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Correlations between the Neutron Star Mass-Radius Relation and the Equation of State of Dense Matter

T0 review · 3 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read For ordinary hadronic equations of state, a neutron star's mass-radius curve can be analytically inverted to the dense-matter EOS with about 0.5% accuracy using power-law fits at two fractional maximum-mass radii.

desk verdict A genuinely new empirical inversion tool with in-sample sub-percent fits, but the abstract's "0.5% for all quantities" is contradicted by the paper's own tables, and no real out-of-sample validation backs it up. read the letter →

arxiv 2412.14645 v2 pith:QJP6QDBS submitted 2024-12-19 astro-ph.SR astro-ph.HEnucl-th

Boyang Sun , James M. Lattimer This is my paper · ORCID
classification astro-ph.SRastro-ph.HEnucl-th
keywords neutronstarsmass-radiusrelationequationofstateTOVequationsanalyticinversionpower-lawcorrelationshybridBayesianstatistics
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

The paper claims that the neutron star mass-radius (M-R) curve contains enough information to reconstruct the dense-matter equation of state (EOS) analytically, without Bayesian model fitting. Its central result is a set of power-law formulae that predict the central energy density, pressure, sound speed, chemical potential, and baryon number density of a star whose mass is a fixed fraction of the maximum mass, using only the maximum mass and two radii at fractional masses. For ordinary hadronic EOSs these predictions are accurate to roughly 0.5% root-mean-square at all mass points. If true, this gives a direct, prior-free alternative to Bayesian inference of the EOS from mass and radius measurements, turning an observed M-R curve into the pressure-energy-density relation.

What carries the argument

The central object is the two-radius power-law fitting formula of Eq. (22): $G_f = a (M_{\max}/M_\odot)^{b} (R_g/10\,\mathrm{km})^{c} (R_h/10\,\mathrm{km})^{d}$, where $G_f$ denotes the central energy density, pressure, sound speed, chemical potential, or baryon density at a star of mass $f M_{\max}$. The coefficients are determined by least-squares fitting on the 316-equation-of-state sample, and the two radii are chosen from an 11-point grid of fractional maximum masses to minimize the root-mean-square error. These formulae translate a point on the mass-radius curve into the thermodynamic state at the star's center, and interpolating over the 11 fractional masses reconstructs the whole equation of state up to the central values at the maximum mass.

What would settle it

Take an equation of state not in the training set, with a different crust treatment or a first-order phase transition, compute its M-R curve, apply Eq. (22), and compare the reconstructed P(E) with the true EOS; if the RMS deviation in pressure at any fractional-mass point exceeds the quoted 0.5-1% (or a few percent near a transition), the claimed semi-universality does not hold for that class.

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Extended reading notes

Core claim

The authors establish that for a suite of 316 hadronic equations of state with maximum masses above two solar masses, the central energy density, pressure, sound speed, baryon chemical potential, and baryon number density of stars at masses equal to f times the maximum mass are determined by a power law in the maximum mass and in the radii at two chosen fractional maximum masses. Optimizing the choice of the two radii brings the fits to better than 1% accuracy and typically about 0.5% root-mean-square. Inverting an entire M-R curve point by point therefore yields the full pressure-energy-density relation, the central sound speed, and the chemical potential relation, with errors of order 1% or less. The same formulae applied to a hybrid star with a first-order phase transition reproduce the EOS away from the transition to a few percent and give the midpoint of the transition correctly, even though no hybrid EOS was used to train the fits. This amounts to an analytic, EOS-insensitive inversion of the Tolman-Oppenheimer-Volkoff equations.

Load-bearing premise

The fitted power-law correlations are assumed to be semi-universal beyond the 316 hadronic equations of state used to determine them, particularly for equations of state with first-order phase transitions, for which the paper tests only one hybrid model.

