{"id":"eab11fb9-85c9-4eb6-bee9-d588e2adbe8e","arxiv_id":"2408.13209","paper_version":2,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":1,"one_line_summary":"Bayesian sampling of ~1M EDF parameter sets combined with subspace-projected CDFT shows that statistical uncertainties bring deformed nuclei 150Nd and 150Sm into agreement with data while near-spherical 136Xe and 136Ba remain outside the predicted bands.","lead":"The paper develops a Bayesian framework to quantify statistical uncertainties in covariant density functional theory by sampling roughly one million parameter sets around the PC-PK1 functional and propagating posteriors to nuclear observables via a subspace-projected method. This allows checking whether low-lying states in specific nuclei fall within the model's uncertainty bands when empirical nuclear-matter and B(E2) data are incorporated.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"SP-CDFT subspace from limited training parameterizations may not faithfully represent wave functions for posterior-sampled EDF sets","rationale":"The reader's weakest_assumption exactly identifies the untested approximation that controls error propagation from the Bayesian posterior to the observables. Because the review was abstract-only, the low-confidence UNVERDICTED verdict already reflects this gap; the full-text description does not alter the load-bearing status of the subspace assumption.","tokens_in":1748,"tokens_out":364,"duration_ms":14247,"concrete_test":"Pick 20 parameter sets from the reported posterior; for each, compute the low-lying spectrum and B(E2) values once with full multireference CDFT and once with the SP-CDFT subspace used in the paper; if the rms deviation in excitation energies or B(E2) exceeds 10% for more than 3 of the 20 sets in the deformed nuclei, the reproduction claim is not robust to the approximation.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim (observables of 150Nd/150Sm reproduced within uncertainties, unlike 136Xe/136Ba) rests on propagating posteriors via SP-CDFT, where target wave functions are expanded in a subspace spanned only by low-lying states from a small set of training parameterizations around PC-PK1. The abstract states this subspace is insufficient for near-spherical nuclei without adding quasiparticle excitations, but provides no quantitative bound on the projection error for deformed cases or for parameter sets far from the training points. Because ~1M samples are drawn from the posterior (itself constrained partly by B(E2) data), any systematic bias in the subspace expansion directly affects whether the reported agreement is genuine or an artifact of the reduced basis.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript develops a Bayesian framework for statistical uncertainty quantification in relativistic point-coupling covariant density functional theory (CDFT). Approximately one million parameter sets are sampled around the PC-PK1 functional; posteriors are conditioned on nuclear-matter saturation properties, chiral-force predictions, and measured B(E2) values. These posteriors are propagated to low-lying states of 150Nd, 150Sm, 136Xe, and 136Ba via the newly introduced subspace-projected CDFT (SP-CDFT), in which target wave functions are expanded in a subspace spanned by low-lying states from a limited set of training parameterizations. The central claim is that observables of the deformed nuclei fall inside the resulting uncertainty bands while those of the near-spherical nuclei do not, indicating that the present model space is insufficient for the latter.","tokens_in":1921,"tokens_out":559,"duration_ms":14780,"significance":"If the SP-CDFT subspace projection is shown to be accurate for the sampled parameter sets, the work supplies a concrete, statistically grounded test of where CDFT discrepancies can be absorbed by parameter uncertainties (deformed cases) versus where they indicate missing physics (spherical cases). The combination of large-scale Monte Carlo sampling with a reduced-basis propagation method is a practical advance for uncertainty quantification in energy-density-functional calculations.","major_comments":[{"comment":"The central claim that deformed-nucleus observables are reproduced within uncertainties rests on the assumption that the subspace spanned by low-lying states from the training parameterizations faithfully represents the wave functions of posterior-sampled EDF sets (abstract and final paragraph). No quantitative bound on the projection error is reported for 150Nd or 150Sm, nor is any validation against full calculations for parameter sets distant from the training points provided. This directly affects whether the reported agreement is genuine or an artifact of the reduced basis.","section":"SP-CDFT method description"},{"comment":"The manuscript states that ~1 million samples are drawn from the posterior and propagated via SP-CDFT, yet supplies no convergence diagnostics for the Monte Carlo sampling nor any measure of posterior widths or sensitivity to the number of training parameterizations. Without these, the widths of the uncertainty bands used to judge agreement for 150Nd/150Sm versus disagreement for 136Xe/136Ba cannot be assessed.","section":"Results on finite-nucleus propagation"}],"minor_comments":[{"comment":"The number and selection criteria for the training parameterizations used to build the SP-CDFT