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Quantum gravity theories often modify spacetime symmetries. In particular, Lorentz invariance may be violated when approaching the Planck scale. Although the scales at which interactions occur in extensive air showers induced by ultra-high-energy cosmic rays in the atmosphere are many orders of magnitude below the Planck scale, these violations might still be observable. In this work, the fluctuations in the number of muons in the extensive air showers measured at the Pierre Auger Observatory are exploited, for the first time, to constrain Lorentz invariance violations. The bounds derived in the hadronic sector are the strongest ever obtained, and do not rely on assumptions about the mass composition of ultra-high-energy cosmic rays. The fluctuations in the number of muons constitute a new and powerful observable to further explore Lorentz invariance in a region of the parameter space not accessible to other observables.

We present measurements of the depth of shower maximum, Xmax, for cosmic-ray-induced extensive air showers recorded by the fluorescence detector of the Pierre Auger Observatory over 17 years. The data set covers primary energies from 10^17.7 eV to beyond 10^19.6 eV. With improved event reconstruction and an exposure 2.4 times larger than in our previous analysis, this work confirms and refines our conclusions on the mass composition at ultra-high energies. The energy evolution of the mean Xmax exhibits a pronounced break at around 10^18.4 eV, providing direct, model-independent evidence for a change in the evolution of the mass composition. Independently, the observed decrease of the Xmax fluctuations with energy indicates a transition toward a heavier and less diverse primary mass composition. No statistically significant declination dependence of the Xmax distributions is observed within the exposure of the Observatory, indicating an isotropic mass composition. The mean and standard deviation of the Xmax distributions, interpreted with air-shower simulations, yield the energy dependence of the average and variance of the logarithmic mass of cosmic rays arriving at Earth. Furthermore, energy-dependent fractional abundances of four representative primary-mass groups (p, He, CNO, Fe) are obtained by fitting the observed Xmax distributions in each energy bin with a weighted sum of elemental templates. These results provide strong evidence against a long-standing assumption that ultra-high-energy cosmic rays are predominantly protons: above ~10^18.4 eV, the average cosmic-ray mass increases, accompanied by a steadily decreasing diversity in the elemental composition.

The Auger Engineering Radio Array (AERA) measures radio emission from high-energy extensive air showers. Consisting of 153 autonomous radio-detector stations spread over \\(17\\)\\,km\\(^2\\), it detects radio waves in the frequency range of \\(30\\) to \\(80\\)\\,MHz. Accurate characterization of the detector response is crucial for proper interpretation of the collected data. Previously, this was achieved through laboratory measurements of the analog chain and simulations and measurements of the antenna's directional response. In this paper, we perform an absolute calibration using the continuously monitored sidereal modulation of the diffuse Galactic radio emission. Calibration is done by comparing the average frequency spectra recorded by the stations with predictions from seven different models of the full radio sky, accounting for the system response, which includes the antenna, filters, and amplifiers. The analysis of the calibration constants over a period of seven years shows no relevant and no significant ageing effect in the AERA antennas. This result confirms the long-term stability of the detector stations and demonstrates the possibility for a radio detector to effectively monitor ageing effects of other detectors operating over extended periods.

The energy spectrum of cosmic rays above 2.5 EeV has been measured across the declination range \\(-90^ +44.8^\\) using data from \\( 310,000\\) events accrued at the Pierre Auger Observatory from an exposure of \\((104,900 3,100)\\) km\\(^2\\,\\)sr\\(\\,\\)yr. No significant variations of energy spectra with declination are observed, after allowing or not for non-uniformities across the sky arising from the well-established dipolar anisotropies in the arrival directions of ultra-high energy cosmic rays. Additionally, the instep feature in the spectrum at \\(\\) 10 EeV reported previously is now established at a significance above \\(5\\,\\). The quasi-uniformity of the energy spectrum across declinations disfavors an origin for the instep from a few distinctive sources.

The Pierre Auger Observatory, located in La Pampa Amarilla, Argentina, has been continuously acquiring data since 2004. It comprises a surface detector array covering 3,000 km\\(^2\\) and 27 fluorescence telescopes, designed to detect extensive air showers initiated by ultra-high-energy cosmic rays. An upgrade to the Observatory was commissioned in 2024, enhancing the existing water-Cherenkov detectors with additional radio antennas, surface scintillator detectors, and a buried scintillator array. This compilation of contributions to the 39th International Cosmic Ray Conference, held in Geneva, Switzerland (July 15-24, 2025), presents recent results from the Pierre Auger Collaboration, addressing a wide range of fundamental questions in astroparticle physics. The included papers cover measurements of the energy spectrum, mass composition, and arrival directions of ultra-high-energy cosmic rays, investigations of hadronic interactions in extensive air showers, and searches for ultra-high-energy photons and neutrinos. Additional topics include radio detection techniques, solar-related phenomena, and atmospheric events such as ELVES and TGFs. The list also contains first results and performance evaluations of the upgraded detectors, AugerPrime, along with reports on outreach and social engagement initiatives conducted by the Collaboration.

