{"id":"fa849e88-f5d5-416f-8fda-2de9853184bc","arxiv_id":"2505.19721","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Including realistic SK backgrounds, the time of the last observed supernova neutrino can help distinguish neutron star equations of state.","lead":"This paper simulates a nearby supernova as seen by Super-Kamiokande, now including realistic detector noise, and uses the time of the last detected neutrino to tell different neutron star models apart. A short or long last-neutrino time points to different nuclear equations of state, which could be tested the next time a galactic star explodes.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Background rejection for Tlast is claimed at 5σ, but the sliding-window search has no trials correction; with the quoted post-cut rate a lone background event is selected as Tlast in a few percent of realizations, and the 'negligible background impact' assertion in Section 4.2 is unquantified.","rationale":"The paper's central claim is plausible: the Shen and Togashi Tlast distributions are separated by roughly 40 s, much larger than simple background-rate perturbations would produce, and the simulation pipeline (SKSNSim plus Mori et al. backgrounds) is a reasonable first treatment of realistic SK conditions. I therefore do not reject the central claim. However, the statistical support for background rejection is less secure than the text suggests. The reader identified the adopted background rate as the weakest assumption; I agree the background treatment is the right place to look, but the sharper problem is internal to the method. The 5σ criterion in Table 1 appears to be applied to a fixed interval, while the analysis actually searches a sliding window over the entire burst and takes the last event found. This is a classic trials-factor problem. Using the paper's own numbers, the expected number of surviving background events above 8 MeV over 200 s is about 0.03, so a false Tlast from background will occur in a few percent of realizations. That is not enough to erase the Shen-Togashi separation, but it is enough to invalidate the unquantified claim that background impact is negligible, especially for the long-Tlast models where late-time discrimination matters most. The requested check, background-only runs and signal-with/without-background comparisons, would settle the magnitude. Since the reader's verdict is already CONDITIONAL and this concern strengthens rather than reverses the need for conditionality, the verdict should remain unchanged, with the added requirement that the background false-positive rate be quantified before the discrimination claim is accepted.","tokens_in":19136,"tokens_out":14070,"duration_ms":166107,"concrete_test":"Generate 10^4 background-only mock samples from the quoted Mori et al. (2022) spectrum after FV and spallation cuts, apply the Section 3.3 Tlast algorithm with Twid = 5 s and Eth = 8 MeV over a 200 s window, and record the fraction of realizations in which any Tlast is selected and its time distribution. Separately, compare signal+background and signal-only Tlast distributions for the 32 models under identical Twid/Eth. If background-only samples yield a Tlast in more than about 1% of realizations, or if removing backgrounds shifts the mean of any model's Tlast by more than its quoted 1σ error, the 'negligible background impact' statement in Section 4.2 is falsified, and the discrimination probabilities in Figures 13 and 14 require a trials-corrected background treatment.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing weak point is the background-rejection argument that makes Tlast a clean, model-discriminating observable. In Section 3.3, the (Twid, Eth) pairs in Table 1 are chosen so that one event in a window is more than 5σ significant against background, and Section 4.2 states that the background impact in Figures 13 and 14 is negligible. But the background rate quoted after FV and spallation cuts is 8.2e-3 s^-1 above 5 MeV; with Eth = 8 MeV, the paper says about 98% of background events are rejected, leaving roughly 1.6e-4 s^-1. For Twid = 5 s the expected background count per window is about 8e-4, so a single event is not a 5σ fluctuation in the proper Poisson sense (p about 8e-4, roughly 3σ). More importantly, the algorithm slides this window over the entire post-burst period and defines Tlast as the last event found. Over a 200 s search the expected number of background events is about 0.03, so in about 3% of realizations a lone background event occurring after the true signal tail will be recorded as Tlast. This is not a 5σ-controlled contamination, and it biases Tlast late, preferentially in the long-Tlast models such as Togashi that are central to the discrimination claim. The manuscript never quantifies this false-positive rate; the assertion in Section 4.2 that background contamination is negligible is therefore unsupported and should be demonstrated, not assumed.