Pith. sign in

REVIEW 3 major objections 5 minor 1 cited by

Bayesian inference of strangeon matter using the measurements of PSR J0437-4715 and GW190814

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Under a discrete set of possible quark numbers, the authors' Bayesian analysis finds that current data select the 18-quark strangeon and predict maximum masses near 3.6 solar masses.

desk verdict Useful posterior constraints on the strangeon EOS, but the headline Nq=18 claim does not survive the paper's own evidence table and is driven by a prior boundary. read the letter →

arxiv 2411.14938 v3 pith:BIWDE5NJ submitted 2024-11-22 astro-ph.HE nucl-th

Wen-Li Yuan , Chun Huang , Chen Zhang , Enping Zhou , Renxin Xu This is my paper · ORCID
classification astro-ph.HEnucl-th
keywords strangeonmatterequationofstateBayesianinferenceNICERgravitationalwavesGW190814PSRJ0437-4715maximummass
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper asks whether the dense matter inside compact stars could be a solid lattice of strangeons—clusters of roughly ten to thirty quarks bound by the strong force—and which cluster size observations select. The authors run a Bayesian inference on a Lennard-Jones description of strangeon matter, combining NICER mass-radius measurements of PSR J0030+0451, PSR J0740+6620, and the newly measured PSR J0437-4715 with the gravitational-wave events GW170817 and GW190814. Their central result is that the data favor strangeons made of 18 quarks, a state symmetric in color, flavor, and spin, over the minimum 9-quark alternative. The inferred equation of state is stiff: the maximum mass is about 3.58–3.65 solar masses at 90% confidence, the radius of a 1.4-solar-mass star is about 12.0–12.2 km, and the 2.6-solar-mass secondary of GW190814 is easily accommodated. If right, this would tie compact-star observations directly to the multiquark structure of strongly interacting matter.

What carries the argument

The machinery is a scaled Lennard-Jones equation of state for strangeon matter. Strangeons interact through $U(r)=4\epsilon[(\sigma/r)^{12}-(\sigma/r)^6]$, and the resulting density and pressure lead to the key identity of Eq. (4): after scaling by $\tilde{\epsilon}=\epsilon/N_q$ and $\bar n=N_q n/n_{\rm sur}$, the mass-radius relation depends only on $\tilde{\epsilon}$ and the surface baryon density $n_{\rm sur}$. This degeneracy is why the paper compares discrete $N_q$ values through Bayesian evidence rather than fitting $\epsilon$ and $N_q$ separately. The model comparison runs on Bayes factors $\log K=\log(Z_1/Z_2)$, and the preferred configuration is the quark-$\alpha$ state, 18 quarks arranged symmetrically in color, flavor, and spin.

What would settle it

Rerun the same Bayesian analysis with the prior lower bound on $\epsilon$ lowered from 10 MeV to about 1 MeV (or with a continuous prior on $N_q$); if the Bayes factor against $N_q=9$ stops being enormous, the claimed preference is prior-driven. Observationally, measure the radius of a compact star near 2.6 solar masses: the strangeon EOS predicts roughly 14.3 km, and a measured radius far from that value would falsify the stiff branch.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that a Bayesian comparison of nested finite-$N_q$ strangeon models, using the same likelihoods for each, selects $N_q=18$ with decisive evidence once PSR J0437-4715 is included. Without that pulsar, the Bayes factor for $N_q=18$ over $N_q=9$ is about 99.5; with it, the factor is 89,322. The authors identify $N_q=18$ with the quark-$\alpha$ state, whose $2\times3\times3=18$ internal degrees of freedom are exactly filled by spin, flavor, and color symmetry. With $N_q$ fixed at 18, the posterior predictions are $M_{\max}=3.58^{+0.16}_{-0.12}\,M_\odot$ for the three-parameter EOS and $3.65^{+0.18}_{-0.16}\,M_\odot$ for the two-parameter EOS at 90% confidence, with radii $12.04^{+0.27}_{-0.31}$ km and $12.16^{+0.26}_{-0.31}$ km for a 1.4-solar-mass star. Both parameterizations agree, which the authors take as evidence that the inferred stiffness is a property of strangeon matter rather than of one particular parametrization.

Load-bearing premise

The preference for 18-quark strangeons rests on the assumed lower limit for the potential-well depth and on restricting the quark number to a few discrete values, because the star's mass-radius curve depends on the depth per quark rather than the total depth; with a lower allowed depth, 9-quark strangeons could fit the data and the strong evidence gap would shrink.