Editorial extensions

If this is right

  • If the 0.5% correlations hold for real dense-matter equations of state, then measurements of several neutron star masses and radii can be converted directly into central pressure and energy-density estimates for each observed star.
  • The method provides a Bayesian-prior-free cross-check: EOS bands produced by parametric Bayesian analyses can be compared with the direct analytic inversion of the same M-R data, exposing prior-induced systematic differences.
  • The reconstruction also yields the central sound speed, baryon density, and chemical potential at each fractional mass, providing additional thermodynamic information that can be confronted with nuclear-theory predictions.
  • For hybrid stars with first-order phase transitions, the inversion smooths over the transition but still recovers the transition midpoint, so it can flag the presence of a strong phase transition when the reconstructed EOS shows an unusual softening or a density discontinuity.
  • The same approach is argued to extend to moments of inertia and tidal deformabilities, which are tightly correlated with mass and radius, broadening the set of observables that can be inverted analytically.

Reading between the lines

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

  • If the semi-universality extends to equations of state beyond the training set, the same power-law coefficients could be applied to invert M-R curves of hybrid or quark-matter stars, but the paper's single hybrid test suggests accuracy degrades near the transition; a systematic study over many hybrid EOSs would quantify this failure mode.
  • The order-of-magnitude improvement gained by adding a second radius suggests that other pairs of nearly independent observables, such as radius plus tidal deformability or radius plus moment of inertia, may yield similarly sharp reconstructions of the central thermodynamic state.
  • If the inversion is truly prior-free, it could serve as a consistency diagnostic for Bayesian analyses: large discrepancies between inverted and Bayesian EOS bands would indicate that the Bayesian prior choice, not the data, is driving the result.
  • The paper notes a fundamental limit to single-point accuracy from the non-uniqueness of central density and pressure for a given (M,R) point, so the achievable precision of any inversion is bounded by how much structure the M-R curve carries, not just by the fitting function.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper develops an analytic method to invert neutron-star mass-radius (M-R) curves into the underlying equation of state (EOS). The method uses power-law correlations between central values of energy density, pressure, sound speed, chemical potential, and baryon density at fixed fractions f of the maximum mass and two radii selected from the M-R curve (Eq. 22). The coefficients are fit to 316 hadronic EOSs from the Sun et al. (2024a) tabulation with Mmax >= 2 Msun. The authors claim that the two-radius fits achieve RMS accuracies of typically 0.5% for all quantities at all mass points, that the method works reasonably well for hybrid stars with first-order phase transitions, and that it provides an analytic alternative to Bayesian inversion. They also present fixed-mass-grid fits for application to observational data (Eqs. 29-30) and compare their inferred EOS with published Bayesian results for two NICER sources.

Significance. If the central accuracy claim and the semi-universality of the correlations were established, this would be a valuable fast analytic inversion tool, complementary to Bayesian methods. The paper is strengthened by the use of a large EOS database, an extensive comparison with the TPE approach and the fits of Ofengeim et al. (2023), the release of code in a Zenodo repository, and the tabulation of all fit parameters. However, the main quantitative claim is contradicted by the paper's own tables, the reported errors are purely in-sample with no cross-validation, and the out-of-sample evidence is limited to a single hybrid EOS. These issues currently undermine the paper's significance.

