{"id":"9463058f-db65-4ba8-8f34-e0a3ab3130ee","arxiv_id":"2502.06944","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"A joint fit of IceCube and KM3NeT neutrinos above 5 PeV with Auger cosmic ray data suggests a common origin, and may hint at a new high-energy proton source population.","lead":"Four neutrino events above 5 PeV, three from IceCube and one from KM3NeT, are jointly fitted with ultrahigh-energy cosmic ray data from Auger to test a common origin. Depending on the assumed energy of the KM3NeT event, the fit hints at a new proton source population or a cosmogenic 'GZK' neutrino interpretation.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The quantitative flux and GZK conclusions hinge on an unvalidated ARCA effective-area proxy (20% of IceCube NT) and on testing only 100 PeV / 1 EeV energy hypotheses while ignoring the 220 PeV best fit; both choices directly set the likelihood of the single KM3NeT event, and the preferred model…","rationale":"The reader's weakest-assumption analysis identifies the same load-bearing concern: the unvalidated ARCA effective-area approximation and the binary energy hypotheses (100 PeV / 1 EeV) ignoring the 220 PeV best fit. My reading of the paper confirms this is the most fragile link in the argument. The central quantitative conclusion — a common-origin UHECR model describing the combined data and, in the 1 EeV case, a first GZK neutrino — depends on the expected rate of the single KM3NeT event, which is set by two ad hoc choices. Table 2 shows the high-energy neutrino deviance differences between models are small (a few units), so systematic shifts in effective area or energy can easily flip the preferred interpretation. The paper is otherwise careful and transparent about these choices, and the qualitative statement that a handful of >5 PeV events exist is secure. The reader's CONDITIONAL verdict is appropriate and should not change; the concern reinforces the conditions rather than overturning the result.","tokens_in":15798,"tokens_out":3579,"duration_ms":33781,"concrete_test":"Recompute the KM3NeT expected counts and rerun the joint fit using the official KM3NeT/ARCA effective area for the 21-DU configuration (or, failing that, a detector simulation validated against the published event), with the true energy treated as a nuisance parameter centered at 220 PeV with the published 68% interval rather than fixed at 100 PeV or 1 EeV. Record Dν,hi and the best-fit proton-component parameters. If the preferred scenario changes or the ΔD between UHECR and SPL models falls below about 2, the paper's central flux and GZK claims are not supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's quantitative claims — a flux emerging above 5 PeV, a 30 PeV peak, or a GZK neutrino — all hinge on how the one KM3NeT event is modeled. In Methods Eq. (6), Dν,hi is a saturated Poisson likelihood over binned (energy, zenith, flavor) counts; the expected count for the KM3NeT event is m = flux × livetime × effective area. That effective area is not a KM3NeT/ARCA quantity; it is defined in the main text as 'roughly 20% of the NT effective area,' scaled by livetime to 2% of IceCube NT exposure. No uncertainty or validation is given for this factor. Because there is exactly one observed event in that sample, a factor-of-two error in effective area directly changes the best-fit flux normalization by roughly a factor of two and changes Dν,hi by O(1), comparable to the ΔD differences in Table 2 between UHECR and SPL models (36.4 vs 38.6 for 100 PeV; 40.1 vs 45.3 for 1 EeV). The second hypothesis choice is equally consequential: the paper tests 100 PeV and 1 EeV, but the published best fit is 220+570−110 PeV. The 100 PeV scenario yields a 30 PeV source-neutrino peak; the 1 EeV scenario requires a new pure-proton population and yields a cosmogenic GZK interpretation. These are not two minor variants; they are opposite physical conclusions obtained by fixing one event's energy to extreme values and ignoring the data's own best estimate. The proton component is then added only in the 1 EeV case and fit to the very event it explains, so the 'first GZK neutrino' claim is not an independent prediction but a condition of the analysis setup. The existence of four >5 PeV events is robust, but the quantitative flux and common-origin/GZK conclusions are contingent on detector and energy assumptions that are not tested.