Editorial extensions

If this is right

  • If strangeon matter is the true ground state, the dense-matter equation of state is stiff enough to support compact stars up to roughly 3.8 solar masses, comfortably above the 2.6-solar-mass secondary of GW190814.
  • The GW190814 secondary can be a strangeon star without needing a large pairing gap, which distinguishes this model from some color-flavor-locked quark star scenarios.
  • The inferred radius of a 1.4-solar-mass star is about 12.0–12.2 km, consistent with the small radius reported for PSR J0437-4715 and with the GW170817 tidal-deformability constraint.
  • The three-parameter and two-parameter models give consistent posteriors, suggesting the observable predictions are governed mainly by the per-quark potential depth and the surface baryon density rather than by the total quark number.
  • A future radius measurement of a compact star near 2.6 solar masses would provide a sharp test of the predicted stiff branch of the strangeon EOS.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • My inference: the enormous Bayes factor against $N_q=9$ is likely produced by the prior floor $\epsilon\ge10$ MeV. Because the mass-radius relation depends on $\tilde{\epsilon}=\epsilon/N_q$, the 9-quark model is confined to $\tilde{\epsilon}\ge1.11$ MeV while the data favor $\tilde{\epsilon}\approx0.6$ MeV; lowering the floor would let $N_q=9$ reach the favored region and would probably erase the
  • A quick test would be to rerun the same inference with a lower bound on $\epsilon$ near 1 MeV or with a continuous prior on $N_q$; if the evidence gap collapses, the $N_q=18$ conclusion is a prior choice rather than a data-driven feature.
  • If the stiff strangeon EOS is right, the 2.6-solar-mass secondary of GW190814 would be predicted to have a radius near 14.3 km, a quantity that future X-ray or gravitational-wave observations could measure and thereby discriminate between strangeon matter and other stiff quark-matter models.
  • The paper's degeneracy result suggests that future data should be used to constrain $\tilde{\epsilon}$ and $n_{\rm sur}$ jointly; mass-radius measurements at several different masses would break the remaining parameter correlations.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper performs Bayesian inference of the strangeon matter equation of state (EOS), using a Lennard-Jones based three-parameter model (Nq, epsilon, nsur) and a two-parameter model (tilde_epsilon, nsur). The analysis incorporates NICER mass-radius measurements of PSR J0030+0451, PSR J0740+6620, and the recent PSR J0437-4715, together with gravitational-wave constraints from GW170817 and GW190814. The authors report posterior constraints on the EOS parameters, M-R relations, maximum masses around 3.5-3.65 solar masses, and claim that the data support a strangeon with Nq=18, symmetric in color, flavor, and spin spaces. The paper emphasizes that the three-parameter and two-parameter model results are consistent.

Significance. If the Nq=18 claim were robust, this would be an interesting microphysical inference connecting neutron star observations to the internal structure of strangeons. The paper also demonstrates a reusable open-source Bayesian inference framework and includes the recent PSR J0437-4715 measurement in a strangeon EOS analysis. The M-R and maximum-mass constraints are plausible and potentially useful. However, the central Nq preference claim is not supported by the evidence table and is dominated by a prior-boundary effect, as detailed in the major comments. The consistency between the three- and two-parameter models is a built-in consequence of the model reparametrization rather than an independent validation.

major comments (3)
  1. [Section IV.A, Table I] The evidence values in Table I do not support the claim that Nq=18 is preferred over other Nq values. With PSR J0437-4715 included, log Z = -36.0 for Nq=27 and -36.7 for Nq=18, giving a Bayes factor of exp(0.7) ~ 2.0 in favor of Nq=27. The text states that the evidence "reaches a local maximum at Nq=18 compared to Nq=24 and Nq=9 models," but Nq=27 has higher evidence than Nq=18. The subsequent claim that "the preference for Nq=18 is further strengthened" under PSR J0437-4715 is inconsistent with the paper's own table. The abstract's statement that the results "support" Nq=18 is therefore not supported by the reported evidence.
  2. [Section III.A and Eq. (4)] The large Bayes factor against Nq=9 (K=89,322 quoted in Section IV.A) is an artifact of the prior lower bound on epsilon. Equation (4) shows that the M-R relation depends only on tilde_epsilon = epsilon/Nq and nsur. With the uniform prior epsilon in [10,170] MeV and the discrete grid Nq = 9,18,21,24,27, the implied tilde_epsilon ranges are [1.11,18.9] MeV for Nq=9 and [0.56,9.4] MeV for Nq=18. The posterior for both the two-parameter model and the fixed-Nq=18 model concentrates at tilde_epsilon ~ 0.5-0.7 MeV (Table II), a region that Nq=9 cannot access because its tilde_epsilon lower bound is 1.11 MeV. The huge evidence ratio against Nq=9 therefore reflects the prior boundary rather than a data-driven feature. A sensitivity test with a lower epsilon lower bound (or a continuous treatment of Nq) is needed before any claim about Nq preference can be made.
  3. [Section II.A and Section IV.B] The claimed consistency between the three-parameter and two-parameter models is a reparametrization consequence of Eq. (4), not an independent check of the physics. Since the M-R relation and the EOS depend only on tilde_epsilon = epsilon/Nq and nsur, fixing Nq in the three-parameter model and fitting (epsilon, nsur) is equivalent to fitting (tilde_epsilon, nsur) with a rescaled prior. The agreement of the inferred tilde_epsilon values is therefore built into the model definition. The paper should present this agreement as a validation of the numerical sampling, not as a new physical prediction or as independent support for Nq=18.
minor comments (5)
  1. [Section IV.A] In the sentence listing Bayes factors, "17 9872" appears to be a typographical error for "179 872" (or "179872") for the Nq=27 versus Nq=9 comparison.
  2. [Abstract and Section V] The phrase "with a relatively strong Bayesian evidence" for Nq=18 is misleading given Table I, where the only decisive comparison is against Nq=9, and that comparison is prior-dominated as noted above.
  3. [Section III.A] The text says the choice of the tilde_epsilon prior in the two-parameter model is "based on our prior choices for epsilon and Nq separately," but the two-parameter model uses an independent uniform prior U(0.3,3) MeV; this sentence should be clarified to avoid implying a derived prior.
  4. [Section IV.A] The word "consquently" should be "consequently."
  5. [Table II] The row for the three-parameter model lists "[epsilon/Nq (MeV)]" in brackets but the table caption does not define this derived quantity; please define it in the caption.