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper develops a practical analysis framework for identifying the last supernova-neutrino event, Tlast, in Super-Kamiokande, with realistic backgrounds. Signal events are generated with SKSNSim for proto-neutron-star cooling models using four nuclear equations of state (Shen, LS220, Togashi, and Furusawa-Togashi) and several baryon masses, while background events are sampled from the in-situ SK measurement of Mori et al. (2022). After applying fiducial-volume and spallation cuts, the authors choose a time window Twid = 5 s and energy threshold Eth = 8 MeV, claim that these provide 5-sigma background rejection, and define Tlast as the last event found by a forward-sliding window. Tlast distributions from 1000 realizations are compared across models, and a backward-time analysis using the cumulative event count from Tlast and the time difference T500 - T1000 is used in a Bayesian model-selection calculation. The paper concludes that Tlast can differentiate core-collapse supernova models with different PNS masses and equations of state, and in particular that the Shen and Togashi EOSs can be effectively distinguished.","tokens_in":19503,"tokens_out":8603,"duration_ms":89505,"significance":"If the background-rejection step is quantitatively sound, this paper delivers a practical, ready-to-use recipe for the next galactic supernova and demonstrates that timing information alone carries EOS-discriminating power beyond the total event count. The strengths are the clearly specified Monte Carlo pipeline, the use of actual SK background rates from Mori et al. (2022), the large number of realizations, and the public release of the simulation code and neutrino light-curve data. The central new claim, however, rests on the unsupported assertion that background contamination is negligible, so the practical applicability claimed in the title and conclusion is not yet established.","major_comments":[{"comment":"The 5-sigma background-rejection claim is not demonstrated by a transparent calculation. Section 3.2 gives the post-cut background rate as 8.2e-3 s^-1 above 5 MeV, and Section 3.3 states that Eth = 8 MeV rejects about 98% of background, yielding roughly 1.6e-4 s^-1 above 8 MeV. For the chosen Twid = 5 s, the expected number of background events per window is then about 8e-4, so the probability of observing at least one background event is about 8e-4, which is a roughly 3-sigma one-sided fluctuation rather than 5 sigma. The caption of Table 1 says all listed (Twid, Eth) pairs exclude background at greater than 5 sigma, but the Poisson calculation is not shown. Please provide the exact test, including whether it is one- or two-sided, which background rate is used, and how the Eth-dependent spectrum is integrated, and correct the criterion if the calculation does not reach 5 sigma.","section":"Section 3.3, Table 1"},{"comment":"The assertion that the background impact in Figures 13 and 14 is negligible is unsupported because the promised comparison with background-free mock samples is not shown. The sliding-window algorithm searches the entire post-burst interval, so a lone background event after the true signal tail can define Tlast. With a background rate of approximately 1.6e-4 s^-1 above 8 MeV over a 200 s search, the expected number of such events is about 0.03, meaning a few percent of realizations will have a background event selected as Tlast. This biases Tlast late and preferentially affects the long-Tlast Togashi models that are central to the paper's discrimination claim. Please quantify the false-positive rate directly, report the with- and without-background Tlast distributions (for example by overlaying them), and revise the claim accordingly.","section":"Section 4.2, Figures 13 and 14"},{"comment":"The background rate and spectral shape are treated as fixed inputs with no uncertainty, yet they determine both the 5-sigma thresholds of Table 1 and all Tlast distributions. Since the background rate of 8.2e-3 s^-1 above 5 MeV is an empirical estimate, the robustness of the chosen Twid and Eth and of the final model-separation probabilities to plausible variations in this