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper analyzes the four reported neutrino events above 5 PeV (three IceCube events and one KM3NeT/ARCA candidate) together with the lower-energy IceCube astrophysical flux and the Pierre Auger Observatory's UHECR spectrum and composition data. It uses a phenomenological UHECR source model that accounts for in-source and propagation neutrino production, and it presents joint likelihood fits under two assumed energies for the KM3NeT event: 100 PeV, which yields a source-neutrino peak near 30 PeV, and 1 EeV, which requires an additional pure-proton UHECR population and leads the authors to interpret the KM3NeT event as the first observed GZK neutrino. The paper also presents a model-independent segmented flux that shows an emerging flux above 5 PeV and projects IceCube-Gen2 sensitivity to discriminate between the scenarios.","tokens_in":16259,"tokens_out":5880,"duration_ms":54543,"significance":"If the quantitative results held, this would be a valuable first combined UHECR-neutrino fit and a useful framework for next-generation detectors. The paper has clear strengths: it uses the latest public Auger Xmax distributions rather than only their moments, constructs an explicit saturated-Poisson likelihood for the sparse high-energy neutrino sample, and tests two physically motivated energy scenarios. However, the quantitative conclusions rest on an approximate, unvalidated ARCA effective area and on fixing the single KM3NeT event's energy to two extreme values while ignoring the published best fit. The 1 EeV scenario introduces a new proton component after the fact and fits it to the same event it is used to explain. The paper is therefore best viewed as an exploratory scenario study rather than a measurement of the >5 PeV flux, despite the abstract's stronger wording.","major_comments":[{"comment":"The ARCA21 effective area is approximated as 'roughly 20% of the NT effective area' with no uncertainty, validation, or reference to a KM3NeT effective-area calculation. In Eq. (6), the high-energy likelihood is a saturated Poisson sum over the four events, and the expected count for the KM3NeT event scales linearly with this effective area. A factor-of-two error in the area therefore changes the derived flux normalization by roughly a factor of two and changes Dν,hi by O(1), which is comparable to the model-discrimination differences in Table 2 (Dν,hi of 36.4 vs. 38.6 for 100 PeV and 40.1 vs. 45.3 for 1 EeV). Because this proxy directly sets the weight of the single KM3NeT event, the 'measurement' of the flux above 5 PeV is not robust unless the proxy is validated or its uncertainty is propagated. The paper should either use published ARCA acceptance information or present the flux with an uncertainty that accounts for this approximation, and soften the measurement claim accordingly.","section":"The highest-energy events from IceCube and KM3NeT"},{"comment":"Table 1 tests only Eν = 100 PeV and Eν = 1 EeV for the KM3NeT event, while the cited KM3NeT analysis [13] gives a best-fit energy of 220+570-110 PeV under an E^-2 spectrum assumption. These two hypotheses are not minor variants; they lead to opposite physical conclusions, namely a ~30 PeV source-neutrino peak versus an EeV-scale cosmogenic component. The 220 PeV best fit is never considered, and no energy-resolution smearing or posterior marginalization is applied. Since the single KM3NeT event dominates Dν,hi, the analysis should marginalize over the published energy reconstruction, or at minimum include the 220 PeV hypothesis and show how the conclusions vary continuously with the assumed energy, before claiming that either scenario is favored.","section":"Diffuse joint fit with UHECR and neutrinos"},{"comment":"The additional pure-proton population is introduced only in the 1 EeV scenario and adds three free parameters (Methods: 'This second proton component adds 3 additional free parameters'). It is fit to the same combined dataset that motivated its introduction, including the single 1 EeV event. The statement that the KM3NeT event 'would be interpreted as the first observed GZK neutrino' is therefore not a prediction of the model but a consistency check of a post-hoc component. The text should clearly label this as a scenario test rather than evidence for a GZK origin, and the conclusion should not present the GZK interpretation as a discovery-level implication.","section":"1 EeV case: Implications for the cosmogenic neutrino flux"},{"comment":"The preference for the UHECR model over the single-power-law neutrino model in the high-energy channel is ΔDν,hi = 2.2 for the 100 PeV case and 5.2 for the 1 EeV case, based on only four events above 5 PeV. These differences are well within Poisson fluctuations and are not accompanied by a significance estimate. The abstract's claim that the detections 'underscore the existence of a flux' at these energies and the conclusion's 'hints of an emerging population' are not supported by a quantitative threshold. A p-value or profile-likelihood significance for the excess over a no-flux or single-power-law hypothesis is needed before the result can be called a flux measurement rather than an upper-limit-driven hint.","section":"Table 2 and statistical significance"},{"comment":"The total joint deviances are large: D = 2354.1 with Ndof = 1689 for the 100 PeV UHECR model and D = 1939.4 with Ndof = 1686 for the 1 EeV model. No goodness-of-fit discussion is provided, and the paper does not address whether the excess deviance reflects underestimated systematic uncertainties