{"id":"77e97f66-1371-4a2d-bb93-f25db9ffe5bb","arxiv_id":"2501.18027","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Experimental baryon and meson mass spectra show Wigner-like (chaotic) level spacing statistics, while most quark model and lattice QCD spectra show Poisson-like (regular) statistics.","lead":"This paper studies the spacing patterns of known particle masses (baryons and mesons) and compares them with theoretical predictions from quark models and lattice QCD. It finds that the experimental mass spectra look chaotic, while most theoretical spectra look regular, suggesting current models miss key features of how quarks interact.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Resolution-driven loss of closely spaced resonances would create Wigner repulsion from a Poisson spectrum, and the paper's missing-levels argument only covers random level loss, not this selection effect.","rationale":"The reader's weakest assumption identifies exactly the load-bearing concern: whether the experimental resonance lists are an unbiased sample. My independent reading of the paper confirms that the missing-resonance argument in Sec. III.A.1 and the conclusions addresses only the Poisson-ward shift from random level loss, and does not treat the resolution-driven loss of closely spaced pairs, which would push the NNSD toward Wigner. The Introduction itself acknowledges that overlapping resonances and background can veil states, making this a concrete physical effect rather than a hypothetical one. The proposed simulation would directly test whether this selection bias can reproduce the reported p-values, and it uses the paper's own method and sample structure. I do not see a different, more basic flaw: the distorted-distribution method is an improvement over naive comparisons, the error-bar smearing check is useful even though it does not address selection bias, and the theoretical-model comparisons are internally consistent. The existing CONDITIONAL verdict is therefore appropriate; it should stand unless the proposed test rules the bias out.","tokens_in":15218,"tokens_out":3669,"duration_ms":54415,"concrete_test":"Generate synthetic spectra with Poisson NNSD using the same sequence lengths as the RPP baryon and meson samples (14 sequences, 53 levels; 23 sequences, 129 levels) and the same mean spacing. Remove every level that lies closer than a resolution threshold d to a neighbor, scanning d from 5 to 20 MeV, then apply exactly the local-unfolding and distorted K-S protocol of Sec. II. If the filtered synthetic sample yields pDW and pDP values comparable to the reported experimental values (roughly pDW=0.8, pDP=0.26 for baryons and pDW=0.38, pDP=0.13 for mesons), then the observed Wigner-like repulsion is an artifact of resolution-driven missing levels. Repeat with GOE parent spectra as a control.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim rests on the experimental RPP sequences being a representative sample of the true hadron spectrum. The authors handle missing states through the known result that randomly dropped levels push the NNSD toward Poisson (Sec. III.A.1, citing [35,38]); but experimental incompleteness is not random deletion. Finite resolution and the 'overlap of baryons' acknowledged in the Introduction preferentially hide nearly degenerate resonances. In a Poisson spectrum, unresolved close pairs are removed, so P(s) tends to zero at small s, mimicking the Wigner repulsion that the paper treats as the principal signature of chaos. The error-bar robustness test only Gaussian-smears the retained masses; it does not simulate the removal of close pairs. Therefore the observed baryon values pDW=0.82 and pDP=0.26, and the meson values pDW=0.38 and pDP=0.13, could in principle be produced by resolution and selection bias even if the complete underlying spectrum is Poisson-like. The claim that mesons are 'safely incompatible' with Poisson is also too strong, since pDP=0.13 sits above the p<0.10 rejection threshold. The central experiment-versus-theory dichotomy thus has an uncontrolled observational confound at its foundation.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper compares the nearest-neighbor spacing distributions (NNSD) of experimental baryon and meson mass spectra from the Review of Particle Physics with those of spectra from constituent quark models and a lattice QCD calculation. Because the spectra are split into very short symmetry sequences, the authors construct 'distorted' Wigner, Poisson, and Berry-Robnik reference distributions that reproduce the finite-sequence distortion induced by local unfolding, and they use Kolmogorov-Smirnov tests and moment comparisons to quantify agreement. For baryons, the experimental NNSD is closer to Wigner (p_DW=0.82, p_DP=0.26) than are the three quark-model sets, whose p_DW values are about 10^-4. For mesons, the experimental NNSD is intermediate, with a Berry-Robnik fit f=0.78 and p_DP=0.13, while most theoretical sets are compatible with Poisson and incompatible with Wigner. The authors conclude that the experimental spectra are chaotic-like, the theoretical spectra are generally Poisson-like, and