Circularity Check

2 steps flagged · score 6.0 of 10

The headline Nq=18 claim reduces to the chosen epsilon prior and discrete Nq grid, because Eq. (4) makes the M-R sequence depend only on tilde_epsilon = epsilon/Nq and nsur; the paper's own evidence table even slightly favors Nq=27.

  1. self definitional [Section II.A Eq. (4); Section III.A priors; Section IV.A Bayes-factor discussion]
    "By defining ˜ϵ = ϵ/Nq and ¯n = Nqn/nsur, the simpler form of strangeon matter EOS can be derived as follows [53]: ... In other words, changing the values of ϵ and Nq while keeping the ˜ϵ constant does not impact the M-R relations. ... in this Bayesian analysis we choose ϵ spanning in the range of 10 − 170 MeV. ... we assume the parameter Nq takes values from the set Nq = 9, 18, 21, 24, 27"

    Eq. (4) makes the M-R sequence depend only on tilde_epsilon = epsilon/Nq and nsur, so all Nq choices give identical stellar models at fixed tilde_epsilon; the likelihood is flat in Nq. The evidence differences in Table I therefore come entirely from the priors. With the Section III.A bounds, Nq=9 forces tilde_epsilon >= 1.11 MeV while the posteriors in Table II concentrate at tilde_epsilon ~ 0.5–0.7 MeV; Nq=18 can access that region. Hence K=89,322 against Nq=9 is a prior-boundary effect, not a data-driven feature. Also Table I shows log Z(Nq=27) = -36.0 > log Z(Nq=18) = -36.7 (K=2.01), so Nq=18 is not even the preferred discrete value. The headline Nq=18 preference reduces to the chosen epsilon lower bound and discrete grid.

  2. self definitional [Section IV.B and Section V (Summary)]
    "The free parameters for strangeon matter EOS can be reduced to two by defining ˜ϵ = ϵ/Nq and ¯n = Nqn/nsur. ... the parameters ˜ϵ and nsur fully determine the EOS stiffness and the shape of the M-R curve. ... Despite differences in their theoretical formulations, the results from both models exhibit consistency."

    The claimed consistency between the three-parameter and two-parameter models is built in by Eq. (4): the two-parameter model is exactly the three-parameter model at fixed Nq with (epsilon, Nq) replaced by their ratio. Any Bayesian inference on (epsilon/Nq, nsur) at fixed Nq must reproduce the two-parameter posterior up to the different prior measure on the ratio, so the consistent prediction is a reparametrization identity rather than an independent cross-check.

full rationale

The maximum-mass, radius, and tidal-deformability constraints are genuine posterior predictions and are not circular. However, the central Nq=18 claim is prior-driven: Eq. (4) makes Nq drop out of the stellar structure equations except through the ratio tilde_epsilon = epsilon/Nq, so the data cannot distinguish Nq values at fixed tilde_epsilon. The large Bayes factor against Nq=9 is produced by the epsilon >= 10 MeV lower bound, and the paper's own evidence table gives Nq=27 a slightly higher log Z than Nq=18. The model comparison Nq=18 vs Nq=9 is thus equivalent to comparing the chosen priors, not to inferring a microphysical bound state. The paper's consistency between three- and two-parameter models is also a reparametrization identity. Self-citations such as [53] for Eq. (4) and [84] for the inference package are not load-bearing here because the algebra is explicit and the posterior computations are standard; no independent circularity arises from those citations. Overall score 6: partial circularity, where the headline Nq prediction reduces to the prior construction while the M-R and maximum-mass results retain independent content.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central inference rests on the strangeon LJ-potential EOS (Eqs. 1-4) with constants A12=6.2, A6=8.4, mq=300 MeV, on uniform priors for epsilon and nsur, and on a discrete prior for Nq. The Nq=18 preference is governed by the epsilon prior lower bound and the equivalence of the three- and two-parameter models. The GW190814 constraint assumes the secondary is a compact object.