major comments (3)
  1. [Abstract, §3, Tables 2-3] The central accuracy claim, 'typically 0.5% for all quantities at all mass points,' is contradicted by the paper's own tables. The RMS errors defined in Eq. (17) for the two-radius fits of Eq. (22) include <delta P> = 1.26% at f = 1, 2.51% at f = 3/5, and 3.13% at f = 1/3 (Table 2); <delta cs> = 5.74% at f = 1 (Table 2); and <delta n> approximately 0.8-1.4% at all f (Table 3). The statement in §3 that 'the average accuracy for P is better than 0.6% except for 1/3 <= f <= 3/5' is also inconsistent with the f = 1 entry of <delta P> = 1.26%. The abstract and §5 overstate the method's fidelity even on the training set.
  2. [§3, Eqs. (22)-(23)] The reported accuracies are in-sample RMS errors: the coefficients in Eq. (22) are fit by minimizing the chi-square of Eq. (23) over the same 316-EOS set, and the optimized pairs (gmin, hmin) are selected by the same minimization on the same data. No cross-validation, holdout set, or independent hadronic EOS compilation is used. The paper itself states in §5 that 'a future project will be to utilize several versions of parameterized EOSs to validate the fitting parameters found here.' Without such validation, the claim that the correlations are 'semi-universal' is not established; the (g,h) selection in particular could inflate apparent accuracy through overfitting.
  3. [§5, Figs. 7-8] The only out-of-sample test with first-order phase transitions is a single construction (BSk22 + MIT bag with B = 80 MeV fm^-3), discussed qualitatively as accurate to a few percent. Given that the abstract generalizes to 'hybrid stars with first-order phase transitions' and that this case is the sole evidence for robustness beyond the hadronic training set, the generalization is not yet supported. A systematic scan over bag constants and hadronic EOSs, or at least over a few representative transition pressures and densities, is needed to justify the abstract's claim.
minor comments (4)
  1. [Table 4] The value of aE for Mj = 1.3 Msun is listed as 0.08501, which is likely a typo for 0.8501; also, the values of bnu for Mj = 1.5 and 1.4 Msun are identical (-0.05371), which seems suspicious and should be checked.
  2. [§3] The phrase 'increases the RMF accuracies' appears to be a typo; it should be 'RMS accuracies.'
  3. [Captions of Figs. 2 and 5] The caption of Fig. 2 references Eq. (23) for the reconstructed points, but the fits are defined by Eq. (22), while Eq. (23) defines the chi-square; similarly, the caption of Fig. 5 references Eq. (23) where Eq. (29) is meant.
  4. [§4 and §5] The notation for the nuclear saturation energy density is inconsistent: the text uses both Es and E0; additionally, the hadronic EOS 'BSk22' is sometimes written as 'BSK22' in the captions of Figs. 7 and 8. Please unify the notation.

Circularity Check

1 steps flagged · score 4.0 of 10

Headline 0.5% accuracy is a training-set RMS error on the authors' own 316-EOS sample, with out-of-sample validation explicitly deferred; the inversion method itself retains independent content via the hybrid test.

  1. fitted input called prediction [Abstract; Section 3, Eqs. (21)-(23) and Table 2; Section 5]
    "Root-mean-square fitting accuracies, for EOSs without large first-order phase transitions, are typically 0.5% for all quantities at all mass points. [...] A future project will be to utilize several versions of parameterized EOSs to validate the fitting parameters found here."

    The quoted 0.5% accuracy is computed with Eq. (17) on the same 316 EOSs from the authors' Sun et al. (2024a) tabulation that were used to minimize chi^2 in Eqs. (21)-(23). The reported RMS errors are therefore the optimized training-set residuals, not out-of-sample prediction errors. The paper then presents these in-sample accuracies as the basis for inverting an 'arbitrary' M-R curve, while Section 5 explicitly states that validation of the fitting parameters is a future project. The only out-of-sample test is a single hand-picked BSk22+MIT-bag hybrid, so the headline accuracy claim is statistically forced by the fit rather than independently confirmed.

full rationale

The derivation chain is not circular in a definitional sense: Eq. (22) is an empirical regression from fractional-maximum-mass radii and Mmax to central E, P, cs, mu, and n, and the paper does not define those target quantities in terms of the fit outputs. The TOV forward direction is used only to generate the training data, and the hybrid-star test in Section 5 is a genuine out-of-sample check. However, the central quantitative claim of 'typically 0.5% for all quantities' is an in-sample training error on the authors' own EOS sample; the paper itself concedes that validation of the fitting parameters is deferred to future work. In addition, the paper's own Tables 2 and 3 do not support the 0.5% statement for several quantities and mass points (e.g., pressure RMS errors of 1.26%, 2.51%, and 3.13% at f=1, 3/5, and 1/3; sound-speed RMS error of 5.74% at f=1), which is a correctness/overclaim issue rather than a circular-reasoning issue. The self-citation to Sun et al. (2024a) supplies the training database, not an unverified uniqueness theorem, so it is not load-bearing circularity by itself. Overall, the method has independent content, especially through the out-of-sample hybrid reconstruction and comparison with Ofengeim et al. (2023), but the headline accuracy is a fitted input presented as a general predictive accuracy, giving partial circularity.