rate (for example a factor of two, or a different spectral index above 8 MeV) should be shown. Without such a sensitivity study, the claim that the analysis is realistic is not fully supported.","section":"Section 3.2 and Section 3.3, Figure 3"}],"minor_comments":[{"comment":"In the conclusion, the symbol TSlast appears to be a typo for Tlast; please correct it.","section":"Section 5"},{"comment":"The model labels in these figures are rendered as unreadable glyph sequences; please replace them with legible labels or a separate legend.","section":"Figures 13 and 14"},{"comment":"The statement that Tlast is inconsistent with the measured background at more than 5 sigma significance should specify whether the significance is one-sided or two-sided and how the sliding-window search over time is treated.","section":"Section 3.3"},{"comment":"The Bayesian probabilities are computed with PDFs obtained from the same simulation pipeline that generated the mock data; a sentence stating that the quoted percentages are an in-sample, idealized upper bound on discrimination would prevent over-interpretation.","section":"Section 4.2, Equation (4)"},{"comment":"The first paragraph contains a stray phrase, 'and makes their observation', after a citation; please fix the grammar.","section":"Section 1"}],"recommendation":"major_revision","confidential_remarks":"The paper is part of a series and extensively cites prior work by the same group, which is appropriate; the new contribution beyond Paper II and Suwa et al. (2025) could be articulated more crisply. The main technical issue is not novelty but the missing quantitative support for the 5-sigma background-rejection claim and the unquantified false-positive rate of the Tlast search. These are fixable within the scope of the manuscript, so I recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First, the useful part: this is Paper VI in a program that keeps improving. The genuinely new elements are the incorporation of measured SK background rates (Mori et al. 2022) into the SKSNSim pipeline, the 5σ event-selection criterion, the addition of Furusawa-Togashi EOS cooling models, and the Bayesian model-discrimination maps under realistic backgrounds. The MC pipeline is specified clearly, with 1000 realizations per model and quoted error bars, and the code and PNS cooling data are public. For the subfield, this is a practical step toward using late-phase timing on a real SK burst.\n\nNow the soft spots. The 5σ claim is the load-bearing one and it does not hold up as stated. Section 3.3 says the (Twid, Eth) pairs in Table 1 are chosen so that a single event is inconsistent with background at more than 5σ, but the Poisson calculation is never shown. With the quoted post-FV, post-spallation rate of 8.2e-3 s^-1 above 5 MeV, and about 98% rejection at Eth=8 MeV, the surviving rate is roughly 1.6e-4 s^-1. In a 5 s window the expected background count is about 8e-4, so the probability of seeing one event is about 8e-4, which is closer to 3σ than 5σ. And the method slides that window over the entire post-burst period; over 200 s the expected background contamination is about 0.03 events, so in a few percent of realizations a lone background event after the true signal tail will be tagged as Tlast. That biases Tlast late, preferentially for the long-Tlast models like Togashi that the discrimination argument leans on. The statement in Section 4.2 that background impact is \"negligible\" is not backed by the shown mock comparison—no quantitative false-positive rate is given.\n\nThe central argument is not dead, but the 5σ language needs correction and the false-positive rate should be explicitly quantified. The Bayesian discrimination maps should be recomputed or at least accompanied by a contamination rate. The in-sample nature of the sensitivity study (same models generate mock data and define the posterior) is a limitation, but they do not fit parameters, so it is not circular—just optimistic about model truncation. The background rate from Mori et al. (2022) is treated as a known constant; if the real rate during a burst differs, the thresholds shift.