that missing resonances cannot account for the discrepancy.","tokens_in":15508,"tokens_out":5770,"duration_ms":56935,"significance":"If the central experiment-versus-theory contrast is correct, the result is significant for hadron spectroscopy: it would indicate that standard constituent quark models and the Hadron Spectrum Collaboration lattice calculation do not reproduce the spectral fluctuation properties of the empirical spectrum, and that the real baryon and meson dynamics are closer to chaotic than to integrable. The paper's methodological contribution—building an ensemble of distorted reference distributions to account for short-sequence local-unfolding bias—is useful, clearly explained, and reproducible in outline. The explicit K-S p-values, moment analysis, and Gaussian error-bar robustness studies are valuable strengths. However, the interpretation is currently stronger than the evidence: the quantitative Berry-Robnik fractions are fitted parameters, the meson 'safely incompatible with Poisson' claim is not supported by the reported p-value, and the central contrast is vulnerable to an uncontrolled observational selection effect that the paper does not address.","major_comments":[{"comment":"The missing-resonances argument in Sec. III.A.1 (citing Refs. [35,38]) assumes that missing levels are randomly deleted, which is known to shift the NNSD toward Poisson. However, the dominant experimental incompleteness in the RPP resonance lists is not random deletion: finite resolution and the 'overlap of baryons' mentioned in the Introduction preferentially remove closely spaced resonances, which is exactly the small-s region that distinguishes Wigner from Poisson behavior. The error-bar robustness test in Sec. III.A.1 only adds Gaussian fluctuations to the retained masses; it does not simulate the removal of unresolved close pairs. A Poisson spectrum with a resolution-dependent loss of close pairs can produce apparent level repulsion. A quantitative test—for example, applying a resolution threshold to synthetic Poisson and Wigner spectra with the same sequence lengths—is needed before the RPP data can be used as strong evidence for chaotic dynamics. This is load-bearing because the paper's central experiment-versus-theory dichotomy rests on the experimental NNSD exhibiting Wigner-like repulsion.","section":"Sec. III.A.1 and Sec. III.A.2"},{"comment":"The abstract and conclusions describe the experimental meson spectrum as 'safely incompatible' with Poisson, but the K-S test gives p_DP=0.13, which is above the paper's own rejection threshold of p≲0.10. The Poisson null hypothesis therefore cannot be rejected for the experimental meson NNSD. The data are indeed more consistent with the distorted Wigner/Berry-Robnik references than with the distorted Poisson reference, but the wording should be softened to 'not excluded' or 'marginally incompatible,' and the headline claim should not rest on p_DP=0.13.","section":"Sec. III.B.1 and Table II"},{"comment":"The Berry-Robnik percentages (f=0.78 for mesons and f=0.63 for model V) are obtained by fitting the free parameter f to the same NNSD that is subsequently compared with P_DBR(f,s). The reported p_DBR values and moment agreement are therefore not independent tests of the fit. The manuscript should present a parameter-count-adjusted goodness-of-fit comparison, or a cross-validated statistic, before quoting '78% chaos' and '63% chaos' as quantitative results. The qualitative experiment-versus-theory contrast does not depend on these fits, but the quantitative claims do.","section":"Sec. III.B.1 and Sec. III.B.2, Eq. (5)"}],"minor_comments":[{"comment":"The notation in Eq. (2) is visually ambiguous: the denominators should be written as E_{k-v} and E_{k+v} rather than as 'Ek−v − Ek+v', which is easy to misread as a single subtraction of two energies.","section":"Sec. II, Eq. (2)"},{"comment":"The manuscript states that the analysis uses the 'last updated experimental data' from the Review of Particle Physics, but Ref. [37] is the 2014 edition. If this manuscript is submitted in 2025, the authors should update to the current RPP edition and check whether new or revised resonance assignments change the sequence construction or the reported p-values.","section":"Sec. I and Sec. III.A.1"},{"comment":"For the meson theory sets, the K-S p-values p_DW=0.038 (K1) and p_DW=0.083 (E) are only moderately below the 0.10 threshold. The statement that these sets are 'incompatible with the Wigner correlations' would be more accurate as 'rejected at the 10% level but with marginal significance' for these two cases.","section":"Sec. III.B.2"},{"comment":"The y-axis label 'N(p−value)' is unconventional; using 'Count' or 'Frequency' would be clearer, and the histograms would benefit from reporting the bin width used.","section":"Figs. 4 and 8"}],"recommendation":"major_revision","confidential_remarks":"The paper is a continuation of previous work by the same group, and the methodological improvement over Ref. [34] is incremental but real. The main risk is that the central experiment-versus-theory conclusion is currently not protected against the resolution-driven selection effect described in my major comment. If the authors can supply a quantitative simulation of unresolved close-pair loss, or otherwise demonstrate that the RPP completeness is not biased against small spacings, I would be willing to support publication. The 'safely incompatible with Poisson' wording for mesons should also be corrected regardless."