Ultra-high-energy cosmic rays are known to be mainly of extragalactic origin, and their propagation is limited by energy losses, so their arrival directions are expected to correlate with the large-scale structure of the local Universe. In this work, we investigate the possible presence of intermediate-scale excesses in the flux of the most energetic cosmic rays from the direction of the supergalactic plane region using events with energies above 20 EeV recorded with the surface detector array of the Pierre Auger Observatory up to 31 December 2022, with a total exposure of 135,000 km^2 sr yr. The strongest indication for an excess that we find, with a post-trial significance of 3.1, is in the Centaurus region, as in our previous reports, and it extends down to lower energies than previously studied. We do not find any strong hints of excesses from any other region of the supergalactic plane at the same angular scale. In particular, our results do not confirm the reports by the Telescope Array collaboration of excesses from two regions in the Northern Hemisphere at the edge of the field of view of the Pierre Auger Observatory. With a comparable integrated exposure over these regions, our results there are in good agreement with the expectations from an isotropic distribution.

We report an investigation of the mass composition of cosmic rays with energies from 3 to 100 EeV (1 EeV=\\(10^18\\) eV) using the distributions of the depth of shower maximum \\(X_max\\). The analysis relies on \\(50,000\\) events recorded by the Surface Detector of the Pierre Auger Observatory and a deep-learning-based reconstruction algorithm. Above energies of 5 EeV, the data set offers a 10-fold increase in statistics with respect to fluorescence measurements at the Observatory. After cross-calibration using the Fluorescence Detector, this enables the first measurement of the evolution of the mean and the standard deviation of the \\(X_max\\) distributions up to 100 EeV. Our findings are threefold: (1.) The evolution of the mean logarithmic mass towards a heavier composition with increasing energy can be confirmed and is extended to 100 EeV. (2.) The evolution of the fluctuations of \\(X_max\\) towards a heavier and purer composition with increasing energy can be confirmed with high statistics. We report a rather heavy composition and small fluctuations in \\(X_max\\) at the highest energies. (3.) We find indications for a characteristic structure beyond a constant change in the mean logarithmic mass, featuring three breaks that are observed in proximity to the ankle, instep, and suppression features in the energy spectrum.

We present measurements of the atmospheric depth of the shower maximum \\(X_max\\), inferred for the first time on an event-by-event level using the Surface Detector of the Pierre Auger Observatory. Using deep learning, we were able to extend measurements of the \\(X_max\\) distributions up to energies of 100 EeV (\\(10^20\\) eV), not yet revealed by current measurements, providing new insights into the mass composition of cosmic rays at extreme energies. Gaining a 10-fold increase in statistics compared to the Fluorescence Detector data, we find evidence that the rate of change of the average \\(X_max\\) with the logarithm of energy features three breaks at \\(6.50.6~(stat)1~(sys)\\) EeV, \\(11 2~(stat)1~(sys)\\) EeV, and \\(315~(stat)3~(sys)\\) EeV, in the vicinity to the three prominent features (ankle, instep, suppression) of the cosmic-ray flux. The energy evolution of the mean and standard deviation of the measured \\(X_max\\) distributions indicates that the mass composition becomes increasingly heavier and purer, thus being incompatible with a large fraction of light nuclei between 50 EeV and 100 EeV.

The Pierre Auger Collaboration has embraced the concept of open access to their research data since its foundation, with the aim of giving access to the widest possible community. A gradual process of release began as early as 2007 when 1% of the cosmic-ray data was made public, along with 100% of the space-weather information. In February 2021, a portal was released containing 10% of cosmic-ray data collected from 2004 to 2018, during Phase I of the Observatory. The Portal included detailed documentation about the detection and reconstruction procedures, analysis codes that can be easily used and modified and, additionally, visualization tools. Since then the Portal has been updated and extended. In 2023, a catalog of the 100 highest-energy cosmic-ray events examined in depth has been included. A specific section dedicated to educational use has been developed with the expectation that these data will be explored by a wide and diverse community including professional and citizen-scientists, and used for educational and outreach initiatives. This paper describes the context, the spirit and the technical implementation of the release of data by the largest cosmic-ray detector ever built, and anticipates its future developments.

Results are presented for the measurement of large-scale anisotropies in the arrival directions of ultra-high-energy cosmic rays detected at the Pierre Auger Observatory during 19 years of operation, prior to AugerPrime, the upgrade of the Observatory. The 3D dipole amplitude and direction are reconstructed above \\(4\\,\\)EeV in four energy bins. Besides the established dipolar anisotropy in right ascension above \\(8\\,\\)EeV, the Fourier amplitude of the \\(8\\) to \\(16\\,\\)EeV energy bin is now also above the \\(5\\) discovery level. No time variation of the dipole moment above \\(8\\,\\)EeV is found, setting an upper limit to the rate of change of such variations of \\(0.3\\%\\) per year at the \\(95\\%\\) confidence level. Additionally, the results for the angular power spectrum are shown, demonstrating no other statistically significant multipoles. The results for the equatorial dipole component down to \\(0.03\\,\\)EeV are presented, using for the first time a data set obtained with a trigger that has been optimized for lower energies. Finally, model predictions are discussed and compared with observations, based on two source emission scenarios obtained in the combined fit of spectrum and composition above \\(0.6\\,\\)EeV.