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

The method is an empirical, data-calibrated inversion. The central sub-percent accuracy claim rests on a training set of 316 hadronic EOSs, an assumed power-law form, a chosen grid of fractional masses, and the assumption that the selected two-radius pairs generalize. No new physical entities are introduced. The TPE analysis provides motivation but not the coefficients. The absence of first-order-transition EOSs in training is a domain assumption explicitly tested on only one hybrid model.

free parameters (4)
  • Two-radius power-law coefficients (a, b, c, d) for E, P, cs/c, P/E, n, mu at 11 fractional masses f (Tables 2-3) = Tabulated in Tables 2 and 3, e.g., for E at f=1: a=1.644, b=-0.1408, c=-10.46, d=8.614
    Determined by least-squares minimization of Eq. (23) over the 316-EOS training sample. These are the core free parameters that map (Mmax, Rg, Rh) to central EOS quantities.
  • General inversion formula coefficients (Eq. 29 and Eq. 30, Tables 5-6) = Tabulated in Tables 5 and 6
    Second-order polynomial coefficients in ln M and ln R fitted to 8 fixed masses times 316 EOSs; include a slope term gG(dR/dM) in Eq. 30.
  • Single-radius power-law coefficients (Eq. 21 and Eq. 28, Tables 1 and 4) = Tabulated in Tables 1 and 4
    The simpler one-radius fits, superseded by the two-radius fits but used for comparison.
  • Optimized fractional radius pairs (gmin, hmin) for each f = Listed in Tables 2 and 3, e.g., for f=1 with E, g=0.95 and h=0.9
    The two fractional-maximum-mass radii that minimize the in-sample RMS error for each quantity at each f. This discrete selection is a data-fitted model-selection layer.
assumptions (5)
  • standard math TOV equations correctly model neutron star structure and give a unique M-R curve for each EOS
    The entire method assumes the TOV equations (Tolman 1934; Oppenheimer & Volkoff 1939) as the forward model. Used throughout.
  • domain assumption The EOS tabulation of Sun et al. (2024a) with Mmax >= 2 M⊙ is representative of the true dense-matter EOS
    The fit coefficients are calibrated on this sample; the paper assumes the correlations generalize. The Mmax cut and the SLy4 crust are imposed, not derived. See §2 and §3.
  • ad hoc to paper Power-law functional forms (Eqs. 22, 29) adequately capture the correlations over the relevant range
    The functional form is chosen for convenience and not derived; the TPE analysis provides qualitative motivation, but the power-law exponents are free.
  • ad hoc to paper The grid of 11 fractional masses f is sufficient for reconstructing the EOS by interpolation
    The choice of f-grid is described as "arbitrary" in §3; accuracy and sensitivity to grid density are not explored.
  • domain assumption Neglect of first-order phase transitions in the training set does not invalidate the fits for hybrid EOSs
    The fits are applied to hybrid stars in §5 despite no phase-transition EOSs in the training sample; the single BSk22+bag test suggests but does not guarantee performance.

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Pith. "Pith review of Correlations between the Neutron Star Mass-Radius Relation and the Equation of State of Dense Matter." pith.science (2026). https://pith.science/paper/QJP6QDBS

@misc{pith2026241214645,
  author       = {Pith},
  title        = {Pith review of: Correlations between the Neutron Star Mass-Radius Relation and the Equation of State of Dense Matter},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QJP6QDBS}},
  note         = {Machine review of arXiv:2412.14645}
}
abstract