in the Auger spectrum and Xmax data or a genuine model inadequacy. Given the claim that the model 'is able to describe the combined data', this issue should be addressed explicitly, for instance by showing the contribution of each dataset to the deviance and discussing the role of energy-scale and hadronic-model systematics.","section":"Methods and Table 2"}],"minor_comments":[{"comment":"The section heading contains a typo: 'T able 1' should be 'Table 1'.","section":"The highest-energy events from IceCube and KM3NeT"},{"comment":"The KM3NeT row lists the energy as '100, 1000' PeV while the text uses '100 PeV and 1 EeV'; for consistency, either use PeV throughout or explicitly state that 1 EeV = 1000 PeV.","section":"Table 1"},{"comment":"The legend entries 'IceCube Cascades 2020 (used)' and 'IceCube Cascades 2020 (not used)' are not defined in the figure captions; the text explains that blue points are included and gray upper limits excluded, but the captions should state this explicitly.","section":"Figs. 2 and 3"},{"comment":"For upper limits the text sets yi = σ−i = 0, which makes the first equation (αi − 1)θi = 0; please specify how αi and θi are determined in this degenerate case.","section":"Methods, Eq. (5)"},{"comment":"The paper uses 'E2' in figure axis labels without a superscript; this is a formatting issue, but it would be clearer to render it as E² or E^2 consistently.","section":"General notation"}],"recommendation":"major_revision","confidential_remarks":"The paper is exploratory and the authors are candid about limited statistics in places, but the abstract and conclusion overstate the strength of the evidence. The central load-bearing issues are the unvalidated ARCA effective-area proxy and the arbitrary energy hypotheses for the single KM3NeT event; both are fixable in revision by adding uncertainty propagation, considering the published best-fit energy, and reframing the GZK interpretation as a scenario test. The paper fits the journal's scope well and would be a useful contribution after these revisions, but I would not recommend acceptance in its current form."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"This is the first real attempt to fit the >5 PeV neutrino events from IceCube and KM3NeT together with UHECR spectrum and composition data, and that alone makes it worth reading. The model-independent piecewise flux reconstruction in Fig. 2 does show an emerging flux above 5 PeV, and the authors are appropriately careful not to oversell it—they explicitly say there are not enough statistics to distinguish the SPL from the UHECR-origin model. The use of public data, the full Xmax distributions, and the physically motivated UFA source model are all pluses.\n\nThe soft spots are exactly where the reader's report puts them. The ARCA effective area is approximated as roughly 20% of the IceCube NT effective area, with no uncertainty and no validation. That single factor directly sets the expected rate for the one KM3NeT event, and a factor-of-two error changes the high-energy neutrino deviance by O(1), which is comparable to the model differences in Table 2. The energy hypotheses are also a real problem: the paper tests 100 PeV and 1 EeV, but the published best fit is 220 PeV. The two scenarios lead to opposite physical conclusions—a 30 PeV source-neutrino peak versus a GZK proton component—so the main claims are conditional on a choice that is not actually tested. The proton component in the 1 EeV case is introduced and fit to the very event it is meant to explain, so calling the KM3NeT event the first GZK neutrino is a statement about the model's assumptions, not an independent prediction. The post-hoc exclusion of the Auger DNN sigma(Xmax) data is also a bit convenient, though the authors give a reason.\n\nThat said, the central observation—four neutrino events above 5 PeV across two detectors—is robust, and the paper is honest about its own limitations. The large deviances and high free-parameter count are concerning but not disqualifying for a phenomenological joint fit. This is a serious paper for the multimessenger and UHECR community, and it deserves a proper peer review. I would encourage the referees to require either a validation of the ARCA effective area or a demonstration that the conclusions survive a factor-of-2 variation, and to ask the authors to include the 220 PeV scenario or a full energy-uncertainty treatment. With those revisions, the paper would be a solid contribution.","headline":"Useful joint fit of >5 PeV neutrinos and UHECRs, but the two headline conclusions hinge on an unvalidated ARCA effective-area proxy and on testing only 100 PeV and 1 EeV for the KM3NeT event.","tokens_in":16868,"tokens_out":1673,"would_cite":true,"duration_ms":16820,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Four neutrino events above 5 PeV, fit jointly with Auger cosmic-ray data, point to a common origin in ultrahigh-energy cosmic-ray sources, with the KM3NeT event being either