free parameters (4)
  • epsilon (Lennard-Jones potential depth) = 11.02 to 12.63 MeV (68.3% CI across cases)
    Fitted from NICER/GW data in the three-parameter model; posterior near 11-12 MeV.
  • nsur (surface baryon number density) = 0.18 to 0.23 fm^-3
    Fitted surface baryon density; posterior near 0.18-0.23 fm^-3.
  • eps_tilde (per-quark potential depth) = 0.48 to 0.62 MeV
    Effective parameter in the two-parameter model; posterior near 0.5-0.6 MeV.
  • Nq (number of quarks per strangeon) = 18 (discrete prior set 9,18,21,24,27)
    Discrete model-selection parameter; conclusion depends on the prior range for epsilon.
assumptions (5)
  • domain assumption Strangeon matter EOS is described by the Lennard-Jones potential with A12=6.2, A6=8.4, and quark mass mq=300 MeV (Eqs. 1-4).
    Phenomenological model taken from prior strangeon literature; not derived from QCD.
  • ad hoc to paper Priors: epsilon uniform on [10,170] MeV, nsur uniform on [0.17,0.36] fm^-3, Nq in {9,18,21,24,27}.
    The lower bound on epsilon excludes the best-fit eps_tilde for Nq=9 and is not varied in a sensitivity test.
  • domain assumption GW190814's secondary is a compact star, so its mass of 2.59+0.08-0.09 Msun is a lower bound on the maximum mass.
    If the secondary is a black hole, the Case 4 maximum-mass and radius posteriors do not follow.
  • standard math TOV equations and Bayes theorem with nuisance-marginalized likelihoods apply.
    Standard framework for EOS inference; the paper follows Refs. [64,83].
  • domain assumption Reported NICER credible intervals and GW likelihoods are treated as independent measurements.
    Standard practice in EOS inference; no cross-calibration is discussed.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Bayesian inference of strangeon matter using the measurements of PSR J0437-4715 and GW190814." pith.science (2026). https://pith.science/paper/BIWDE5NJ

@misc{pith2026241114938,
  author       = {Pith},
  title        = {Pith review of: Bayesian inference of strangeon matter using the measurements of PSR J0437-4715 and GW190814},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BIWDE5NJ}},
  note         = {Machine review of arXiv:2411.14938}
}
abstract

The observations of compact star inspirals from LIGO/Virgo combined with mass and radius measurements from NICER provide a valuable tool to study the highly uncertain equation of state (EOS) of dense matter at the densities characteristic of compact stars. In this work, we constrain the solid states of strange-cluster matter, called strangeon matter, as the putative basic units of the ground state of bulk strong matter using a Bayesian statistical method, incorporating the mass and radius measurements of PSR J0030+0451, PSR J0740+6620, and the recent data for the $1.4\ M_{\odot}$ pulsar PSR J0437-4715. We also include constraints from gravitational wave events GW170817 and GW190814. Under the prior assumption of a finite number of quarks in a strangeon, $N_{\rm q}$, our analysis reveals that current mass-radius measurements favor a larger $N_{\rm q}$. Specifically, the results support the scenario where a strangeon forms a stable bound state with $N_{\rm q}=18$, symmetric in color, flavor, and spin spaces, compared to the minimum $N_{\rm q}$ prior. The comparative analyses of the posterior EOS parameter spaces derived from three-parameter model and two-parameter model demonstrate a consistent prediction under identical observational constraints. In particular, our results indicate that the most probable values of the maximum mass are found to be $3.58^{+0.16}_{-0.12}\ M_{\odot}$ ($3.65^{+0.18}_{-0.16}\ M_{\odot}$) at $90\%$ confidence level for three-parameter (two-parameter) EOS considering the constraints of GW190814. The corresponding radii for $1.4\ M_{\odot}$ and $2.1\ M_{\odot}$ stars are $12.04^{+0.27}_{-0.31}~\rm km$ ($12.16^{+0.26}_{-0.31}~\rm km$) and $13.43^{+0.31}_{-0.32}~\rm km$ ($13.60^{+0.29}_{-0.34}~\rm km$), respectively. This result may impact interestingly on the research of multiquark states, which could improve our understanding of the nonperturbative strong force.

