{"id":"5c260428-6832-4446-902e-f77ce17e5546","arxiv_id":"2412.03546","paper_version":3,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"low","formal_verification":"none","parameter_count":0,"one_line_summary":"Bayesian and frequentist analyses show the equal-mass approximation for neutrino masses remains adequate for Planck+DESI data, provided the oscillation-motivated lower bounds on the neutrino mass sum are imposed.","lead":"This paper tests whether the tight new limits on the sum of neutrino masses from Planck and DESI data change if the three neutrino masses are modeled with the physically possible normal or inverted hierarchies instead of the usual three-equal-masses approximation. It finds the approximation is still good, but only if the lower mass bounds from neutrino oscillation experiments are imposed, and it explains why.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The robustness claim is only demonstrated on Planck PR3 + DESI BAO; the DESI-baseline ACT/PR4 lensing data are excluded, so the central conclusion is conditional on those data not changing the hierarchy comparison.","rationale":"The reader correctly identifies the excluded lensing datasets as the weakest assumption, and I agree. I considered other potential objections: the frequentist assumption of asymptotic normality for boundary-corrected intervals is acknowledged and secondary; the use of halofit is standard; the comparison in Fig. 5 directly supports the prior-dominated loosening. None of these threaten the central claim. The only step that could invalidate the practical conclusion is the untested inclusion of ACT/PR4 lensing. The paper gives computational reasons only, not physical evidence, for expecting no change. CMB lensing is the channel whose amplitude depends on the free-streaming scale kfs, which differs between hierarchies; tighter lensing data could in principle break the degeneracy between total mass and mass splitting. Because the paper's own profile likelihoods are indistinguishable only within numerical noise, the check is feasible and decisive. I therefore recommend a conditional acceptance rather than outright rejection: the analysis is careful, reproducible, and internally consistent for its stated dataset, but the 'Planck+DESI' claim should be verified against the DESI baseline lensing data before being taken as the final word on robustness.","tokens_in":16902,"tokens_out":6436,"duration_ms":68875,"concrete_test":"Use the public desilike likelihood to run pinc profile-likelihood minimizations for DM, NH, and IH over Mtot in [0,0.2] eV, adding Planck PR4 lensing and ACT DR6 lensing to the Planck PR3 + DESI BAO baseline; construct Feldman-Cousins 95% upper limits both without and with lower bounds 0.06/0.1 eV. If the relative ordering or loosening of NH/IH versus DM changes by more than about 0.01 eV relative to Tables I-II, the excluded data alter the conclusion; otherwise the concern is resolved.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The paper's central conclusion is that the degenerate-mass (DM) approximation remains adequate for physically motivated NH/IH for 'Planck+DESI' data once oscillation lower bounds are imposed. However, in Sec. III the authors explicitly exclude Planck PR4 and ACT lensing from the analysis, stating they 'expect that it will not alter the main conclusions.' These are not peripheral: the DESI 2024 baseline result includes both lensing datasets, and CMB lensing is precisely the observable most sensitive to the neutrino free-streaming scale, which differs among DM, NH, and IH. If the lensing likelihood is added, the Mtot likelihood can become steeper or develop hierarchy-dependent shape changes; the Bayesian loosening caused by the 0.06/0.1 eV lower bounds could then differ from the reported 0.13/0.16 eV values. The paper's own Fig. 4 shows the profile likelihoods agree only at the level of numerical noise for 0<Mtot<0.2 eV, so a small physical difference in the excluded lensing channel could be enough to shift the relative upper limits. The claim is internally consistent for the stated dataset, but the headline 'also for Planck+DESI data' is broader than what is tested, since the DESI baseline includes the excluded lensing data. This is an acknowledged limitation rather than a detected error, but it is the load-bearing unverified step.