• [1]

    G. Amelino-Camelia, J. R. Ellis, N. E. Mavromatos, D. V. Nanopoulos, and S. Sarkar, Nature 393, 763 (1998)

  • [2]

    G. Amelino-Camelia, J. R. Ellis, N. E. Mavromatos, and D. V. Nanopoulos, Int. J. Mod. Phys. A 12, 607 (1997)

  • [3]

    J. R. Ellis, N. E. Mavromatos, and A. S. Sakharov, Astropart. Phys. 20, 669 (2004)

  • [4]

    R. Gambini and J. Pullin, Phys. Rev. D 59, 124021 (1999)

  • [5]

    S. M. Carroll, J. A. Harvey, V. A. Kostelecky, C. D. Lane, and T. Okamoto, Phys. Rev. Lett. 87, 141601 (2001)

  • [6]

    J. Ellis, N. E. Mavromatos, and D. V. Nanopoulos, "Microscopic recoil model for light-cone fluctuations in quantum gravity," Phys. Rev. D, vol. 61, p. 027503, Dec 1999.[Online]. Available: https://link.aps.org/doi/10.1103/PhysRevD.61.027503

  • [7]

    D. Colladay and V. A. Kosteleckỳ, Phys. Rev. D 58(11), 116002 (1998)

  • [8]

    G. Amelino-Camelia, Nature 408(6813), 661 (2000)

  • [9]

    S. Liberati and L. Maccione, Ann. Rev. Nucl. Part. Sci. 59, 245 (2009)

  • [10]

    J. Abraham, P. Abreu, M. Aglietta, C. Aguirre, D. Allard, I. Allekotte, J. Allen, P. Allison, J. Alvarez-Muniz, M. Ambrosio, et al., Physical review letters 101(6), 061101 (2008)

  • [11]

    T. Abu-Zayyad, R. Aida, M. Allen, R. Anderson, R. Azuma, E. Barcikowski, J. W. Belz, D. R. Bergman, S. A. Blake, R. Cady, et al., The Astrophysical Journal Letters 768(1), L1 (2013)

  • [12]

    R. Abbasi, Y. Abe, T. Abu-Zayyad, M. Allen, Y. Arai, R. Arimura, E. Barcikowski, J. Belz, D. Bergman, S. Blake, et al., Astroparticle Physics 151, 102864 (2023)

  • [13]

    R. J. Protheroe and H. Meyer, Phys. Lett. B 493, 1 (2000)

  • [14]

    K. Toma, et al., Phys. Rev. Lett. 109, 241104 (2012)

  • [15]

    J. Albert, E. Aliu, H. Anderhub, L. Antonelli, P. Antoranz, M. Backes, C. Baixeras, J. Barrio, H. Bartko, D. Bastieri, et al., Phys. Lett. B 668(4), 253 (2008)

  • [16]

    V. A. Acciari, S. Ansoldi, L. A. Antonelli, A. Arbet Engels, D. Baack, A. Babić, B. Banerjee, U. Barres de Almeida, J. A. Barrio, J. Becerra González, et al., Phys. Rev. Lett 125(2), 021301 (2020)

  • [17]

    M. L. Ahnen, S. Ansoldi, L. Antonelli, C. Arcaro, A. Babić, B. Banerjee, P. Bangale, U. B. De Almeida, J. Barrio, J. B. González, et al., The Astrophysical Journal Supplement Series 232(1), 9 (2017)

  • [18]

    J. Albert, E. Aliu, H. Anderhub, P. Antoranz, A. Armada, C. Baixeras, J. Barrio, H. Bartko, D. Bastieri, J. Becker, et al., The Astrophysical Journal 669(2), 862 (2007)

  • [19]

    T. Zhang, F. -W. Shu, Q. -W. Tang, and D. -H. Du, Eur. Phys. J. C 80(11), 1062 (2020)

  • [20]

    J. D. Scargle, J. P. Norris, and J. Bonnell, The Astrophysical Journal 673(2), 972 (2008)

  • [21]

    LHAASO Collaboration*†, Z. Cao, F. Aharonian, Q. An, Axikegu, L. Bai, Y. Bai, Y. Bao, D. Bastieri, X. Bi, et al., Science 380(6652), 1390 (2023)

  • [22]

    Y. -M. Yang, X. -J. Bi, and P. -F. Yin, Journal of Cosmology and Astroparticle Physics 2024(04), 060 (2024)

  • [23]

    K. H. Knuth, Digital Signal Processing 95, 102581 (2019)

  • [24]

    J. Ellis, N. Mavromatos, and D. Nanopoulos, Physics Letters B 665(5), 412 (2008)

  • [25]

    T. Piran and D. D. Ofengeim, Phys. Rev. D 109(8), L081501 (2024)

  • [26]

    U. Jacob and T. Piran, Journal of Cosmology and Astroparticle Physics 2008(01), 031 (2008)

  • [27]

    N. Aghanim, Y. Akrami, M. Ashdown, J. Aumont, C. Baccigalupi, M. Ballardini, A. J. Banday, R. Barreiro, N. Bartolo, S. Basak, et al., Astronomy & Astrophysics 641, A6 (2020)

  • [28]

    LHAASO collaboration, Science Advances 9(46), 2778 (2023)

  • [29]

    C. E. Shannon, Bell System Technical Journal 27(3), 379 (1948)

  • [30]

    A. Rényi, "On measures of entropy and information," in Proceedings of the fourth Berkeley symposium on mathematical statistics and probability, volume 1: contributions to the theory of statistics, vol. 4. University of California Press, 1961, pp. 547–562.

  • [31]

    C. Tsallis, Journal of statistical physics 52, 479 (1988)

  • [32]

    Z. Cao, F. Aharonian, Axikegu, Y. Bai, Y. Bao, D. Bastieri, X. Bi, Y. Bi, W. Bian, A. Bukevich, et al., Physical Review Letters 133(7), 071501 (2024)

  • [33]

    D. J. Gross and P. F. Mende, Nuclear Physics B 303(3), 407 (1988)

  • [34]

    D. Amati, M. Ciafaloni, and G. Veneziano, Physics Letters B 197(1-2), 81 (1987)

  • [35]

    J.-J. Wei and X.-F. Wu, "Tests of lorentz invariance," in Handbook of X-ray and Gamma-ray Astrophysics. Springer, 2022, pp. 1–30.

  • [36]

    J. Ellis, N. E. Mavromatos, D. V. Nanopoulos, A. S. Sakharov, and E. K. Sarkisyan, Astroparticle Physics 25(6), 402 (2006)

  • [37]

    J. Ellis, R. Konoplich, N. E. Mavromatos, L. Nguyen, A. S. Sakharov, and E. K. Sarkisyan-Grinbaum, Physical Review D 99(8), 083009 (2019)

  • [38]

    H. Song and B. -Q. Ma, The Astrophysical Journal 983(1), 9 (2025)

  • [39]

    V. Vasileiou, A. Jacholkowska, F. Piron, J. Bolmont, C. Couturier, J. Granot, F. W. Stecker, J. Cohen-Tanugi, and F. Longo, Physical Review D—Particles, Fields, Gravitation, and Cosmology 87(12), 122001 (2013)