Figures

Figures reproduced from arXiv: 2411.14938 by the authors.

Figure 1
Figure 1. FIG. 1. The M-R relations within the two-parameter model for var [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Left panel: The posterior distribution of the model parameters under the constraints of PSR J0030 + 0451 and PSR J0740 + 6620 at [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The posterior distributions of the three-parameter model EOS at fixed [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. The M-R posterior distributions at [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Strangeon Ergostars

    astro-ph.HE 2026-01 conditional novelty 6.0 of 10

    Strangeon-matter equations of state support dynamically stable, uniformly rotating ergostars with about 0.01 solar masses of extractable energy.

Reference graph

Works this paper leans on

111 extracted references · 71 canonical work pages · cited by 1 Pith paper

  1. [1]

    [8, 11, 12], for PSR J0030 + 0451 we use the result from Ref

    Constraints from NICER data We consider the masses and radii inferred from the NICER data by Riley et al. [8, 11, 12], for PSR J0030 + 0451 we use the result from Ref. [11] ( M = 1 .34+0.15 −0.16 M⊙ and R = 12.71+1.14 −1.19 km) and the heavy pulsar PSR J0740 + 6620 (M = 2 .072+0.067 −0.066 M⊙ and R = 12 .39+1.30 −0.98 km) by X-ray pulse profile modeling o...

  2. [2]

    Here, we incorporate the constraints from the gravita- tional wave events GW170817 [9, 10] and GW190814 [55] reported by the LIGO Scientific Collaboration

    Constraints from gravitational wave events The tidal deformability inferred from gravitational wave detection of binary neutron star mergers have also led to a steady improvement in our understanding of the dense matter EOS. Here, we incorporate the constraints from the gravita- tional wave events GW170817 [9, 10] and GW190814 [55] reported by the LIGO Sc...

  3. [3]

    Madsen, 1999, Hadrons in Dense Matter and Hadrosynthe- sis, 162

    J. Madsen, 1999, Hadrons in Dense Matter and Hadrosynthe- sis, 162

    1999

  4. [4]

    Weber, 2005, Prog

    F. Weber, 2005, Prog. Part. Nucl. Phys., 54, 193

    2005

  5. [5]

    Oertel, M

    M. Oertel, M. Hempel, T. Kl¨ahn, et al. 2017, Rev. Mod. Phys., 89, 015007

    2017

  6. [6]

    G. Baym, T. Hatsuda, T. Kojo, et al. 2018, Rep. Prog. Phys., 81, 056902

    2018

  7. [7]

    Baiotti, 2019, Prog

    L. Baiotti, 2019, Prog. Part. Nucl. Phys., 109, 103714

    2019

  8. [8]

    Komoltsev, & A

    O. Komoltsev, & A. Kurkela, 2022, Phys. Rev. Lett., 128, 202701

    2022

Show all 111 references
  1. [9]

    M. C. Miller, F. K. Lamb, A. J. Dittmann, et al. 2021, Astro- phys. J. Lett., 918, L28

    2021

  2. [10]

    T. E. Riley, et al., Astrophys. J. 918, L27 (2021)

    2021

  3. [11]

    B. P. Abbott, et al., Phys. Rev. Lett. 119, 161101 (2017)

    2017

  4. [12]

    B. P. Abbott, et al., Phys. Rev. Lett. 121, 161101 (2018)

    2018

  5. [13]

    T. E. Riley, et al., Astrophys. J. 887, L21 (2019)

    2019

  6. [14]

    Vinciguerra, T

    S. Vinciguerra, T. Salmi, A. L. Watts, et al. 2024, Astrophys. J., 961, 62

    2024

  7. [15]

    M. C. Miller, F. K. Lamb, A. J. Dittmann, et al. 2019, Astro- phys. J. Lett., 887, L24

    2019

  8. [16]

    Choudhury, T

    D. Choudhury, T. Salmi, S. Vinciguerra, et al. 2024, Astro- phys. J. Lett., 971, L20

    2024

  9. [17]

    Rutherford, M

    N. Rutherford, M. Mendes, I. Svensson, et al. 2024, Astro- phys. J. Lett., 971, L19

    2024

  10. [18]

    A. R. Bodmer, 1971, Phys. Rev. D, 4, 1601

    1971

  11. [19]

    Witten, 1984, Phys

    E. Witten, 1984, Phys. Rev. D, 30, 272

    1984

  12. [20]

    Chakrabarty, 1993, Phys

    S. Chakrabarty, 1993, Phys. Rev. D, 48, 1409

    1993

  13. [21]

    M. Dey, I. Bombaci, J. Dey, et al. 1998, Phys. Lett. B, 438, 123. 10

    1998

  14. [22]