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper tests whether the common assumption of three degenerate-mass (DM) neutrinos remains a good approximation for the physically motivated normal (NH) and inverted (IH) hierarchies when inferring the sum of neutrino masses from Planck and DESI data. The authors run both Bayesian MCMC analyses and frequentist profile-likelihood analyses for DM, one-massive/two-massless (1M), NH, and IH, using Planck PR3 CMB spectra and lensing plus DESI BAO. They find that, for Planck alone and for Planck+DESI BAO, the tightest Bayesian bounds come from the DM (and, in combination with DESI, 1M) approximation, while NH and IH produce looser bounds because of the lower mass floors M_tot > 0.06 eV and > 0.1 eV imposed by oscillation experiments. The frequentist profile likelihoods show that all hierarchies fit the data similarly well, and the authors demonstrate in Fig. 5 that imposing the NH/IH lower bounds on the DM approximation reproduces the full NH/IH posteriors. The central conclusion is that the DM approximation is adequate for the Planck+DESI BAO dataset, provided the corresponding lower neutrino mass bounds are enforced.","tokens_in":17126,"tokens_out":4167,"duration_ms":45508,"significance":"If the central claim holds, the paper provides a useful validation of the DM approximation used in DESI-era neutrino mass analyses, while also clarifying that the apparent loosening of constraints under NH/IH is driven by the oscillation-motivated lower bounds rather than by differences in the cosmological predictions. The frequentist cross-check with Feldman-Cousins intervals is a valuable addition, as it separates prior effects from model differences. The paper ships publicly available likelihood code and plotting notebooks, which strengthens reproducibility. The main limitation is that the analysis excludes ACT DR6 and Planck PR4 lensing, which are part of the DESI 2024 baseline; the authors state that they expect this not to change the conclusions, but that expectation is not tested here.","major_comments":[{"comment":"The central claim that the DM approximation remains good \"also for Planck+DESI data\" is established only for Planck PR3 CMB spectra and lensing plus DESI BAO, not for the full DESI 2024 baseline, which includes ACT DR6 and Planck PR4 lensing. Since CMB lensing is the observable most sensitive to the different free-streaming scales of DM, NH, and IH, the conclusion requires either an explicit test with those datasets or a restriction of the headline claim to the dataset actually analyzed. The current wording of the abstract and conclusions overstates the scope of the test, despite the acknowledgment in Sec. III.","section":"Section III and Sec. V/Abstract"}],"minor_comments":[{"comment":"The frequentist upper limits for NH and IH without lower bounds (0.07 eV and 0.06 eV) lie below the oscillation lower bounds for those hierarchies; the text notes this, but the table would be clearer if these entries were explicitly flagged as unphysical.","section":"Table II"},{"comment":"The statement that the four profile likelihoods agree \"at the level of the numerical noise in the minimizations\" is not quantified; reporting the minimizer tolerance or a small repeated-minimization study would make this claim more concrete.","section":"Sec. IV.B"},{"comment":"The phrase \"more than 2 sigma away from 0.06 eV\" is ambiguous because no sigma-interpretation is defined for the extrapolated parabolic minimum; a short clarification would help.","section":"Sec. IV.B"},{"comment":"The sentence \"we expect that it will not alter the main conclusions\" is a reasonable caveat, but it should be repeated in the abstract or conclusions so that readers do not conflate the tested dataset with the full DESI baseline.","section":"Sec. III"}],"recommendation":"major_revision","confidential_remarks":"The paper is carefully done and the main mechanism (lower bounds dominate over hierarchy modeling) is convincing for the dataset analyzed. The one load-bearing issue is the mismatch between the headline 'Planck+DESI' claim and the fact that ACT/PR4 lensing are excluded. If the authors can either include those lensing data or explicitly restrict the title/abstract/conclusions to Planck PR3 + DESI BAO, the paper would be acceptable. No concerns about circularity or excessive claims beyond that scope."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a careful, honest robustness check. It confirms that the degenerate-mass approximation used in DESI neutrino mass analyses is adequate for Planck+DESI data, as long as you impose the lower bound on Mtot from oscillation experiments. That was suspected from forecasts and older Planck analyses, but this is the first explicit test with the actual 2024 DESI BAO data.\n\nWhat it does well: the question is sharply posed, and the analysis is thorough. They use both Bayesian posteriors and frequentist profile likelihoods, with public code and data. The key comparison, Figure 5, is convincing: imposing the NH or IH lower bound on the degenerate-mass model reproduces the full NH/IH posteriors. The frequentist analysis shows all neutrino models fit the data similarly well, so the looser bounds (0.13 eV for NH, 0.16 eV for IH) are driven by the prior boundary, not by a hierarchy-dependent fit. The paper also correctly warns against the one-massive-neutrino approximation, which is a worse fit.\n\nSoft spots: the main one is the dataset. They use Planck PR3 plus DESI BAO, excluding the ACT and Planck PR4 lensing data that appear in the DESI baseline result. They say they expect that won't change conclusions, and that's plausible — their profile likelihoods are nearly identical across hierarchies in the relevant Mtot range, and the difference is dominated by the lower bound. But it is an expectation, not a demonstration. If CMB lensing sharpens the Mtot likelihood or adds hierarchy-dependent shape, the quantitative comparison could shift. I would not call this a fatal flaw, but it is the load-bearing unverified step. A second, minor caveat: the profile likelihoods are parabolic fits, so near the boundary there is some numerical uncertainty; they acknowledge this.