We develop an analytic method of inverting the Tolman-Oppenheimer-Volkoff (TOV) relations to high accuracy. In principle, a specified $\mathcal{E}\mbox{-}P$ relation gives a unique $M\mbox{-}R$ relation, and vice-versa. Our method is developed from the strong correlations that are shown to exist between the neutron star mass-radius curve and the equation of state (EOS) or pressure-energy density relation. Selecting points that have masses equal to fixed fractions of the maximum mass, we find a semi-universal power-law relation between the central energy densities, pressures, sound speeds, chemical potentials and number densities of those stars, with the maximum mass and the radii of one or more fractional maximum mass points. Root-mean-square fitting accuracies, for EOSs without large first-order phase transitions, are typically 0.5% for all quantities at all mass points. The method also works well, although less accurately, in reconstructing the EOS of hybrid stars with first-order phase transitions. These results permit, in effect, an analytic method of inverting an arbitrary mass-radius curve to yield its underlying EOS. We discuss applications of this inversion technique to the inference of the dense matter EOS from measurements of neutron star masses and radii as a possible alternative to traditional Bayesian approaches.

Figures

Figures reproduced from arXiv: 2412.14645 by the authors.

Figure 1
Figure 1. Solid lines show M-R (left panel) and P-E (right panel) relations for the BSk26 (black), SLy4 (blue), MS1 (red) and DD2 (green) EOSs. Filled circles with numbers (squares with letters) show where 2 EOSs have the same M, R (E, P) pairs. and power-law approaches are given in [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Fidelity of two-radius power-law fits fractional maximum mass inversion technique. Left panel: Solid lines show the P-E relations for BSk26, SLy4, MS1 and DD2 EOSs. Points show Ec and Pc values reconstructed from Eq. (23) at the indicated Mmax fractions. The side and lower panels show logarithmic errors at each Mmax fraction. The lowest panel shows the true deviation ∆P from the EOS, defined in Eq. (24). Right panel… view at source ↗
Figure 3
Figure 3. The same as [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Histogram showing the number of EOSs with particular ranges of pressure RMS errors at the 11 fiducial points f along the M-R curves for the 312 EOSs in the tabulation of Sun et al. (2024a) for which Mmax ≥ 2M⊙. Upper portion shows results for the method of Ofengeim et …
Figure 5
Figure 5. Figure 5: Comparison of two-radius and inverse slope power-law fits for the general mass-radius inversion technique. Left panel: Solid lines show the P-E relation for the BSk26, SLy4, MS1 and DD2 equations of state. Points show the reconstructed Ec and Pc from Eq. (29) at the in…
Figure 6
Figure 6. Figure 6: The lower and upper gold confidence ellipses (68% and 95%) correspond to the inversion of the corresponding PSR J0437-4715 and J0740+6620 M-R uncertainty regions, respectively, both assumed to be uncorrelated double Gaussian probability distributions, using Eq. (30) fo…
Figure 7
Figure 7. Figure 7: Left panel: mass-radius curves for the purely hadronic star formed with the BSk22 EOS (solid curve) and a hybrid star with a first-order phase transition to the MIT massless, charge neutral, two-flavor quark bag model EOS with B = 80 MeV (dashed curve). Black (red) fil…
Figure 8
Figure 8. Figure 8: The same as the right panel of [PITH_FULL_IMAGE:figures/full_fig_p018_8.png]

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Forward citations

Cited by 3 Pith papers

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Reference graph

Works this paper leans on

23 extracted references · 16 canonical work pages · cited by 3 Pith papers

  1. [1]

    2023, Phys

    Brandes, L., Weise, W., & Kaiser, N. 2023, Phys. Rev. D, 108, 094014, doi: 10.1103/PhysRevD.108.094014

    doi:10.1103/physrevd.108.094014 2023

  2. [2]

    2023a, The Astrophysical Journal, 952, 147, doi: 10.3847/1538-4357/acdef0 —

    Cai, B.-J., Li, B.-A., & Zhang, Z. 2023a, The Astrophysical Journal, 952, 147, doi: 10.3847/1538-4357/acdef0 —. 2023b, Phys. Rev. D, 108, 103041, doi: 10.1103/PhysRevD.108.103041

    doi:10.3847/1538-4357/acdef0

  3. [3]

