{"id":"bb6c819f-5532-4b60-989e-17147e5cfbda","arxiv_id":"2504.20589","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"For anisotropic quark stars in full general relativity, f-mode frequency scales linearly with the square root of average density, and normalized damping time follows a linear trend with compactness, with anisotropy shifting both relations.","lead":"This paper computes the vibration frequencies and gravitational-wave damping times of hypothetical quark stars whose internal pressure is not equal in all directions, using Einstein's full theory of gravity. The authors derive compact formulas that could help future gravitational-wave observations probe the equation of state and internal anisotropy of such stars.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Solver inherited from Paper-I is not validated for quark stars; the finite surface density of the MIT bag EOS may invalidate the computed complex frequencies, so a benchmark against existing quark-star f-mode results is needed.","rationale":"The reader's weakest assumption correctly identifies the unvalidated solver from Paper-I as the load-bearing uncertainty. I sharpen this concern by pointing to a specific physical feature unique to quark stars: the finite surface density of the MIT bag EOS, which requires careful handling of the surface boundary conditions in the complex-frequency eigenvalue problem. Even though the paper cites Paper-I, which is peer-reviewed, the physical setup here is different (quark matter with a sharp surface vs. neutron-star matter), so the transfer of numerical techniques is not automatic. Independently, the paper does provide some positive evidence: the trends in Figures 4–9 are smooth and qualitatively consistent with known neutron-star f-mode behavior, and the fits have high R^2 values, suggesting internal consistency. The empirical relations also have only five fit parameters (c0–c3, d0–d3, etc. for each EOS), and the data span wide ranges in mass and tau, so the fit is not trivially underdetermined. Nonetheless, none of this guards against a systematic error in the underlying eigenvalues. The proposed benchmark directly tests the most fragile part of the pipeline—the solver's ability to handle the quark-star surface—and would settle whether the central claims are trustworthy. The verdict should remain conditional pending this validation; if the benchmark passes, the paper's conclusions would be substantially supported, and if it fails, the empirical formulas would need correction or retraction.","tokens_in":18595,"tokens_out":7324,"duration_ms":76149,"concrete_test":"Benchmark the inherited solver against independent quark-star f-mode calculations. Using the same MIT bag EOS (B = 56 MeV/fm^3) and the same mass-radius models, compute the l=2 polar f-mode frequency and damping time in the isotropic limit tau = 0 with an independently implemented perturbation code. A direct comparison target is the published isotropic quark-star result for a 1.4 M_sun star (e.g., Sotani & Harada 2003, Yip et al. 1999); both Re(omega) and Im(omega) should agree to within a few percent. In addition, run a numerical convergence test by doubling the radial grid resolution and checking that the complex eigenvalue stabilizes. If the benchmark matches and convergence is shown, the solver's surface treatment is reliable. If it does not match, the fitted C(tau), D(tau), J(tau), and K(tau) are unreliable, and the central scaling claims are unsupported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claims—the linear F versus sqrt(rho_avg) relation (Eq. 8–10) and the linear R^4/(T M^3) versus M/R relation (Eq. 9)—inherit every error in the complex f-mode eigenvalue omega. Section III states: 'We use the analytical expressions presented in Paper-I, as well as exactly same numerical techniques,' but does not reproduce the perturbation equations, boundary conditions, or any test-case validation. This deferral is especially problematic because quark stars differ structurally from the neutron stars in Paper-I: the MIT bag EOS (Eq. 3) has p_r = (rho - 4B)/3, so at the surface p_r = 0 but rho = 4B ≈ 2.5e14 g/cm^3, a genuine density discontinuity. A correct complex-frequency calculation requires matching the interior perturbation solution to the exterior outgoing-wave solution at the stellar surface, with proper junction conditions for the metric and fluid variables, including the vanishing Lagrangian pressure perturbation. If Paper-I's code was designed for neutron-star EOS tables where the surface density smoothly goes to zero, or if it silently assumes continuous density at the surface, then both Re(omega) (frequency) and especially Im(omega) (damping time) would be systematically wrong. Since all fitted coefficients (Tables I–IV) are anchored to these numerical eigenvalues, the reported quasi-universal scaling could be an artifact of solver error rather than a physical property of anisotropic quark stars. The paper also reports no error bars or convergence tests for the eigenvalues, so the statistical quality of the fits (R^2 ≈ 0.99) cannot compensate for a possible systematic surface-matching error.