a 30 PeV source component or the first GZK neutrino.","keywords":["astrophysical neutrinos","ultrahigh-energy cosmic rays","cosmogenic neutrinos","GZK effect","multi-messenger astronomy","IceCube","KM3NeT/ARCA","Pierre Auger Observatory"],"falsifier":"A statistically significant measurement of the neutrino flux above 5 PeV by IceCube-Gen2—showing a smooth single power law continuing from lower energies with no recovery near 30 PeV and no excess near 1 EeV—would rule out the paper's common-origin UHECR interpretation as the dominant source of these neutrinos.","tokens_in":15589,"feed_emoji":"🔭","tokens_out":11335,"duration_ms":89023,"temperature":0.7,"pith_summary":"This paper tries to establish that the four neutrino events detected above 5 PeV—three by IceCube and one by KM3NeT/ARCA—are the first indications of a distinct neutrino flux linked to ultrahigh-energy cosmic rays. The authors build a single phenomenological model of cosmic-ray sources and fit it simultaneously to the neutrino data, to the Pierre Auger cosmic-ray spectrum, and to the full distributions of air-shower depths of maximum. The resulting model describes all three datasets, and its predicted neutrino flux shows a spectral recovery: around 30 PeV if the KM3NeT event truly has an energy of 100 PeV, or around 1 EeV if that event is actually at 1 EeV, in which case a second pure-proton source population is required. In the 1 EeV case the KM3NeT event would be the first observed cosmogenic, GZK neutrino, and protons above 10 EeV would reappear in the cosmic-ray flux. The result matters because it shows that a handful of high-energy events can already discriminate between neutrinos produced inside cosmic-ray sources and neutrinos produced during propagation, and it sharpens the prediction for next-generation detectors.","feed_headline":"Four neutrinos above 5 PeV point to a cosmic-ray link","feed_subtitle":"A joint fit of IceCube, KM3NeT and Auger data ties the highest-energy neutrinos to ultrahigh-energy cosmic-ray sources.","key_machinery":"The load-bearing object is the paper's phenomenological UHECR source model: an injected cosmic-ray spectrum with a rigidity-dependent cutoff, a parameterized source environment that reprocesses nuclei and produces neutrinos, and pre-tabulated propagation through the cosmic microwave and extragalactic background light. The neutrino flux is not added by hand; it follows from the same interactions that shape the cosmic-ray spectrum and composition, which is why a joint fit to Auger and the neutrino data is a genuine test of common origin. For the 1 EeV scenario a pure-proton component with a much higher rigidity cutoff is added. The statistical machinery is a joint deviance that sums a saturated Poisson likelihood for the four events above 5 PeV, a multinomial likelihood over the full Xmax distributions from Auger, and a gamma-distribution likelihood for IceCube's measured flux from 30 TeV to 2 PeV.","core_discovery":"The central claim is that the combined IceCube, KM3NeT/ARCA, and Auger datasets can be described by a common-origin model in which ultrahigh-energy cosmic rays generate the neutrinos, so the >5 PeV events are not a separate phenomenon. Under the 100 PeV interpretation of the KM3NeT event, the model's neutrino flux has a recovery peaking around 30 PeV, produced by cosmic-ray interactions with the extragalactic background light. Under the 1 EeV interpretation, the baseline sources cannot make such an energetic neutrino, so the model adds a second population of pure protons with rigidity above 10 EeV; that population produces a proton recovery at Earth above 10 EeV and a cosmogenic neutrino component, making the KM3NeT event the first observed GZK neutrino. The paper thus asserts that, although the statistics are minimal, the existing multimessenger data already favor a UHECR-linked flux above 5 PeV and can differentiate the two production channels.","pith_inferences":["The paper tests only two discrete energies for the KM3NeT event; the reconstructed best fit of 220 PeV lies between them, so the real physical scenario is likely intermediate, and future analyses should treat the energy as a continuous nuisance parameter.","If the 1 EeV scenario is correct, the same pure-proton population that makes GZK neutrinos should also produce a small flux of ultrahigh-energy gamma rays through photopion and Bethe-Heitler interactions, offering an independent multimessenger test the paper does not carry out.","Because the 'emergence' of the >5 PeV flux rests on four events, its shape is not yet measured; single additional events at tens of PeV from IceCube or ARCA in the next few years will be more decisive than re-fitting the current sample."],"forward_implications":["The four events above 5 PeV and the Auger spectrum and composition can be simultaneously described by one source model, so the >5 PeV events do not by themselves require a new class of sources unless the KM3NeT event is at the highest energies.","If