    1998, Nucl

    Schaeffer, R. 1998, Nucl. Phys. A, 635, 231

    work page 1998

  4. [4]

    2024, Ap

    Choudhury, D., Salmi, T., Vinciguerra, S., & et al. 2024, Ap. J. Lett., 971, L20

    work page 2024

  5. [5]

    J., Miller, M

    Dittmann, A. J., Miller, M. C., Lamb, F. K., & et al. 2024, Ap. J., 974, 295

    work page 2024

  6. [6]

    T., Pennucci, T

    Fonseca, E., Cromartie, H. T., Pennucci, T. T., & et al. 2021, Ap. J. Lett., 915, L12

    work page 2021

  7. [7]

    M., & Snell, J

    Grinstead, C. M., & Snell, J. L. 1997, Introduction to Probability (Providence, RI: American Mathematical Society)

    work page 1997

  8. [8]

    M., & Prakash, M

    Lattimer, J. M., & Prakash, M. 2001, ApJ, 550, 426, doi: 10.1086/319702

    doi:10.1086/319702 2001

Show all 23 references
  1. [9]

    M., & Prakash, M

    Lattimer, J. M., & Prakash, M. 2011, What a Two Solar Mass Star Really Means, ed. S. Lee (Singapore: World Scientific)

    2011

  2. [10]

    1992, Astrophys

    Lindblom, L. 1992, Astrophys. J., 398, 569

    1992

  3. [11]

    2019, Phys Rev Lett, 122, 122701

    McLerran, L., & Reddy, S. 2019, Phys Rev Lett, 122, 122701

    2019

  4. [12]

    Ofengeim, D. D. 2020, Phys. Rev. D, 101, 103029

    2020

  5. [13]

    D., Shternin, P

    Ofengeim, D. D., Shternin, P. S., & Piran, T. 2023, Astronomy Letters, 49, 567–574, doi: 10.1134/s1063773723100055

    2023 doi

  6. [14]

    R., & Volkoff, G

    Oppenheimer, J. R., & Volkoff, G. M. 1939, Phys. Rev., 55, 374

    1939

  7. [15]

    J., Bailes, M., Flynn, C., & et al

    Reardon, D. J., Bailes, M., Flynn, C., & et al. 2024, Ap. J. Lett., 971, L18

    2024

  8. [16]

    E., & Ruffini, R

    Rhoades, C. E., & Ruffini, R. 1974, Phys. Rev. Lett., 32, 324

    1974

  9. [17]

    2024, The Astrophysical Journal Letters, 971, L19, doi: 10.3847/2041-8213/ad5f02

    Rutherford, N., Mendes, M., Svensson, I., et al. 2024, The Astrophysical Journal Letters, 971, L19, doi: 10.3847/2041-8213/ad5f02

    2024 doi

  10. [18]

    2024, Ap

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

    2024

  11. [19]

    Sun, B., Bhattiprolu, S., & Lattimer, J. M. 2024a, Phys. Rev. C, 109, 055801, doi: 10.1103/PhysRevC.109.055801 20 Sun and Lattimer

    doi

  12. [20]

    Sun, B., Xu, K., & Lattimer, J. 2024b, Visualization Software for Analytic Inversion of an Arbitrary Neutron Star M-R Curve into its Underlying Pressure-Energy Density Relation, Zenodo, doi: 10.5281/zenodo.14064108

    doi

  13. [21]

    Tolman, R. C. 1934, Relativity, Thermodynamics and Cosmology (Oxford: Clarendon Press)

    1934

  14. [22]

    2013, Science, 341, 365

    Yagi, K., & Yunes, N. 2013, Science, 341, 365

    2013

  15. [23]

    Zhao, T., & Lattimer, J. M. 2018, Phys Rev D, 98, 063030 —. 2020, Phys Rev D, 102, 023021 —. 2022, Phys. Rev. D, 106, 123002, doi: 10.1103/PhysRevD.106.123002

    2018 doi

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