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies quadrupole (l=2) f-modes of non-rotating, anisotropic quark stars in full general relativity, using the Horvat ansatz for pressure anisotropy and two quark-matter equations of state: the MIT bag model and the interacting Dey-Bagchi EOS-A. Static configurations are obtained from the modified TOV equations and restricted to configurations with ∂M/∂ρ_c > 0 and non-negative tangential sound speed squared. The complex f-mode eigenfrequencies are computed with the numerical framework developed in the authors' earlier neutron-star paper (Paper-I), and are converted to frequency F = Re(ω)/(2π) and damping time T = 1/Im(ω). The central claims are: (i) F is approximately linear in the square root of the mean density, with slope C(τ) and intercept D(τ) that depend on the anisotropy parameter τ (Eqs. (8) and (10)), fitted as cubic polynomials in τ; (ii) the normalized inverse damping time R⁴/(TM³) is linear in compactness M/R, with slope J(τ) and intercept K(τ) fitted as quartic polynomials (Eq. (9)); and (iii) various monotonic and threshold-crossing trends of F and T with mass and τ hold for both EOSs. All final expressions are explicitly presented as semi-empirical fits calibrated to the authors' own numerical data; the perturbation equations, boundary conditions, and solver validation are deferred to Paper-I.","tokens_in":18932,"tokens_out":11257,"duration_ms":108638,"significance":"If the underlying complex-frequency calculations are correct, this paper extends the well-known quasi-universal f-mode scaling relations from isotropic neutron stars to anisotropic quark stars, using full general relativity rather than the Cowling approximation employed in earlier anisotropic quark-star studies. The two-EOS comparison (non-interacting MIT bag versus interacting EOS-A) and the physically motivated stability restrictions on the tangential sound speed give the study a clear scope, and the paper is commendably explicit that its final expressions are semi-empirical fits rather than derivations. The resulting relations (10) and (9), with the fitted coefficients in Tables I–IV, are falsifiable in the sense that future gravitational-wave observations of f-modes could test them, and they provide a practical mapping from (M, R, τ) to (F, T) for two benchmark EOSs. The quantitative impact is, however, conditional on verification of the inherited complex-frequency solver, which is not demonstrated in this manuscript.","major_comments":[{"comment":"Every reported value of F and T, and therefore every fitted coefficient in Tables I–IV, inherits the numerical complex eigenfrequency ω, but the perturbation equations, boundary conditions, and surface junction conditions are not reproduced here: §III states only that the authors 'use the analytical expressions presented in Paper-I, as well as exactly same numerical techniques.' This deferral is particularly consequential for the MIT bag EOS, whose surface has p_r = 0 at a finite energy density ρ = 4B (Eq. (3)), i.e., a genuine density discontinuity that must be handled in the matching to the outgoing-wave exterior. I therefore ask for a benchmark of the τ = 0 sequences against existing full-GR quark-star f-mode results (e.g., Sotani & Harada, Phys. Rev. D 68, 024019 (2003); Kojima & Sakata, Prog. Theor. Phys. 108, 801 (2002)), together with a grid-convergence statement for Re(ω) and Im(ω); the manuscript's central scaling claims cannot be assessed without it.","section":"III (first paragraph); IV (Tables I–IV)"},{"comment":"The selection of 'stable' configurations entering the fits is not unambiguous: §II.C defines two different boundaries (∂M/∂ρ_c = 0 and v_st² ≥ 0), but §IV.A says only that the fits cover 'a range of stable quark star masses, from 0.8 M_⊙ to the maximum stable mass' without stating which boundary is applied for each τ. Since the f-mode frequency tends to zero as a stellar model approaches