subspace are not stated explicitly; this information should be added to the methods section for reproducibility.","section":"Methods"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the careful reading of our manuscript and the constructive comments, which have helped identify areas where additional validation and diagnostics will strengthen the presentation. We address each major comment below and will revise the manuscript accordingly.","responses":[{"response":"We agree that a quantitative assessment of the projection error is necessary to substantiate the reliability of SP-CDFT for the sampled parameter sets. In the revised manuscript we will add a dedicated subsection that reports the projection error on excitation energies and B(E2) values for 150Nd and 150Sm, obtained by comparing SP-CDFT results against full CDFT calculations performed for a representative subset of posterior samples lying outside the original training set. This will include explicit error bounds and a discussion of how the subspace dimension affects the accuracy.","revision_made":"yes","referee_comment":"The central claim that deformed-nucleus observables are reproduced within uncertainties rests on the assumption that the subspace spanned by low-lying states from the training parameterizations faithfully represents the wave functions of posterior-sampled EDF sets (abstract and final paragraph). No quantitative bound on the projection error is reported for 150Nd or 150Sm, nor is any validation against full calculations for parameter sets distant from the training points provided. This directly affects whether the reported agreement is genuine or an artifact of the reduced basis."},{"response":"We acknowledge the need for explicit convergence checks and sensitivity measures. The revised version will include standard MCMC diagnostics (trace plots, autocorrelation times, and effective sample size) for the ~1 million posterior samples, together with the reported posterior widths for the EDF parameters and the propagated observables. We will also add a brief sensitivity study showing how the uncertainty bands change when the number of training parameterizations used to construct the SP-CDFT subspace is varied.","revision_made":"yes","referee_comment":"The manuscript states that ~1 million samples are drawn from the posterior and propagated via SP-CDFT, yet supplies no convergence diagnostics for the Monte Carlo sampling nor any measure of posterior widths or sensitivity to the number of training parameterizations. Without these, the widths of the uncertainty bands used to judge agreement for 150Nd/150Sm versus disagreement for 136Xe/136Ba cannot be assessed."}],"tokens_in":1519,"tokens_out":483,"duration_ms":17081,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The paper's core contribution is a concrete pipeline: draw ~1M samples from a nine-parameter point-coupling EDF around PC-PK1, update the posterior with saturation properties plus chiral predictions and measured B(E2) values, then push the samples through a new subspace-projected CDFT to get uncertainty bands on low-lying observables. That combination, especially the projection step for deformed systems, is not in the earlier EDF uncertainty literature they cite. It is a clear incremental step that lets people attach statistical errors to deformed-nucleus predictions without running full calculations for every parameter set. The abstract shows the bands covering the data for 150Nd and 150Sm while missing for 136Xe and 136Ba, which is the kind of concrete comparison that makes the method usable. The circularity burden stays low because the constraints are independent of the final observables. The main soft spot is exactly the one the stress-test flags: the subspace is built from low-lying states of only a small training set, and the paper gives no numerical bound on projection error for parameter sets away from those training points or for the deformed cases where they claim success. Without that, or without a convergence test on the Monte Carlo or posterior widths, it is difficult to know whether the reported agreement is robust or partly an artifact of the reduced basis. The spherical-nucleus failure is presented as expected and fixable by adding quasiparticles, which is fair. This is aimed at nuclear-structure groups already using covariant EDFs who need uncertainty estimates for deformed systems. It is solid enough on the method side and relevant enough on the application side that a serious editor should send it to referees rather than desk-reject, even though the validation of the projection will need tightening.","headline":"This gives a workable Bayesian route to error bars on CDFT for deformed nuclei via million-sample posteriors and subspace projection, but the projection step lacks the checks needed to trust the reported agreement.","tokens_in":2435,"tokens_out":429,"would_cite":false,"duration_ms":12418,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":{"model":"grok-4.3","evidence":[],"headline":"SP-CDFT emulator + Bayesian EDF posterior sampling is standard nuclear DFT UQ; no overlap with RS forcing chain","alignment":"orthogonal","rationale":"The paper's machinery (subspace-projected CDFT via eigenvector continuation on training MR-CDFT states, ~1M quasi-MC samples around PC-PK1, implausibility screening on nuclear-matter observables, posterior propagation to B(E2) and 