    Chakrabarty, S

    S. Chakrabarty, S. Raha, & B. Sinha, 1989, Phys. Lett. B, 229, 112

    1989

  15. [23]

    Buballa, & M

    M. Buballa, & M. Oertel, 1999, Phys. Lett. B, 457, 261

    1999

  16. [24]

    G. X. Peng, H. C. Chiang, J. J. Yang, et al. 1999, Phys. Rev. C, 61, 015201

    1999

  17. [25]

    X. J. Wen, X. H. Zhong, G. X. Peng, et al. 2005, Phys. Rev. C, 72, 015204

    2005

  18. [26]

    A. Li, R. X. Xu, & J. F. Lu, 2010, Mon. Not. R. Astron. Soc., 402, 2715

    2010

  19. [27]

    E. P. Zhou, X. Zhou, & A. Li, 2018, Phys. Rev. D,97, 083015

    2018

  20. [28]

    C. M. Li, Y . Yan, J. J. Geng, et al. 2018, Phys. Rev. D, 98, 083013

    2018

  21. [29]

    C. J. Xia, T. Maruyama, N. Yasutake, et al. 2019, Phys. Rev. D, 99, 103017

    2019

  22. [30]

    G. X. Peng, H. C. Chiang, B. S. Zou, et al. 2000, Phys. Rev. C, 62, 025801

    2000

  23. [31]

    Bai, & Y

    Z. Bai, & Y . X. Liu. 2021, Eur. Phys. J. C,81, 612

    2021

  24. [32]

    C. J. Xia, , Z. Zhu, X. Zhou, et al. 2021, Chinese Phys. C, 45, 055104

    2021

  25. [33]

    W. L. Yuan, A. Li, Z. Q. Miao, et al. 2022, Phys. Rev. D, 105, 123004

    2022

  26. [34]

    Y . R. Zhou, C. Zhang, J. Zhao, et al. 2024, Phys. Rev. D,110, 103012

    2024

  27. [35]

    X. L. Zhang, Y . F. Huang, & Z. C. Zou, 2024, Front. Astron. Space Sci., 11, 1409463

    2024

  28. [36]

    Holdom, J

    B. Holdom, J. Ren, & C. Zhang, 2018, Phys. Rev. Lett., 120, 222001

    2018

  29. [37]

    T. Zhao, W. Zheng, F. Wang, et al. 2019, Phys. Rev. D, 100, 043018

    2019

  30. [38]

    Ren, & C

    J. Ren, & C. Zhang, 2020, Phys. Rev. D, 102, 083003

    2020

  31. [39]

    Zhang, 2020, Phys

    C. Zhang, 2020, Phys. Rev. D, 101, 043003

    2020

  32. [40]

    Zhang, & R

    C. Zhang, & R. B. Mann, 2021, Phys. Rev. D, 103, 063018

    2021

  33. [41]

    L. Q. Su, C. Shi, Y . F. Huang, et al. 2024, Astrophys.Space Sci., 369, 29

    2024

  34. [42]

    R. X. Xu, 2003, Astrophys. J. Lett., 596, L59

    2003

  35. [43]

    R. X. Xu, D. J. Tao, & Y . Yang, 2006, Mon. Not. R. Astron. Soc., 373, L85

    2006

  36. [44]

    Peng, & R

    C. Peng, & R. X. Xu, 2008, Mon. Not. R. Astron. Soc., 384, 1034

    2008

  37. [45]

    X. Y . Lai, & R. X. Xu, 2009, Mon. Not. R. Astron. Soc., 398, L31

    2009

  38. [46]

    X. W. Liu, , J. D. Liang, R. X. Xu, et al. 2012, Mon. Not. R. Astron. Soc., 424, 2994

    2012

  39. [47]

    E. P. Zhou, J. G. Lu, H. Tong, et al. 2014, Mon. Not. R. Astron. Soc., 443, 2705

    2014

  40. [48]

    X. Y . Lai, & R. X. Xu, 2016, Chinese Phys. C, 40, 095102

    2016

  41. [49]

    X. Y . Lai, Y . W. Yu, E. P. Zhou, et al. 2018, Res. Astron. As- trophys., 18, 024

    2018

  42. [50]

    X. Y . Lai, E. P. Zhou, &R. X. Xu, 2019, Eur. Phys. J. A., 55, 60

    2019

  43. [51]

    X. Y . Lai, C. J. Xia, Y . W. Yu, et al. 2021, Res. Astron. Astro- phys., 21, 250

    2021

  44. [52]

    Y . Gao, X. Y . Lai, L. J. Shao, et al. 2022, Mon. Not. R. Astron. Soc., 509, 2758

    2022

  45. [53]

    Z. Q. Miao, C. J. Xia, X. Y . Lai, et al. 2022, Int. J. Mod. Phys. E, 31, 2250037

    2022

  46. [54]