the radial stability limit, the inclusion or exclusion of near-maximum-mass models materially affects both the claimed 'rapid growth for massive quark stars' and the fitted coefficients in Tables I–IV; please specify the criterion per τ and, ideally, show the sensitivity of the fits to dropping the outermost model.","section":"II.C; III.A; IV.A"},{"comment":"The reported coefficients of determination (0.9971 and 0.9972 for the frequency relations, 0.9988 and 0.9869 for the damping-time relations) are presented without stating which quantity enters Eq. (13): it is not clear whether R² measures the full two-stage expressions (10)–(12) and (9), (14)–(15) against all individual numerical values, or only the intermediate polynomial fits of C, D, J, K versus τ. Moreover, no numerical uncertainty is quoted for any individual F or T, so the scatter about the linear relations in Figs. 4 and 7 cannot be judged; for the EOS-A damping-time fit, R² = 0.9869 is noticeably lower and the authors should show whether the residuals are systematic (e.g., curvature) or random. Please specify the number of models per τ and give residual statistics.","section":"IV.A, Eq. (13); IV.B"},{"comment":"The manuscript is honest that the final expressions are semi-empirical, but the linear F–√ρ_avg relation and the polynomial forms for C, D, J, K are all chosen after inspecting and using the same numerical data; consequently, the verbs 'confirm' (abstract and §V) and the implied predictive scope of Eqs. (10) and (9) exceed what an in-sample calibration demonstrates. A simple holdout test (e.g., fitting the relations on one half of the mass range and evaluating the prediction on the other half) or a statement of the typical residual (in kHz and ms) would quantify the predictive content and is, in my view, necessary before the relations are recommended for asteroseismological use.","section":"Abstract; IV.A; V"}],"minor_comments":[{"comment":"The conclusion states the f-mode frequency range as 1.3–3.5 kHz, while the abstract and §III state 1.3–2.3 kHz for the MIT bag EOS and 1.8–3.4 kHz for EOS-A; please reconcile the 3.4 versus 3.5 discrepancy.","section":"Abstract vs. V"},{"comment":"Equation (10) mixes units implicitly: a reader cannot evaluate C(τ)√(3M/(4πR³)) unless told that M is in M_⊙, R is in km, and the coefficients in Tables I–IV are expressed in kHz per √(M_⊙/km³) and kHz; please state the units explicitly next to Eqs. (10) and (9).","section":"Eq. (10) and Tables I–II"},{"comment":"The text in §IV.A says the EOS-A fits use τ in the range −2 to 1.6, but Fig. 4 (right panel) and Fig. 7 (right panel) show sequences for τ = 2; please clarify whether τ = 2 models enter any of the fits or appear only in the figures.","section":"IV.A vs. Figs. 4–7"},{"comment":"The phrase 'the maximum stable mass decreases as the square of the tangential sound speed becomes negative' is imprecise; the models become unstable when v_st² < 0, and the wording should be corrected to say that the stable maximum mass is reduced by that instability condition.","section":"II.C"},{"comment":"There are several typographical and grammatical errors, including 'In the present, we extend' in §I, 'with using the MIT bag EOS' in the captions of Figs. 1 and 2, and inconsistent capitalization; a careful proofreading pass is needed.","section":"Throughout"},{"comment":"Since the paper's quantitative output consists of numerical eigenvalue sequences and fitted relations, the authors should consider providing the F and T values for every model as supplementary tables or machine-readable data files, rather than only 'on reasonable request,' to allow independent verification of the fits.","section":"VI. Data availability"}],"recommendation":"major_revision","confidential_remarks":"The central concern of this report—the unvalidated, unreproduced complex-frequency solver inherited from Paper-I—is consistent with the reader's conditional verdict, and it separates cleanly from the paper's stated aims: the scaling relations can stand only if the underlying eigenfrequencies are correct. I would ask the editor to require a self-contained statement of the perturbation equations and boundary conditions (or a full appendix), a τ = 0 benchmark against published isotropic quark-star results, and residual diagnostics for the fits before publication. I do not see a novelty or scope problem; the topic fits the journal well. One editorial note: the acknowledgment thanks 'the anonymous referee' for comments on 'the first version' of the manuscript, which reads oddly in what appears to be a first posting of this work; the authors may wish to verify that this is appropriate."