\n\nWho it's for: anyone interpreting DESI-era neutrino mass bounds, especially people who want to know whether the choice of hierarchy matters. The answer — it doesn't, as long as you impose the right lower bound — is useful and should be in the literature. I'd send it to peer review; it deserves a serious referee. I'd cite it in my own work on neutrino mass constraints, with the lensing caveat noted.","headline":"A careful, honest robustness check confirming the degenerate-mass approximation holds for Planck+DESI once the oscillation lower bound is imposed; the main caveat is the excluded ACT/PR4 lensing data.","tokens_in":17695,"tokens_out":2857,"would_cite":true,"duration_ms":27737,"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":"The tight DESI-era upper limits on the sum of neutrino masses do not change when the degenerate-mass assumption is replaced by the normal or inverted hierarchy, once the oscillation-motivated lower bound on the total mass is imposed.","keywords":["neutrino masses","neutrino mass hierarchy","cosmic microwave background","baryon acoustic oscillations","DESI","profile likelihoods","sum of neutrino masses","cosmological constraints"],"falsifier":"Recompute the full NH and IH analyses including Planck PR4 and ACT lensing; if the difference between the NH/IH upper limits and the DM-with-prior limits grows beyond roughly 0.02 eV, or if the relative goodness of fit across hierarchies changes, the robustness claim fails. A second check is a future data combination that pushes the 95% upper limit below 0.06 eV, where the NH floor itself would dominate the posterior and the DM approximation would need revalidation.","tokens_in":16669,"feed_emoji":"🌌","tokens_out":12399,"duration_ms":105686,"temperature":0.7,"pith_summary":"Recent DESI baryon acoustic oscillation data combined with Planck CMB data have produced the tightest cosmological upper limits yet on the sum of neutrino masses. Those analyses usually approximate the three neutrino species as having equal masses (the degenerate-mass, DM, approximation), whereas oscillation experiments allow two physical orderings, normal (NH) and inverted (IH), each with a minimum total mass. This paper asks whether the tight DESI-era limits survive when the physically motivated NH or IH is used instead of the DM shortcut. The Bayesian upper limits do loosen, from $M_\\mathrm{tot} < 0.086\\,\\mathrm{eV}$ under DM to $M_\\mathrm{tot} < 0.13\\,\\mathrm{eV}$ under NH and $M_\\mathrm{tot} < 0.16\\,\\mathrm{eV}$ under IH, but the frequentist analysis shows all hierarchies fit the data equally well. The entire loosening is traced to the lower mass floors imposed by oscillation data rather than to the mass-splitting physics, so the DM approximation remains a good stand-in once those floors are imposed.","feed_headline":"Neutrino mass bound survives a change of hierarchy","feed_subtitle":"Planck+DESI data barely care whether neutrinos are degenerate or ordered, once oscillation floors are imposed.","key_machinery":"The central object is the total neutrino mass $M_\\mathrm{tot} = m_1 + m_2 + m_3$ together with the fixed mass-squared splittings $\\Delta m^2_{21}$ and $\\Delta m^2_{3\\ell}$ from oscillation experiments, which express $M_\\mathrm{tot}$ in terms of the lightest neutrino mass for NH and IH and generate the floors $M_\\mathrm{tot}\\gtrsim 0.06\\,\\mathrm{eV}$ (NH) and $M_\\mathrm{tot}\\gtrsim 0.1\\,\\mathrm{eV}$ (IH). The argument separates prior effects from physical modeling by comparing Bayesian MCMC posteriors with frequentist profile likelihoods, using a boundary-corrected construction of frequentist confidence intervals to handle the physical boundary at $M_\\mathrm{tot}=0$. The control run that carries the argument is the DM approximation run with the NH or IH floor imposed, which matches the full NH/IH posteriors and isolates the lower bound as the cause of the loosened constraints.","core_discovery":"The central claim is that the three-degenerate-masses approximation remains a valid stand-in for the normal and inverted hierarchies for Planck data and for Planck+DESI data, provided the analysis enforces the lower bound on the total neutrino mass implied by oscillation experiments: $M_\\mathrm{tot} \\gtrsim 0.06\\,\\mathrm{eV}$ for NH and $M_\\mathrm{tot} \\gtrsim 0.1\\,\\mathrm{eV}$ for IH. For Planck+DESI, the DM approximation gives a Bayesian 95% upper limit of $M_\\mathrm{tot} < 0.086\\,\\mathrm{eV}$, while the full NH and IH analyses give $M_\\mathrm{tot} < 0.13\\,\\mathrm{eV}$ and $M_\\mathrm{tot} < 0.16\\,\\mathrm{eV}$, respectively; the corresponding frequentist limits are $0.07$, $0.07$, and $0.06\\,\\mathrm{eV}$, and all orderings fit