0νββ NMEs) is a reduced-basis emulator for phenomenological relativistic point-coupling EDFs. It contains no J-cost functional, φ-ladder, 8-tick periodicity, or parameter-free derivation of constants. RS theorems (reality_from_one_distinction, AbsoluteFloorClosure, AlexanderDuality_circle_linking, washburn_uniqueness_aczel, costAlphaLog_high_calibrated_iff, etc.) are never invoked and have no bearing on the nuclear EDF parameter space or the SP-CDFT projection error bounds.","tokens_in":57959,"confidence":"high","tokens_out":210,"duration_ms":5539,"cache_read_input_tokens":38528,"cache_creation_input_tokens":0},"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Statistical uncertainties in covariant density functional theory reproduce low-lying state observables for deformed nuclei but not near-spherical ones.","keywords":["covariant density functional theory","statistical uncertainties","Bayesian inference","nuclear structure","low-lying states","deformed nuclei","subspace projection"],"falsifier":"Performing the same Bayesian propagation with a substantially larger training subspace or with explicit quasiparticle excitations included would show whether the near-spherical nuclei observables remain outside the uncertainty bands.","tokens_in":2645,"feed_emoji":"⚛","tokens_out":654,"duration_ms":13303,"temperature":0.7,"pith_summary":"The paper introduces a Bayesian framework to quantify statistical uncertainties in a relativistic point-coupling energy density functional by sampling roughly one million parameter sets around the PC-PK1 values. Posterior distributions are obtained by conditioning on nuclear matter saturation properties, chiral force predictions, and measured B(E2) values, then propagated to finite nuclei through the subspace-projected CDFT method. This approach expands target wave functions in a subspace built from low-lying states of training parameterizations. The resulting uncertainty bands encompass the data for deformed nuclei 150Nd and 150Sm, while the same bands fail to cover the observables of near-spherical nuclei 136Xe and 136Ba.","feed_headline":"CDFT statistical errors cover deformed nuclei data","feed_subtitle":"Uncertainty bands fit 150Nd and 150Sm observables but leave 136Xe and 136Ba outside the model range","key_machinery":"The subspace-projected (SP)-CDFT approach, which expands the wave functions of target EDF parameter sets in a low-dimensional subspace spanned by low-lying states obtained from a set of training parameterizations.","core_discovery":"Sampling approximately one million parameter sets around PC-PK1 and inferring posteriors from nuclear matter properties and B(E2) data allows propagation via subspace-projected CDFT; the resulting statistical uncertainties bring calculated observables of low-lying states in 150Nd and 150Sm into agreement with experiment, whereas the same framework leaves the observables of 136Xe and 136Ba outside the uncertainty bands.","pith_inferences":["The same sampling and propagation procedure could be applied to additional nuclei to test whether the deformed-versus-spherical distinction persists across the chart.","Adding more experimental constraints such as excitation energies or radii would further narrow the posterior distributions and potentially alter the uncertainty bands."],"forward_implications":["Observables of low-lying states in deformed nuclei 150Nd and 150Sm fall inside the calculated uncertainty bands once statistical errors are included.","Observables of low-lying states in near-spherical nuclei 136Xe and 136Ba remain outside the uncertainty bands.","Extending the model space to quasiparticle excitations is expected to reduce the discrepancy for the near-spherical cases."],"fun_headline_variants":["CDFT uncertainties cover 150Nd and 150Sm but exclude 136Xe and 136Ba","SP-CDFT statistical errors agree with deformed nuclei B(E2) values","Posterior distributions in CDFT fit low-lying states of 150Nd 150Sm","CDFT Bayesian analysis leaves 136Xe and 136Ba outside uncertainty bands"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The limited subspace of low-lying states from the training parameterizations is assumed to be sufficient to represent the wave functions of the target parameter sets for the studied nuclei.","fun_headline_variants_meta":{"raw":{"variants":["CDFT uncertainties cover 150Nd and 150Sm but exclude 136Xe and 136Ba","SP-CDFT statistical errors agree with deformed nuclei B(E2) values","Posterior distributions in CDFT fit low-lying states of 150Nd 150Sm","CDFT Bayesian analysis leaves 136Xe and 136Ba outside uncertainty bands"]},"model":"grok-4.3","cost_usd":0.009051,"raw_usage":{"total_tokens":4066,"prompt_tokens":676,"num_sources_used":0,"completion_tokens":87,"cost_in_usd_ticks":90512000,"prompt_tokens_details":{"text_tokens":676,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":3303,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":676,"tokens_out":87,"duration_ms":17564,"temperature":1.0,"reasoning_tokens":3303,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-05-23T21:27:00.438357+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Performing the same Bayesian propagation with a substantially larger training subspace or with explicit quasiparticle excitations included would show whether the near-spherical nuclei observables remain outside the uncertainty bands.","supporting_citations":[],"review_version":1}