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Bottom line: this is a careful, honest consolidation of results the same group already published, and the methodological core—how to build distorted reference distributions for very short spectral sequences—is genuinely useful. But the strong language about being 'safely incompatible' and the headline chaos percentages goes beyond what the data and fits actually support, and the resolution bias worry is real.\n\nWhat is new and good: the paper applies the short-sequence method from the authors' 2012 meson paper to the baryon spectrum, updates both analyses to the current RPP data, and lays out the distortion problem clearly with concrete examples. The K-S contrast for baryons is stark: pDW = 0.82 for the experimental spectrum versus 10^-4 for all three quark models. That is a real, reproducible difference, and the moments back it up. The error-bar robustness test is sensible, though it only Gaussian-smears the retained masses.\n\nThe soft spots are in proportion. First, 'safely incompatible with Poisson' for the experimental meson spectrum is an overclaim: pDP = 0.13, above the usual 0.10 rejection threshold, and the paper itself concedes it is close. Second, the Berry-Robnik fits for mesons and for model V are descriptive, not independent tests; the f parameter is fitted to the same histogram and then used as the reference, so the 78% and 63% numbers should be read as interpolation parameters, not measured chaos fractions. Third, and most important, the paper does not address the selection effect that preferential loss of closely spaced resonances—due to finite resolution and overlapping broad states—would suppress small spacings and mimic Wigner repulsion. The missing-levels argument only covers random deletion, which pushes toward Poisson; it does not cover resolution-driven deletion of close pairs, which pushes the opposite way. The error-bar test simulates mass uncertainty, not missing close pairs. Without a control—for example, removing close pairs from a Poisson spectrum and checking whether you recover the observed P(s)—the central experiment/theory dichotomy has an uncontrolled observational confound.\n\nWho should read this: people working on hadron spectroscopy, missing resonances, or spectral statistics of short sequences. The method section deserves attention. The strong concluding statements should be treated with caution. I would send it to peer review, mainly because the short-sequence method is worth serious scrutiny and the empirical contrast is important, but I would ask the authors to soften the 'safely' language and to discuss the resolution selection effect as a limitation, or better, to simulate it.","headline":"A careful consolidation of the authors' prior work with a useful short-sequence method, but the strong chaos-versus-integrable claims overreach the statistics and ignore a resolution-driven selection bias.","tokens_in":16021,"tokens_out":3094,"would_cite":true,"duration_ms":38809,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["14.20.-c","14.40.-n","12.39.Ki","12.38.Gc","05.45.Mt"],"model":"deepseek-v4-flash","headline":"Measured light baryon and meson mass spectra show the level-repulsion statistics of chaotic quantum systems, while quark-model and lattice QCD spectra mostly show the uncorrelated statistics of integrable systems.","keywords":["hadron spectroscopy","spectral statistics","random matrix theory","quantum chaos","nearest-neighbor spacing distribution","quark models","lattice QCD","missing resonances"],"falsifier":"Run the full analysis on a synthetic Poisson spectrum that has been passed through a realistic resonance-detection filter that merges or removes pairs of lines closer than the experimental resolution. If the filtered spectrum reproduces the experimental p-values (high p for Wigner, low for Poisson), then the observed level repulsion would be explained by detection bias, and the paper's chaotic interpretation would not be settled.","tokens_in":15001,"feed_emoji":"⚛️","tokens_out":14268,"duration_ms":132846,"temperature":0.7,"pith_summary":"This paper asks whether the measured light baryon and meson masses behave statistically like the energy levels of chaotic quantum systems or integrable ones. Comparing nearest-neighbor spacing distributions, with a new correction for very short symmetry-class sequences, the authors find that the experimental spectra sit close to the random-matrix (GOE/Wigner) prediction—baryons most strongly, mesons at about 78% chaos—while essentially all theoretical spectra from quark models and lattice QCD sit close to the Poisson prediction and are statistically incompatible with chaos. Since missing levels push a spectrum toward Poisson, the fact that the incomplete experimental