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper is the first full-GR computation of f-modes in anisotropic quark stars, and it does what a good numerical asteroseismology paper should: two EOSs, a clean anisotropy ansatz, physically motivated stability cuts, and honest semi-empirical fits rather than overclaiming derivations. The central qualitative results—F linear in sqrt(rho_avg) with anisotropy-dependent slope/intercept, and damping time linear in compactness—are plausible and consistent with what Paper-I found for neutron stars. The high R^2 values are nice, but they only measure in-sample fit quality.\n\nThe main soft spot is that the perturbation equations, boundary conditions, and numerical solver are completely deferred to Paper-I. The authors say they use 'exactly same numerical techniques,' but they do not reproduce the equations or validate the solver for quark stars. This matters more than usual because the MIT bag EOS has a genuine density discontinuity at the surface: p_r = 0 while rho = 4B. If Paper-I's implementation was built for EOS tables with smoothly vanishing surface density, or does not handle the junction conditions for a finite surface density correctly, both Re(omega) and especially Im(omega) could be systematically wrong. The paper never addresses this. That is not proof of an error—the solver may well be fine, and many codes handle strange stars—but as written the reader cannot rule it out. Since all the fitted relations inherit these eigenvalues, this is a real condition on the results, not a cosmetic issue.\n\nTwo smaller issues: there are no error bars or convergence tests on the individual f-modes, and no code or data are provided beyond 'available on reasonable request.' The fits are in-sample; given the number of coefficients, the good R^2 is not a strong out-of-sample guarantee. I would not call any of this fatal—the paper is honest, the physics is sensible, and the trends are well explained—but it is not yet fully auditable.\n\nWho is this for? People building empirical relations for GW asteroseismology of exotic compact stars, and anyone who wants quark-star extensions of the neutron-star anisotropy work. I'd bring it to a reading group in that area. I'd send it to peer review without hesitation, but with a request that the authors either reproduce the perturbation system, validate against an independent code (or against known isotropic quark-star results), and report numerical uncertainties, or at minimum comment explicitly on the surface junction conditions.","headline":"First full-GR f-mode relations for anisotropic quark stars, but the solver is a black box; worth refereeing.","tokens_in":19489,"tokens_out":2420,"would_cite":true,"duration_ms":24690,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Quark-star f-mode frequencies follow a near-universal linear scaling with the square root of average density, with pressure anisotropy shifting the slope and intercept.","keywords":["anisotropic quark stars","f-mode oscillations","full general relativity","MIT bag equation of state","EOS-A","Horvat anisotropy","quasi-universal relations","gravitational-wave asteroseismology"],"falsifier":"Recompute the f-mode frequency and damping time for a fixed stable configuration, say a 1.4 $M_\\odot$ MIT-bag quark star with $\\tau=1$, using an independent full-GR perturbation code or a time-domain gravitational-wave extraction, and compare with the prediction of Eq. (8) plus Tables I and II. A deviation larger than the reported fit residuals would falsify the claimed scaling; likewise, computing a configuration with $\\tau$ outside the fitted ranges and checking whether the cubic polynomial for $C(\\tau)$ still predicts the numerical frequency would settle whether the relation is genuinely universal rather than a fit artifact.","tokens_in":18352,"feed_emoji":"🌊","tokens_out":6306,"duration_ms":61913,"temperature":0.7,"pith_summary":"This paper claims that the fundamental non-radial oscillation mode (f-mode) of quark stars in full general relativity obeys a simple scaling: the frequency is nearly linear in the square root of the star's average density, with the strength and sign of internal pressure anisotropy changing the slope and intercept. The authors solve the anisotropic Tolman-Oppenheimer-Volkoff equations for two quark-matter equations of state (the MIT bag model and the interacting EOS-A), then compute l=2 f-mode frequencies