\n\nThis paper is for people actively planning SK supernova analysis and for EOS modelers who want a quick estimate of what timing information can distinguish. It deserves a serious referee: a journal should send it out, with the expectation of a revision that fixes the statistics.","headline":"Useful incremental step adding realistic SK backgrounds to the Tlast method, but the 5σ background-rejection claim does not survive a trials-corrected Poisson check.","tokens_in":20091,"tokens_out":3195,"would_cite":true,"duration_ms":28965,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Simulations of core-collapse supernova neutrinos in Super-Kamiokande, with realistic experimental backgrounds included, show that the time of the last detected event can differentiate between competing nuclear equations of state and…","keywords":["Core-collapse supernovae","Supernova neutrinos","Neutrino astronomy","Neutron stars","Super-Kamiokande","Proto-neutron star cooling","Nuclear equation of state","Backward-time analysis"],"falsifier":"Use SK's archived quiescent data to measure the background rate above 8 MeV in the fiducial volume after the spallation cut; if it differs from the rate derived from Mori et al. (2022), the $5\\sigma$ selection thresholds and all $T_{\\rm last}$ distributions shift. A quicker check is to rerun the mock pipeline with the background rate doubled and see whether the Shen-versus-Togashi separation in the $T_{\\rm last}$ distributions survives.","tokens_in":18974,"feed_emoji":"💥","tokens_out":17204,"duration_ms":116349,"temperature":0.7,"pith_summary":"The paper claims that the time of the last neutrino event seen by Super-Kamiokande from a nearby supernova can distinguish between competing nuclear equations of state and proto-neutron-star masses, even when realistic detector backgrounds are included. The authors build mock observations that combine simulated supernova-neutrino signals with measured background rates, apply the detector's fiducial-volume and spallation cuts, and define a last-event time $T_{\\rm last}$ via a sliding time window with an energy threshold. If the claim holds, a single galactic supernova at about 10 kpc would yield a direct probe of the equation of state of dense nuclear matter, going beyond what total event counts alone can tell.","feed_headline":"Final supernova neutrino reveals nuclear equation of state","feed_subtitle":"Even with detector backgrounds, the last event's time separates nuclear equation-of-state models at 10 kpc.","key_machinery":"The central mechanism is the $T_{\\rm last}$ determination procedure: count events above an energy threshold $E_{\\rm th}$ within a sliding time window of width $T_{\\rm wid}$, advance the window forward in time, and define $T_{\\rm last}$ as the time of the latest event in the last non-empty window. The pair $(T_{\\rm wid},E_{\\rm th})=(5\\,\\mathrm{s},8\\,\\mathrm{MeV})$ is chosen so that the selected last event is inconsistent with the measured background at more than $5\\sigma$ significance, assuming a background rate of $8.2\\times10^{-3}\\,\\mathrm{s}^{-1}$ in the fiducial volume after the spallation cut. The backward-time analysis then uses $T_{\\rm last}$ as the time origin for cumulative event counts, and the time difference between the 500th-to-last and 1000th-to-last events serves as a statistically sharper observable.","core_discovery":"The paper's central discovery is that $T_{\\rm last}$, the time of the last observed neutrino event selected with a 5-second sliding window and an 8 MeV energy threshold, carries enough information to differentiate between core-collapse supernova models with different proto-neutron-star masses and different nuclear equations of state. In particular, the Shen equation of state gives the shortest $T_{\\rm last}$ and the Togashi equation of state the longest, with the LS220 and Furusawa-Togashi cases in between; the backward-time cumulative distribution from $T_{\\rm last}$ and the time difference between the 500th-to-last and 1000th-to-last events sharpen the separation. A Bayesian calculation using these timing observables can constrain the equation of state, with shorter $T_{\\rm last}$ indicating a lower central density and larger neutron-star radius, and longer $T_{\\rm last}$ indicating abundant heavy nuclei near the surface.","pith_inferences":["The authors do not draw this conclusion, but the $T_{\\rm last}$ sliding window is a one-number summary of the event-time series; using the full spectrum of inter-event intervals on the same mock data could sharpen EOS discrimination further than the $T_{500}$--$T_{1000}$ gap alone.","A testable extension is to apply the same background-aware framework to pre-supernova neutrinos from the silicon-burning phase, where the shorter emission window makes background treatment even more critical for an early-warning trigger.","Scaling the same simulation to a larger water Cherenkov detector with a bigger fiducial volume should push the distance at which EOS separation