the data comparably well. The decisive control experiment is to impose the NH or IH lower bound on the DM approximation itself, which reproduces the full NH and IH posteriors. The paper concludes that the looser NH and IH bounds are an effect of the oscillation-motivated prior floor, not of the ordering's physical predictions.","pith_inferences":["If future runs include Planck PR4 and ACT lensing, the hierarchy-dependence of the likelihood could in principle change; the robustness result should be re-checked with those datasets before being quoted as final.","A push of the upper limit below 0.06 eV would bring the NH floor itself into play, making the hierarchy choice a shape effect rather than a prior effect and invalidating the DM-with-prior shortcut without a dedicated check.","The same prior-versus-modeling separation demonstrated here, comparing profile likelihoods with physically motivated priors imposed on a simplified model, could be applied to other near-boundary cosmological parameters such as curvature or the dark-energy equation of state.","A direct extension is to run the exact NH/IH treatment on the DESI full-shape likelihood once computational cost drops; agreement with DM-with-prior would close the loophole left by the BAO-only analysis."],"forward_implications":["The quoted Planck+DESI upper limits on the neutrino mass sum can be interpreted with the degenerate-mass approximation without needing a full NH/IH treatment, as long as the corresponding lower bound is placed on the prior.","The one-massive-plus-two-massless approximation fits the data worse than DM, NH, or IH and should be avoided in parameter inference.","The looser NH and IH bounds shift the inferred Hubble constant downward relative to the DM case, worsening the Hubble tension.","Bayesian and frequentist upper limits differ by roughly 10-40% in this near-boundary regime, and the paper expects that gap to shrink as data improve.","Imposing the NH or IH lower bound on the DM approximation reproduces the full NH or IH posterior, so the two approaches become interchangeable in practice."],"supporting_citations":[{"why":"Supplies the DESI BAO dataset that, combined with Planck, produces the tight mass limits under study.","marker":"[1]"},{"why":"Gives the DESI full-shape baseline constraint and Planck-pipeline comparisons that frame the paper's dataset choice.","marker":"[6]"},{"why":"Provides the Planck 2018 CMB power-spectra likelihoods used for the CMB data.","marker":"[7]"},{"why":"Defines the Planck 2018 cosmological-parameter baseline and the Mtot-H0 degeneracy the paper revisits.","marker":"[8]"},{"why":"Supplies the neutrino oscillation fit that fixes the mass splittings and yields the 0.06 eV and 0.1 eV lower floors.","marker":"[11]"},{"why":"Earlier demonstration that the degenerate-mass approximation is adequate for cosmology, which this paper extends to DESI.","marker":"[17]"},{"why":"Shows that mass-ordering effects on cosmological observables are small, justifying the DM shortcut.","marker":"[38]"},{"why":"Describes the profile-likelihood and boundary-corrected frequentist method used to separate prior effects from modeling.","marker":"[62]"}],"fun_headline_variants":["Neutrino mass limit holds for all hierarchies","Oscillation floors rescue degenerate neutrino approximation","Hierarchy choice barely moves DESI neutrino bound","Neutrino mass bound robust if oscillation floor imposed","DESI neutrino bound survives ordering test"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The Planck+DESI conclusion depends on the omission of the Planck PR4 and ACT lensing datasets, which the DESI baseline analysis includes; the paper expects but does not test that these datasets would not change the likelihood shape across the different neutrino mass orderings.","fun_headline_variants_meta":{"raw":{"variants":["Neutrino mass limit holds for all hierarchies","Oscillation floors rescue degenerate neutrino approximation","Hierarchy choice barely moves DESI neutrino bound","Neutrino mass bound robust if oscillation floor imposed","DESI neutrino bound survives ordering test"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000251,"raw_usage":{"total_tokens":1629,"prompt_tokens":1088,"completion_tokens":541,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":704,"completion_tokens_details":{"reasoning_tokens":472}},"tokens_in":704,"tokens_out":541,"duration_ms":5574,"temperature":1.0,"reasoning_tokens":472,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T22:16:04.758253+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the full NH and IH analyses including Planck PR4 and ACT lensing; if the difference between the NH/IH upper limits and the DM-with-prior limits grows beyond roughly 0.02 eV, or if the relative goodness of fit across hierarchies changes, the robustness claim fails. A second check is a future data combination that pushes the 95% upper limit below 0.06 eV, where the NH floor itself would dominate the posterior and the DM approximation would need revalidation.","supporting_citations":[],"review_version":1}