and damping times using a full-GR perturbation solver developed in their earlier neutron-star paper. They find frequencies of about 1.3--2.3 kHz for the MIT bag EOS and 1.8--3.4 kHz for EOS-A, with damping times from 60 to 900 ms. They also find that the inverse normalized damping time $R^4/(T M^3)$ falls linearly with compactness $M/R$, and they package both trends into semi-empirical formulas with cubic and quartic dependence on the anisotropy parameter. If right, the same quasi-universal relations known for neutron stars extend to quark stars, giving gravitational-wave astronomers a way to estimate mass, radius, and anisotropy from a measured f-mode.","feed_headline":"Anisotropic quark stars keep a universal f-mode density law","feed_subtitle":"Full-gravity models put quark-star quake frequencies at 1.3–3.4 kHz, with anisotropy changing the slope.","key_machinery":"The load-bearing objects are the two quark-matter equations of state, the Horvat ansatz for pressure anisotropy, and the full-GR f-mode solver carried over from the authors' earlier neutron-star work. The MIT bag EOS is $p_r = (1/3)(\\rho - 4B)$ with $B=56$ MeV fm$^{-3}$; EOS-A comes from a relativistic Hartree-Fock calculation with a modified Richardson potential and density-dependent quark masses. Anisotropy is imposed as $\\chi = \\tau p_r \\mu$, with $\\mu = 2m/r$ the local compactness, so the anisotropy vanishes at the center and in the Newtonian limit. The complex mode frequency $\\omega$ enters through $F = \\mathrm{Re}(\\omega)/(2\\pi)$ and $T = 1/\\mathrm{Im}(\\omega)$, and the numerical machinery solves the linearized Einstein equations on the anisotropic background to produce the frequencies and damping times that are then fit to the two scaling relations. That machinery is doing all the work: the paper's conclusions ride on its accuracy.","core_discovery":"The paper's central discovery is that anisotropy enters the f-mode signature of quark stars in a structured, predictable way. For both equations of state, the f-mode frequency $F$ satisfies $F(M,R,\\tau) \\approx C(\\tau) \\sqrt{3M/(4\\pi R^3)} + D(\\tau)$, where $\\tau$ is the dimensionless Horvat anisotropy strength and $C(\\tau)$, $D(\\tau)$ are well described by cubic polynomials; the coefficient of determination is above 0.997. The inverse normalized damping time $R^4/(T M^3)$ is linear in compactness $M/R$, with slope $J(\\tau)$ and intercept $K(\\tau)$ fitted to quartic polynomials ($R^2 \\approx 0.999$ and 0.987 for the two EOSs). The sign of anisotropy matters physically: positive $\\tau$ (tangential pressure greater than radial) raises the frequency for low and intermediate masses and shortens the damping time, while strongly negative $\\tau$ can make the frequency fall with mass and lengthen damping dramatically. The paper thus claims that the neutron-star quasi-universal f-mode scaling survives in quark stars and carries an anisotropy fingerprint.","pith_inferences":["The same fitting procedure could be applied to other quark-matter EOSs to test whether the coefficients $C(\\tau)$ and $D(\\tau)$ themselves depend on EOS parameters such as the bag constant or interaction strength; if they cluster, the relation might be even more universal than the paper claims.","Because the paper finds that configurations with $\\tau > 1$ become unphysical through negative tangential sound speed, astrophysical applications should probably restrict the fitted relations to $\\tau \\le 1$, a limitation not emphasized in the body of the paper.","If future work maps the anisotropy parameter $\\tau$ to microphysical sources such as viscosity or magnetic fields, the observed sign-dependent frequency shifts could indirectly constrain those interior properties.","The scaling $F \\propto \\sqrt{M/R^3}$ suggests a possible route to extending these relations to rotating or post-merger remnants, but that extension remains speculative and is not tested here."],"forward_implications":["A measured f-mode frequency and damping time from a quark-star candidate could be fed into the paper's formulas to estimate mass, radius, and anisotropy strength directly.","The two equations of state occupy distinct bands, 1.3--2.3 kHz versus 1.8--3.4 kHz, so a future gravitational-wave detection could help discriminate non-interacting from interacting quark matter.","The damping-time difference between positive and negative anisotropy, up to roughly a factor of two to three at fixed mass, provides a potential observable probe of whether tangential pressure exceeds radial pressure inside the