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Rev. Lett."],"accepted":{"date-parts":[[2024,10,30]]},"abstract":"<jats:p>\n                    We present measurements of the atmospheric depth of the shower maximum\n                    <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <a:msub>\n                        <a:mi>X<\/a:mi>\n                        <a:mi>max<\/a:mi>\n                      <\/a:msub>\n                    <\/a:math>\n                    , 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\n                    <c:math xmlns:c=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <c:msub>\n                        <c:mi>X<\/c:mi>\n                        <c:mi>max<\/c:mi>\n                      <\/c:msub>\n                    <\/c:math>\n                    distributions up to energies of 100\u00a0EeV (\n                    <e:math xmlns:e=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <e:msup>\n                        <e:mn>10<\/e:mn>\n                        <e:mn>20<\/e:mn>\n                      <\/e:msup>\n                      <e:mtext>\u2009<\/e:mtext>\n                      <e:mtext>\u2009<\/e:mtext>\n                      <e:mi>eV<\/e:mi>\n                    <\/e:math>\n                    ), 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\n                    <g:math xmlns:g=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <g:msub>\n                        <g:mi>X<\/g:mi>\n                        <g:mi>max<\/g:mi>\n                      <\/g:msub>\n                    <\/g:math>\n                    with the logarithm of energy features three breaks at\n                    <i:math xmlns:i=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <i:mrow>\n                        <i:mn>6.5<\/i:mn>\n                        <i:mo>\u00b1<\/i:mo>\n                        <i:mn>0.6<\/i:mn>\n                        <i:mo stretchy=\"false\">(<\/i:mo>\n                        <i:mrow>\n                          <i:mi>stat<\/i:mi>\n                        <\/i:mrow>\n                        <i:mo stretchy=\"false\">)<\/i:mo>\n                        <i:mo>\u00b1<\/i:mo>\n                        <i:mn>1<\/i:mn>\n                        <i:mo stretchy=\"false\">(<\/i:mo>\n                        <i:mrow>\n                          <i:mi>syst<\/i:mi>\n                        <\/i:mrow>\n                        <i:mo stretchy=\"false\">)<\/i:mo>\n                        <i:mtext>\u2009<\/i:mtext>\n                        <i:mtext>\u2009<\/i:mtext>\n                        <i:mi>EeV<\/i:mi>\n                      <\/i:mrow>\n                    <\/i:math>\n                    ,\n                    <o:math xmlns:o=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <o:mn>11<\/o:mn>\n                      <o:mo>\u00b1<\/o:mo>\n                      <o:mn>2<\/o:mn>\n                      <o:mo stretchy=\"false\">(<\/o:mo>\n                      <o:mrow>\n                        <o:mi>stat<\/o:mi>\n                      <\/o:mrow>\n                      <o:mo stretchy=\"false\">)<\/o:mo>\n                      <o:mo>\u00b1<\/o:mo>\n                      <o:mn>1<\/o:mn>\n                      <o:mo stretchy=\"false\">(<\/o:mo>\n                      <o:mrow>\n                        <o:mi>syst<\/o:mi>\n                      <\/o:mrow>\n                      <o:mo stretchy=\"false\">)<\/o:mo>\n                      <o:mtext>\u2009<\/o:mtext>\n                      <o:mtext>\u2009<\/o:mtext>\n                      <o:mi>EeV<\/o:mi>\n                    <\/o:math>\n                    , and\n                    <u:math xmlns:u=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <u:mn>31<\/u:mn>\n                      <u:mo>\u00b1<\/u:mo>\n                      <u:mn>5<\/u:mn>\n                      <u:mo stretchy=\"false\">(<\/u:mo>\n                      <u:mrow>\n                        <u:mi>stat<\/u:mi>\n                      <\/u:mrow>\n                      <u:mo stretchy=\"false\">)<\/u:mo>\n                      <u:mo>\u00b1<\/u:mo>\n                      <u:mn>3<\/u:mn>\n                      <u:mo stretchy=\"false\">(<\/u:mo>\n                      <u:mrow>\n                        <u:mi>syst<\/u:mi>\n                      <\/u:mrow>\n                      <u:mo stretchy=\"false\">)<\/u:mo>\n                      <u:mtext>\u2009<\/u:mtext>\n                      <u:mtext>\u2009<\/u:mtext>\n                      <u:mi>EeV<\/u:mi>\n                    <\/u:math>\n                    , 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\n                    <ab:math xmlns:ab=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <ab:msub>\n                        <ab:mi>X<\/ab:mi>\n                        <ab:mi>max<\/ab:mi>\n                      <\/ab:msub>\n                    <\/ab:math>\n                    distributions indicates that the mass composition becomes increasingly heavier and purer, thus being incompatible with a large fraction of light nuclei between 50 and 100\u00a0EeV.\n                  <\/jats:p>","DOI":"10.1103\/physrevlett.134.021001","type":"journal-article","created":{"date-parts":[[2025,1,13]],"date-time":"2025-01-13T10:04:41Z","timestamp":1736762681000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":32,"title":["Inference of the Mass Composition of Cosmic Rays with Energies from\n                    <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <mml:msup>\n                        <mml:mn>10<\/mml:mn>\n                        <mml:mn>18.5<\/mml:mn>\n                      <\/mml:msup>\n                    <\/mml:math>\n                    to\n                    <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <mml:mrow>\n                        <mml:msup>\n                          <mml:mrow>\n                            <mml:mn>10<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:mrow>\n                            <mml:mn>20<\/mml:mn>\n                          <\/mml:mrow>\n                        <\/mml:msup>\n                        <mml:mtext>\u2009<\/mml:mtext>\n                        <mml:mtext>\u2009<\/mml:mtext>\n                        <mml:mi>eV<\/mml:mi>\n                      <\/mml:mrow>\n                    <\/mml:math>\n                    Using the Pierre Auger Observatory and Deep Learning"],"prefix":"10.1103","volume":"134","author":[{"given":"A.","family":"Abdul Halim","sequence":"first","affiliation":[{"name":"University of Adelaide"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"P.","family":"Abreu","sequence":"additional","affiliation":[{"name":"Universidade de Lisboa\u2014UL"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M.","family":"Aglietta","sequence":"additional","affiliation":[{"name":"Osservatorio Astrofisico di Torino (INAF)"},{"name":"INFN"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"I.","family":"Allekotte","sequence":"additional","affiliation":[{"name":"Centro At\u00f3mico Bariloche and Instituto Balseiro (CNEA-UNCuyo-CONICET)"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"K.","family":"Almeida Cheminant","sequence":"additional","affiliation":[{"name":"Nationaal Instituut voor Kernfysica en Hoge Energie Fysica 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