    Zhang, Y

    C. Zhang, Y . Gao, C. J. Xia, et al. 2023, Phys. Rev. D, 108, 063002

    2023

  47. [55]

    Zhang, Y

    C. Zhang, Y . Gao, C. J. Xia, et al. 2023, Phys. Rev. D, 108, 123031

    2023

  48. [56]

    P. B. Demorest, T. Pennucci, S. M. Ransom, et al. 2010, Na- ture (London), 467, 1081

    2010

  49. [57]

    Abbott, T

    R. Abbott, T. D. Abbott, S. Abraham, et al. 2020, Astrophys. J. Lett., 896, L44

    2020

  50. [58]

    J. E. Jones, 1924, Proc. R. soc. Lond. Ser. A, 106, 441

    1924

  51. [59]

    A. W. Steiner, J. M. Lattimer, & E. F. Brown, 2010, Astrophys. J., 722, 33

    2010

  52. [60]

    S. K. Greif, G. Raaijmakers, K. Hebeler, et al. 2019, Mon. Not. R. Astron. Soc., 485, 5363

    2019

  53. [61]

    Raaijmakers, T

    G. Raaijmakers, T. E. Riley, A. L. Watts, et al. 2019, Astro- phys. J. Lett., 887, L22

    2019

  54. [62]

    Raaijmakers, S

    G. Raaijmakers, S. K. Greif, T. E. Riley, et al. 2020, Astro- phys. J. Lett., 893, L21

    2020

  55. [63]

    Traversi, P

    S. Traversi, P. Char, & G. Pagliara, 2020, Astrophys. J., 897, 165

    2020

  56. [64]

    W. J. Xie, &B. A. Li, 2021, Phys. Rev. C, 103, 035802

    2021

  57. [65]

    Tak ´atsy, P

    J. Tak ´atsy, P. Kov´acs, G. Wolf, et al. 2023, Phys. Rev. D, 108, 043002

    2023

  58. [66]

    Huang, G

    C. Huang, G. Raaijmakers, A. L. Watts, et al. 2024, Mon. Not. R. Astron. Soc., 529, 4650

    2024

  59. [67]

    K. D. Marquez, T. Malik, H. Pais, et al. 2024, Phys. Rev. D, 110, 063040

    2024

  60. [68]

    2024, Phys

    Guha Roy, D., Venneti, A., Malik, T., et al. 2024, Phys. Lett. B, 859, 139128

    2024

  61. [69]

    Huang, L

    C. Huang, L. Tolos, C. Provid ˆencia, et al. 2024, arXiv:2410.14572

    2024 arXiv

  62. [70]

    Traversi, & P

    S. Traversi, & P. Char, 2020, Astrophys. J., 905, 9

    2020

  63. [71]

    Z. Q. Miao, J. L. Jiang, A. Li, et al. 2021, Astrophys. J. Lett., 917, L22

    2021

  64. [72]

    A. Li, Z. Q. Miao, J. L. Jiang, et al. 2021, Mon. Not. R. Astron. Soc., 506, 5916

    2021

  65. [73]

    Z. Wang, Y . Gao, D. Liang, J. Zhang, & L. J. Shao. 2024, arXiv:2409.11103

    2024 arXiv

  66. [74]

    F. M. da Silva, A. Issifu, L. L. Lopes, et al. 2024, Phys. Rev. D, 109, 043054

    2024

  67. [75]

    Fonseca, H

    E. Fonseca, H. T. Cromartie, T. T. Pennucci, et al. 2021, As- trophys. J. Lett., 915, L12

    2021

  68. [76]

    Salmi, D

    T. Salmi, D. Choudhury, Y . Kini, et al. 2024, Astrophys. J., 974, 294

    2024

  69. [77]

    S. V . Bashinsky, & R. L. Jaffe, 1997, Nucl. Phys. A,625, 167

    1997

  70. [78]

    Wetzorke, F

    I. Wetzorke, F. Karsch, & E. Laermann, 2000, Nucl. Phys. B, Proc. Suppl., 83, 218

    2000

  71. [79]

    F. C. Michel, 1988, Phys. Rev. Lett., 60, 677

    1988

  72. [80]

    Curtis Michel, 1991, Nucl

    F. Curtis Michel, 1991, Nucl. Phys. B, Proc. Suppl., 24, 33

    1991

  73. [81]

    V . G. J. Stoks, R. A. M. Klomp, C. P. F. Terheggen, et al. 1994, Phys. Rev. C, 49, 2950

    1994

  74. [82]

    R. B. Wiringa, V . G. J. Stoks, & R. Schiavilla, 1995, Phys. Rev. C, 51, 38

    1995

  75. [83]