star.","The fit quality above $R^2 \\approx 0.99$ suggests the relations are tight enough to use as practical asteroseismology tools rather than rough order-of-magnitude estimates."],"supporting_citations":[{"why":"Called Paper-I in the text; supplies the full-GR perturbation equations, numerical techniques, and definitions of frequency and damping time that the quark-star computation inherits.","marker":"[47]"},{"why":"Provides the Horvat ansatz $\\chi = \\tau p_r \\mu$ used to model pressure anisotropy throughout the paper.","marker":"[63]"},{"why":"Original strange quark matter EOS with the Richardson potential from which the EOS-A family descends.","marker":"[57]"},{"why":"Improved EOS set by Bagchi et al.; the specific EOS-A used in the paper is taken from this work.","marker":"[58]"},{"why":"Earlier quark-star f-mode study with the MIT bag EOS; supplies the bag constant setting and context for the full-GR frequencies reported here.","marker":"[51]"},{"why":"Establishes the $R^4/M^3$ scaling of the f-mode damping time that motivates the normalized damping-time analysis.","marker":"[68]"},{"why":"Provides the linear relation between inverse normalized damping time and compactness used as the fitting framework for Eq. (9).","marker":"[69]"}],"fun_headline_variants":["Quark star f-modes: anisotropy sets the slope","Anisotropy rewrites quark star quake signature","Full GR: quark star oscillations obey altered scaling","Anisotropy shifts quark star quake frequencies","Quark star f-modes: universal law, anisotropic twist"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The paper's numbers all depend on the assumption that the full-general-relativity f-mode solver developed in the authors' earlier neutron-star paper is accurate for anisotropic quark stars with the Horvat ansatz; the perturbation equations, boundary conditions, and test-case checks are not reproduced here, so if that solver is wrong or does not carry over, every frequency, damping time, and fitted coefficient in this paper would be invalid.","fun_headline_variants_meta":{"raw":{"variants":["Quark star f-modes: anisotropy sets the slope","Anisotropy rewrites quark star quake signature","Full GR: quark star oscillations obey altered scaling","Anisotropy shifts quark star quake frequencies","Quark star f-modes: universal law, anisotropic twist"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00041,"raw_usage":{"total_tokens":2220,"prompt_tokens":1138,"completion_tokens":1082,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":754,"completion_tokens_details":{"reasoning_tokens":1005}},"tokens_in":754,"tokens_out":1082,"duration_ms":10762,"temperature":1.0,"reasoning_tokens":1005,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T05:25:10.594574+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the f-mode frequency and damping time for a fixed stable configuration, say a 1.4 $M_\\odot$ MIT-bag quark star with $\\tau=1$, using an independent full-GR perturbation code or a time-domain gravitational-wave extraction, and compare with the prediction of Eq. (8) plus Tables I and II. A deviation larger than the reported fit residuals would falsify the claimed scaling; likewise, computing a configuration with $\\tau$ outside the fitted ranges and checking whether the cubic polynomial for $C(\\tau)$ still predicts the numerical frequency would settle whether the relation is genuinely universal rather than a fit artifact.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Called Paper-I in the text; supplies the full-GR perturbation equations, numerical techniques, and definitions of frequency and damping time that the quark-star computation inherits."},{"cited_title":"A model finding a new Richardson potential with different scales for confinement and asymptotic freedom, by fitting the properties of ${\\D}^{++}$ and ${\\Om}^{-}$","cited_arxiv_id":"hep-ph/0405194","evidence_quote":"Provides the Horvat ansatz $\\chi = \\tau p_r \\mu$ used to model pressure anisotropy throughout the paper."},{"cited_title":"Recycling strange stars to millisecond periods","cited_arxiv_id":"astro-ph/0111162","evidence_quote":"Improved EOS set by Bagchi et al.; the specific EOS-A used in the paper is taken from this work."},{"cited_title":"Accuracy of relativistic Cowling approximation in protoneutron star asteroseismology","cited_arxiv_id":"2009.05206","evidence_quote":"Earlier quark-star f-mode study with the MIT bag EOS; supplies the bag constant setting and context for the full-GR frequencies reported here."}],"review_version":1}