the KM3NeT event is at 100 PeV, the model predicts a neutrino spectral recovery peaking around 30 PeV from cosmic-ray interactions with the extragalactic background light, and current data cannot yet distinguish this from a single power law.","If the KM3NeT event is at 1 EeV, the model requires a second pure-proton source population with rigidity above 10 EeV, which yields a proton recovery above 10 EeV and makes the event the first observed GZK neutrino.","IceCube-Gen2, with 15 years of optical and radio data, is predicted to detect enough events above 5 PeV to discriminate between a single power law and the 30 PeV or EeV-scale recovery."],"supporting_citations":[{"why":"Supplies the KM3NeT/ARCA event and its energy estimate of 220+570-110 PeV that defines the two scenarios tested in the fit.","marker":"[13]"},{"why":"Provides the IceCube measured flux from about 30 TeV to 2 PeV, the low-energy anchor for the neutrino likelihood.","marker":"[10]"},{"why":"Provides the Pierre Auger cosmic-ray spectrum data the model is fit to above 10^17 eV.","marker":"[25]"},{"why":"Provides the full Xmax distributions used to constrain mass composition, including the long tails that motivate the proton component.","marker":"[1]"},{"why":"Shows that a single low-rigidity UHECR source population fits Auger data alone, setting the baseline that the 1 EeV scenario must extend.","marker":"[31]"},{"why":"Defines the base source model of cosmic-ray injection and propagation that the paper extends into a joint UHECR-neutrino framework.","marker":"[39]"},{"why":"Extends the base model with source-environment interactions and secondary neutrino production, making the neutrino prediction self-consistent.","marker":"[35]"},{"why":"Supplies the latest IceCube exposure and upper limits above 1 EeV used for the non-observation term in the high-energy likelihood.","marker":"[41]"}],"fun_headline_variants":["Neutrino data tie highest-energy cosmic rays to a common source","Joint fit links PeV neutrinos to ultrahigh-energy cosmic rays","KM3NeT event may be the first GZK neutrino","IceCube, KM3NeT, Auger: one model unites neutrinos and cosmic rays","A common origin for ultrahigh-energy neutrinos and cosmic rays"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the KM3NeT/ARCA event's true energy is either 100 PeV or 1 EeV, with its effective area approximated as twenty percent of IceCube's northern-track sample; if the true energy is near the reconstructed best fit of 220 PeV, or if that effective-area approximation is wrong, the predicted recovery shifts and the case for an additional proton population weakens.","fun_headline_variants_meta":{"raw":{"variants":["Neutrino data tie highest-energy cosmic rays to a common source","Joint fit links PeV neutrinos to ultrahigh-energy cosmic rays","KM3NeT event may be the first GZK neutrino","IceCube, KM3NeT, Auger: one model unites neutrinos and cosmic rays","A common origin for ultrahigh-energy neutrinos and cosmic rays"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001516,"raw_usage":{"total_tokens":6096,"prompt_tokens":990,"completion_tokens":5106,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":606,"completion_tokens_details":{"reasoning_tokens":5010}},"tokens_in":606,"tokens_out":5106,"duration_ms":31359,"temperature":1.0,"reasoning_tokens":5010,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-08T14:16:02.104171+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A statistically significant measurement of the neutrino flux above 5 PeV by IceCube-Gen2—showing a smooth single power law continuing from lower energies with no recovery near 30 PeV and no excess near 1 EeV—would rule out the paper's common-origin UHECR interpretation as the dominant source of these neutrinos.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the KM3NeT/ARCA event and its energy estimate of 220+570-110 PeV that defines the two scenarios tested in the fit."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the IceCube measured flux from about 30 TeV to 2 PeV, the low-energy anchor for the neutrino likelihood."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the Pierre Auger cosmic-ray spectrum data the model is fit to above 10^17 eV."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the full Xmax distributions used to constrain mass composition, including the long tails that motivate the proton component."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Shows that a single low-rigidity UHECR source population fits Auger data alone, setting the baseline that the 1 EeV scenario must extend."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the base source model of cosmic-ray injection and propagation that the paper extends into a joint UHECR-neutrino framework."},{"cited_title":"S., Unger, M","cited_arxiv_id":null,"evidence_quote":"Extends the base model with source-environment interactions and secondary neutrino production, making the neutrino prediction self-consistent."}],"review_version":1}