spectra look more chaotic than the complete theoretical ones argues that 'missing resonances' are not the explanation. If correct, this reframes what a hadron model must reproduce: not just individual masses but the fluctuation statistics of the whole spectrum, and it singles out lattice QCD as currently failing to describe the statistical structure of the meson spectrum.","feed_headline":"Measured hadron spectra are chaotic; model spectra look integrable","feed_subtitle":"Mass-spacing statistics of baryons and mesons match random-matrix theory; quark models and lattice QCD mostly do not.","key_machinery":"The central object is the nearest-neighbor spacing distribution (NNSD), $P(s)$, the probability density of the gap between consecutive unfolded energy levels; $P(s)=e^{-s}$ marks integrable (Poisson) dynamics, and the Wigner/GOE form $P(s)=\\frac{\\pi s}{2}e^{-\\pi s^2/4}$ marks chaotic dynamics with time-reversal invariance. The paper's key machinery is a set of 'distorted' reference distributions: Wigner, Poisson, and one-parameter Berry-Robnik spectra are divided into sequences of exactly the same lengths as the data and subjected to the same local unfolding, with an average over 1000 realizations, so that the finite-sequence cutoff (a spacing in a sequence of $l$ levels cannot exceed $l-1$) is baked into the reference. Data are compared to these distorted references with the Kolmogorov-Smirnov test and with the moments of $P(s)$, and robustness is checked by resampling the experimental masses within their error bars.","core_discovery":"The central discovery claimed is a systematic statistical separation between experiment and theory. Once the experimental baryon spectrum from the Review of Particle Physics (RPP), cut at 2.2 GeV, is split into sequences of fixed spin, isospin, and parity, and the meson spectrum, cut at 2.5 GeV, is split into sequences that also fix C-parity, the local-unfolded nearest-neighbor spacing distributions of the data are Wigner-like (baryons) or Berry-Robnik-like with a 78% chaotic fraction (mesons), while the spacing distributions of the three quark-model baryon spectra and of five of the six meson-model spectra, including the lattice QCD set, are Poisson-like and statistically reject the Wigner hypothesis (for baryons $p_{DW}\\approx 10^{-4}$; for lattice QCD $p_{DW}=0.033$). The paper then argues that the usual missing-resonances explanation cannot rescue the models, because randomly missing levels displace a spectrum toward Poisson, the opposite direction from what the data show. The conclusion is that quark models as presently built may not reproduce the low-lying hadron spectrum, and the current lattice QCD calculation does not describe the statistical properties of the meson spectrum.","pith_inferences":["Take a Poisson spectrum, apply a realistic resolution filter that removes or merges closely spaced pairs, and re-run the full analysis; if the filtered spectrum produces Wigner-like p-values, then the experimental level repulsion could arise from detection bias rather than true chaos.","Comparing the V model with the other quark models term by term could identify which interaction component generates the 63% chaotic fraction, since V is the only theoretical meson spectrum compatible with the experimental statistics.","If the spectra are genuinely GOE, random-matrix theory gives a quantitative missing-resonance inventory: starting from a Wigner spectrum and randomly deleting levels produces a known drift toward Poisson, so the observed p-values could be inverted to estimate how many states are still missing.","For lattice QCD, the paper's claim implies a testable trend: as the simulation pion mass approaches its physical value, the meson nearest-neighbor spacing distribution should move from the Poisson-like shape seen here toward Wigner, and newer ensembles can be checked for this."],"forward_implications":["If the experimental baryon spectrum is genuinely Wigner-like, then the quark-model baryon spectra, which reject the Wigner hypothesis at $p\\approx 10^{-4}$, are not merely inaccurate in detail; they lack the chaotic fluctuation structure of the real spectrum, so their predictions about which missing resonances should exist are not trustworthy in their present form.","Because omissions push a spectrum toward Poisson, the missing-resonances explanation for the theory–experiment discrepancy fails: the experimental data are closer to Wigner than the supposedly complete theoretical spectra are.","For mesons, only the set labeled V reproduces the intermediate dynamics (about 63% chaos) needed to match the experimental 78% chaos; the other five theoretical spectra, including the lattice QCD set, behave as integrable or nearly integrable systems and do not describe the statistical properties of the meson spectrum.","Hadron models should be tested for their spectral fluctuation statistics, not only for their energy eigenvalues, since the fluctuation properties encode whether the underlying interaction is chaotic.","The distorted-reference method makes fluctuation analysis applicable to spectra with sequences of only 3–4 levels, extending