
        "epsilon_axes_max": 0.9609756097560975,
        "epsilon_diagonales_max": 0.8918918918918919
      },
      {
        "indice": 2115,
        "ecart_type_Q_expo": 0.1738570579698698,
        "epsilon_axes_max": 0.9687499999999999,
        "epsilon_diagonales_max": 0.869230769230769
      },
      {
        "indice": 5074,
        "ecart_type_Q_expo": 0.17533217639227608,
        "epsilon_axes_max": 0.95,
        "epsilon_diagonales_max": 0.9027027027027027
      },
      {
        "indice": 18522,
        "ecart_type_Q_expo": 0.17339691025144244,
        "epsilon_axes_max": 0.9689655172413792,
        "epsilon_diagonales_max": 0.9291666666666665
      },
      {
        "indice": 18844,
        "ecart_type_Q_expo": 0.1739170698191156,
        "epsilon_axes_max": 0.9365853658536584,
        "epsilon_diagonales_max": 0.9161290322580643
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      {
        "indice": 3203,
        "ecart_type_Q_expo": 0.1755548394865064,
        "epsilon_axes_max": 0.9521739130434781,
        "epsilon_diagonales_max": 0.8866666666666665
      },
      {
        "indice": 11112,
        "ecart_type_Q_expo": 0.17431985868142164,
        "epsilon_axes_max": 0.9809523809523809,
        "epsilon_diagonales_max": 0.8740740740740738
      },
      {
        "indice": 7209,
        "ecart_type_Q_expo": 0.17495817962507512,
        "epsilon_axes_max": 0.9446808510638297,
        "epsilon_diagonales_max": 0.8666666666666666
      }
    ],
    "pire_orientation_epsilon_axes_max": 1.0357142857142856,
    "pire_orientation_epsilon_diagonales_max": 0.9291666666666665,
    "orientations_sans_limite_axes": 0,
    "orientations_sans_limite_diagonales": 0,
    "n_orientations_fixes": 16,
    "ciels_par_amplitude_orientation_fixe": 400,
    "exces_diagonales_max_pire_orientation": 0.6194444444444442,
    "courbe": [
      {
        "epsilon": 0.1,
        "fraction_Z4_superieur_obs": 0.221,
        "Z4_median": 2.473934452223637
      },
      {
        "epsilon": 0.2,
        "fraction_Z4_superieur_obs": 0.234,
        "Z4_median": 2.5639922696599413
      },
      {
        "epsilon": 0.3,
        "fraction_Z4_superieur_obs": 0.317,
        "Z4_median": 2.6910532410993144
      },
      {
        "epsilon": 0.4,
        "fraction_Z4_superieur_obs": 0.421,
        "Z4_median": 2.8715714760226714
      },
      {
        "epsilon": 0.5,
        "fraction_Z4_superieur_obs": 0.522,
        "Z4_median": 3.050156875092896
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      {
        "epsilon": 0.6,
        "fraction_Z4_superieur_obs": 0.672,
        "Z4_median": 3.333094375639174
      },
      {
        "epsilon": 0.8,
        "fraction_Z4_superieur_obs": 0.86,
        "Z4_median": 3.9476160108684386
      },
      {
        "epsilon": 1.0,
        "fraction_Z4_superieur_obs": 0.976,
        "Z4_median": 4.76280104563053
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      {
        "epsilon": 1.25,
        "fraction_Z4_superieur_obs": 0.999,
        "Z4_median": 5.77684375634013
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      {
        "epsilon": 1.5,
        "fraction_Z4_superieur_obs": 1.0,
        "Z4_median": 6.819669592810687
      },
      {
        "epsilon": -0.1,
        "fraction_Z4_superieur_obs": 0.206,
        "Z4_median": 2.444479675310263
      },
      {
        "epsilon": -0.2,
        "fraction_Z4_superieur_obs": 0.254,
        "Z4_median": 2.5534079804547622
      },
      {
        "epsilon": -0.3,
        "fraction_Z4_superieur_obs": 0.346,
        "Z4_median": 2.7126229846315617
      },
      {
        "epsilon": -0.4,
        "fraction_Z4_superieur_obs": 0.413,
        "Z4_median": 2.825696799548898
      },
      {
        "epsilon": -0.5,
        "fraction_Z4_superieur_obs": 0.55,
        "Z4_median": 3.0972231035043185
      },
      {
        "epsilon": -0.6,
        "fraction_Z4_superieur_obs": 0.665,
        "Z4_median": 3.346049521382886
      },
      {
        "epsilon": -0.8,
        "fraction_Z4_superieur_obs": 0.895,
        "Z4_median": 3.9923773271356433
      },
      {
        "epsilon": -1.0,
        "fraction_Z4_superieur_obs": 0.99,
        "Z4_median": 4.708378091165866
      }
    ]
  },
  "autotests": {
    "etat": "OK",
    "alpha_l6": -1.3636363636363655,
    "orientation_retrouvee_ecart_deg": 0.4641273446498668,
    "mu_Q_expo": 0.6082096277081716
  }
}