works beyond 10 kpc, because the signal scales with detector mass while the background rate per kiloton stays roughly constant."],"forward_implications":["A galactic supernova at 10 kpc could yield a measured $T_{\\rm last}$ that separates the Shen and Togashi equations of state, with shorter $T_{\\rm last}$ implying a less compact neutron star and longer $T_{\\rm last}$ implying heavy nuclei near the surface.","The backward-time cumulative distribution anchored at $T_{\\rm last}$, and especially the time gap between the 500th-to-last and 1000th-to-last events, reduces statistical scatter and helps separate models with similar light curves such as LS220 and Furusawa-Togashi.","Late-phase neutrino emission depends mainly on proto-neutron-star mass and radius, not on the progenitor's zero-age main-sequence mass; changing $M_{\\rm ZAMS}$ from 15 to 40 solar masses leaves the late-phase timing information essentially unchanged.","The same $T_{\\rm last}$-based analysis can be applied to any neutrino detector with event-by-event timing, not only Super-Kamiokande."],"supporting_citations":[{"why":"Supplies the in-situ SK background rates above 5 MeV used to set the energy threshold and time window for $T_{\\rm last}$.","marker":"Mori et al. (2022)"},{"why":"Paper I; introduced the backward-time analysis and the PNS cooling neutrino light curves this work extends.","marker":"Suwa et al. (2019)"},{"why":"Paper II; established the equation-of-state dependence of late-phase light curves and provides the model set used here.","marker":"Nakazato et al. (2022)"},{"why":"Provides the SKSNSim event generator that creates the supernova signal mock samples.","marker":"Nakanishi et al. (2024)"},{"why":"Supplies the inverse-beta-decay cross section used to compute event rates.","marker":"Strumia & Vissani (2003)"},{"why":"Quantifies the spallation cut's ~90% background removal in SK.","marker":"Locke et al. (2024)"},{"why":"Provides the ~20% signal loss from the spallation cut applied in the simulation.","marker":"Abe et al. (2024)"},{"why":"Defines the Furusawa-Togashi equation of state introduced and simulated for the first time in this paper.","marker":"Furusawa et al. (2017)"}],"fun_headline_variants":["Last neutrino event reveals nuclear equation of state","Supernova's final neutrino clocks the equation of state","Neutrino timing separates core-collapse models at 10 kpc","T_last from Super-Kamiokande constrains nuclear models","Last observed neutrino distinguishes equations of state"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the background rate above 5 MeV in the fiducial volume after the spallation cut, $8.2\\times10^{-3}\\,\\mathrm{s}^{-1}$ taken from Mori et al. (2022), is a known constant when choosing the 5 s / 8 MeV selection; if the real background rate or spectrum differs during a supernova burst, the $5\\sigma$ thresholds and all $T_{\\rm last}$ distributions shift.","fun_headline_variants_meta":{"raw":{"variants":["Last neutrino event reveals nuclear equation of state","Supernova's final neutrino clocks the equation of state","Neutrino timing separates core-collapse models at 10 kpc","T_last from Super-Kamiokande constrains nuclear models","Last observed neutrino distinguishes equations of state"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000206,"raw_usage":{"total_tokens":1376,"prompt_tokens":905,"completion_tokens":471,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":521,"completion_tokens_details":{"reasoning_tokens":394}},"tokens_in":521,"tokens_out":471,"duration_ms":4116,"temperature":1.0,"reasoning_tokens":394,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T14:07:37.685715+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Use SK's archived quiescent data to measure the background rate above 8 MeV in the fiducial volume after the spallation cut; if it differs from the rate derived from Mori et al. (2022), the $5\\sigma$ selection thresholds and all $T_{\\rm last}$ distributions shift. A quicker check is to rerun the mock pipeline with the background rate doubled and see whether the Shen-versus-Togashi separation in the $T_{\\rm last}$ distributions survives.","supporting_citations":[{"cited_title":"2019, ApJ, 881, 139, doi: 10.3847/1538-4357/ab2e05","cited_arxiv_id":null,"evidence_quote":"Paper I; introduced the backward-time analysis and the PNS cooling neutrino light curves this work extends."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the Furusawa-Togashi equation of state introduced and simulated for the first time in this paper."}],"review_version":1}