quantum-chaos tests to short spectral sets beyond hadron spectroscopy, such as nuclear spectra."],"supporting_citations":[{"why":"Supplies the experimental baryon and meson resonance lists that the whole comparison is built on.","marker":"[37]"},{"why":"Previous baryon spectral analysis whose conclusion is refined here; establishes the model–experiment incompatibility.","marker":"[34]"},{"why":"Previous meson analysis introducing the short-sequence method and the 78% chaos estimate that this paper updates.","marker":"[36]"},{"why":"Supplies the CI quark-model baryon spectrum used as one of the theoretical comparisons.","marker":"[2]"},{"why":"Supplies the L1 and L2 quark-model baryon spectra used as theoretical comparisons.","marker":"[3]"},{"why":"Supplies the GI quark-model meson spectrum used as a theoretical comparison.","marker":"[18]"},{"why":"Supplies the K1 and K2 quark-model meson spectra; their difference pinpoints the role of the confinement interaction.","marker":"[15]"},{"why":"Supplies the lattice QCD meson spectrum whose Poisson-like statistics is a main result.","marker":"[20]"},{"why":"Supplies the V quark-model meson spectrum, the only theoretical set compatible with the experimental statistics.","marker":"[16]"},{"why":"Provides the result that missing levels shift a spectrum toward Poisson, used to argue missing resonances cannot explain the discrepancy.","marker":"[35]"}],"fun_headline_variants":["Hadron data chaotic, quark models integrable","Experiment sees chaos, models see order in hadrons","Real hadrons Wigner-like, models Poisson-like","Quark and lattice models show Poisson, data Wigner","Chaotic hadron data contrasts integrable models"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole comparison assumes that the published experimental resonance lists, after cutting at 2.2/2.5 GeV and discarding short sequences, are an unbiased sample of the true hadron spectrum—specifically, that experimental difficulty in resolving closely spaced resonances does not systematically delete small spacings, since deleting small spacings would itself produce the level repulsion the paper takes as the signature of chaos.","fun_headline_variants_meta":{"raw":{"variants":["Hadron data chaotic, quark models integrable","Experiment sees chaos, models see order in hadrons","Real hadrons Wigner-like, models Poisson-like","Quark and lattice models show Poisson, data Wigner","Chaotic hadron data contrasts integrable models"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000495,"raw_usage":{"total_tokens":2412,"prompt_tokens":915,"completion_tokens":1497,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":531,"completion_tokens_details":{"reasoning_tokens":1422}},"tokens_in":531,"tokens_out":1497,"duration_ms":14633,"temperature":1.0,"reasoning_tokens":1422,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T00:58:16.348686+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the full analysis on a synthetic Poisson spectrum that has been passed through a realistic resonance-detection filter that merges or removes pairs of lines closer than the experimental resolution. If the filtered spectrum reproduces the experimental p-values (high p for Wigner, low for Poisson), then the observed level repulsion would be explained by detection bias, and the paper's chaotic interpretation would not be settled.","supporting_citations":[{"cited_title":"Heusler, S","cited_arxiv_id":null,"evidence_quote":"Supplies the experimental baryon and meson resonance lists that the whole comparison is built on."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Previous baryon spectral analysis whose conclusion is refined here; establishes the model–experiment incompatibility."},{"cited_title":"Bohigas, M.J","cited_arxiv_id":null,"evidence_quote":"Previous meson analysis introducing the short-sequence method and the 78% chaos estimate that this paper updates."},{"cited_title":"In this case we do not expect the effect of distortio n to be so noticeable as for the experimental spectrum, as the dimensions of the sequences are not so small","cited_arxiv_id":null,"evidence_quote":"Supplies the CI quark-model baryon spectrum used as one of the theoretical comparisons."},{"cited_title":"level re- pulsion","cited_arxiv_id":null,"evidence_quote":"Supplies the L1 and L2 quark-model baryon spectra used as theoretical comparisons."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the K1 and K2 quark-model meson spectra; their difference pinpoints the role of the confinement interaction."},{"cited_title":"The failure could be due to the fact that the calculation is made at an unrealistic pion mass","cited_arxiv_id":null,"evidence_quote":"Supplies the lattice QCD meson spectrum whose Poisson-like statistics is a main result."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the V quark-model meson spectrum, the only theoretical set compatible with the experimental statistics."},{"cited_title":"Berry and M","cited_arxiv_id":null,"evidence_quote":"Provides the result that missing levels shift a spectrum toward Poisson, used to argue missing resonances cannot explain the discrepancy."}],"review_version":1}