    Machleidt, 2001, Phys

    R. Machleidt, 2001, Phys. Rev. C, 63, 024001

    2001

  76. [84]

    D. J. Reardon, M. Bailes, R. M. Shannon, et al. 2024, Astro- phys. J. Lett., 971, L18

    2024

  77. [85]

    Raaijmakers, S

    G. Raaijmakers, S. K. Greif, K. Hebeler, et al. 2021, Astro- phys. J. Lett., 918, L29

    2021

  78. [86]

    Huang, T

    C. Huang, T. Malik, J. Cartaxo, et al. 2024, arXiv:2411.14615

    2024 arXiv

  79. [87]

    Huang, G

    C. Huang, G. Raaijmakers, A. L. Watts, L. Tolos, C. Provid ˆencia, N. Osborn, & N. Whitsett, 2023, GitHub Repository, version 1.9. https://doi.org/10. 5281/zenodo.10927600; https://github.com/ ChunHuangPhy/EoS_inference/tree/v.1.9

    2023

  80. [88]

    Buchner, 2021, arXiv e-prints, arXiv:2101.09604

    J. Buchner, 2021, arXiv e-prints, arXiv:2101.09604. https: //johannesbuchner.github.io/UltraNest/; https://arxiv.org/abs/2101.09604 [stat.CO]

    2021 arXiv

  81. [89]

    R. E. Kass and A. E. Raftery, Bayes Factors, Journal of the American Statistical Association 90, no. 430, pp. 773–795 (1995)

    1995

  82. [90]

    Bombaci, A

    I. Bombaci, A. Drago, D. Logoteta, et al. 2021, Phys. Rev. Lett., 126, 162702. doi:10.1103/PhysRevLett.126.162702 11

    2021 doi

  83. [91]

    Z. Cao, L. W. Chen, P. C. Chu , et al. 2022, Phys. Rev. D,106, 083007

    2022

  84. [92]

    H. Chen, W. Chen, X. Liu, et al. 2016, Phys. Rep., 639, 1-121

    2016

  85. [93]

    F. Guo, C. Hanhart, U. Meißner, et al. 2018, Rev. Mod. Phys., 90, 015004

    2018

  86. [94]

    A. W. Steiner, S. Reddy, & M. Prakash, 2002, Phys. Rev. D, 66, 094007

    2002

  87. [95]

    Alford, & K

    M. Alford, & K. Rajagopal, 2002, J. High Energy Phys., 2002, 031

    2002

  88. [96]

    Alford, & S

    M. Alford, & S. Reddy, 2003, Phys. Rev. D, 67, 074024

    2003

  89. [97]

    Huang, P

    M. Huang, P. Zhuang, & W. Chao, 2003, Phys. Rev. D, 67, 065015

    2003

  90. [98]

    Mannarelli, K

    M. Mannarelli, K. Rajagopal, & Sharma, R. 2007, Phys. Rev. D, 76, 074026

    2007

  91. [99]

    Roupas, G

    Z. Roupas, G. Panotopoulos, & I. Lopes, 2021, Phys. Rev. D, 103, 083015

    2021

  92. [100]

    Ivanytskyi, & D

    O. Ivanytskyi, & D. Blaschke, 2022, Phys. Rev. D, 105, 114042

    2022

  93. [101]

    W. L. Yuan, J. Chao, & A. Li, 2023, Phys. Rev. D, 108, 043008

    2023

  94. [102]

    W. L. Yuan,&A. Li, 2024, Astrophys. J., 966, 3

    2024

  95. [103]

    Gholami, I

    H. Gholami, I. A. Rather, M. Hofmann, et al. 2024, arXiv:2411.04064

    2024 arXiv

  96. [104]

    McLerran, &R

    L. McLerran, &R. D. Pisarski, 2007, Nucl. Phys. A, 796, 83

    2007

  97. [105]

    T. K. Herbst, J. M. Pawlowski, & B.-J. Schaefer, 2011, Phys. Lett. B, 696, 58

    2011

  98. [106]

    G. Y . Shao, M. di Toro, V . Greco, et al. 2011, Phys. Rev. D, 84, 034028

    2011

  99. [107]

    Kojo, 2012, Nucl

    T. Kojo, 2012, Nucl. Phys. A, 877, 70

    2012

  100. [108]

    T. Q. Zhao, &J. M. Lattimer, 2020, Phys. Rev. D, 102, 023021

    2020

  101. [109]

    G. Q. Cao, 2022, Phys. Rev. D, 105, 114020

    2022

  102. [110]

    C. J. Xia, H. M. Jin, & T. T. Sun, 2023, Phys. Rev. D, 108, 054013

    2023

  103. [111]

    B. K. Gao, & M. Harada, 2024, arXiv:2410.16649

    2024 arXiv

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.