{"id":"dc4c315b-97d3-489e-a42b-5777d9a21656","arxiv_id":"2504.21348","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":2.0,"correctness_risk":"high","formal_verification":"none","parameter_count":2,"one_line_summary":"Anisotropic compact star models in linear f(Q,T) gravity are claimed to be viable and stable, but the supporting formulas are internally inconsistent and depend on hand-picked parameters.","lead":"The paper models four observed compact stars as anisotropic spheres in a modified gravity called f(Q,T), using a simple linear model and a standard metric ansatz. The authors conclude the stars are viable and stable, but the printed equations contain internal contradictions and the model parameters are chosen by hand.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Equations (35)-(37) cannot be derived from the generic system (31)-(33) with f=hQ+kT; the h^2 and 2k^2+k-1 denominators are algebraically impossible, so the plots built on them are unverified.","rationale":"This stress-test pass focused on whether the central claim—that the four compact stars are physically viable and stable—is actually established. The most load-bearing link is the explicit field equations (35)-(37), because every subsequent plot and stability criterion is a function of those expressions. The reader's weakest assumption identifies exactly this link, and the printed equations contain a concrete algebraic red flag: the density denominator contains h^2 while the pressure denominators contain k^2, even though h enters the original system (31)-(33) only through multiplicative factors in front of geometric terms. Since f_QQ=0, no term proportional to h can appear in the coefficient matrix of the linear system; hence after a legitimate solve, h can only rescale the numerators. The appearance of h^2 in a denominator indicates that the explicit equations were not obtained by a straightforward algebraic reduction of (31)-(33). This is an internal inconsistency, not a disagreement with external consensus, so it directly undermines the central claim. I grant that the paper includes standard f(Q,T) framework material and a valid matching solution (the constants (40) are consistent with the correct first derivative of the Schwarzschild exterior even though the printed derivative condition has a factor-2 typo). Those elements do not rescue the field-equation reduction. The identical printed formulas for ωr/ωt and Γr/Γt, despite the anisotropic pressures, are additional symptoms of the same unreliability, but the field-equation break is the load-bearing one. Since the computation cannot be reproduced from the printed equations, and no alternative derivation or code is provided, the central claim is unverified. I therefore recommend keeping the reader's REJECT verdict unchanged.","tokens_in":16606,"tokens_out":8637,"duration_ms":81487,"concrete_test":"Use a computer algebra system to substitute f(Q,T)=hQ+kT, with f_Q=h, f_QQ=0, f_T=k, into Eqs. (31)-(33), treating ρ, p_r, p_t as unknowns. Solve the resulting linear system and compare every coefficient with Eqs. (35)-(37). As a numerical cross-check, evaluate both the solved and printed expressions at, say, r=R/2 for one Table 1 star with h=2, k=3; any difference in the density or pressure values identifies the break in the derivation chain. If the printed (35)-(37) do not reproduce the solved system, the figures and stability conclusions in Sections 3-4 are not supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that the four compact stars in Table 1 are physically viable and stable rests on the explicit field equations (35)-(37), which were obtained by inserting f(Q,T)=hQ+kT (Eq. 34) into the generic equations (31)-(33). This reduction is not algebraically consistent. Because f_QQ=0, f_Q=h and f_T=k, the system (31)-(33) is linear in the fluid variables, and h appears only in the inhomogeneous geometric terms (hQ and the h(...) brackets). It cannot appear in the denominators of the solved expressions. The denominator '2h^2+k-1' in (35), and '2k^2+k-1' in (36) and (37), are therefore impossible from a correct solve of (31)-(33). A correct 3x3 linear solve would produce denominators that are functions of k alone, e.g. factors like 1+3k/2 from the kT trace terms. No derivation of (35)-(37) is given in the paper, and the printed formulas are the sole basis for Figures 2-10, the energy conditions, the TOV equilibrium, the causality condition, and the adiabatic-index stability analysis. If (35)-(37) are not correct, the central claim is unsubstantiated regardless of the graphical output.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript constructs anisotropic compact star models in f(Q,T)=hQ+kT extended symmetric teleparallel gravity. Starting from the generic field equations (31)-(33), the authors adopt the linear model (34), the metric ansatz (38), fix the constants a,b,c by matching to the observed masses and radii of four compact stars (Table 1), and then examine energy conditions, EoS parameters, TOV equilibrium, causality, and adiabatic stability (Sections 3-4). The conclusion is that all four proposed stars are physically viable and stable. The paper also includes appendices deriving the non-metricity scalar Q and its variation.","tokens_in":16889,"tokens_out":9210,"duration_ms":89288,"significance":"If the explicit field equations (35)-(37) were correct, the paper would be a standard application of the f(Q,T) framework to neutron-star-like objects, one of many such ansatz-based studies. The use of four observational data sets and the explicit appendices for Q are useful. However, the central technical step—the reduction of the generic field equations to the explicit expressions—is algebraically inconsistent, and the EoS and adiabatic-index formulas are identical for the radial and tangential components despite the claimed anisotropy. As a result, the plots and the conclusion of viability and stability are not supported. The manuscript therefore does not meet the standard for publication in its present form.","major_comments":[{"comment":"The explicit field equations cannot be obtained from the generic system (31)-(33) with f(Q,T)=hQ+kT. Substituting f_Q=h, f_T=k, f_QQ=0 into (31)-(33) gives a system that is linear in (rho,p_r,p_t), with the fluid-coupling matrix depending only on k; for the signs shown, the determinant is (1+k)^2, so the denominators of the solved expressions can contain only k (e.g., factors (1+k)^2), not h or h^2. The displayed denominator 2h^2+k-1 in (35) and 2k^2+k-1 in (36)-(37) is therefore algebraically impossible, and the manuscript gives no derivation of these equations. Because (35)-(37) are the basis for Figures 2-10 and all subsequent physical conclusions, the central claim is unsupported.","section":"Section 2, Eqs. (35)-(37)"},{"comment":"The radial and tangential EoS parameters omega_r and omega_t are printed with identical expressions, and the adiabatic indices Gamma_r and Gamma_t in (46)-(47) are also identical. This is inconsistent with the anisotropic matter model (30) and with the reported finding p_t > p_r. Either the anisotropic reduction is incorrect, or the printed stability formulas are wrong; in either case the causality and adiabatic-index stability analysis (Figures 9-10) and the anisotropy-based TOV analysis (Figure 8) are not valid.","section":"Section 3.3 and Section 4.2"},{"comment":"The TOV equilibrium condition is not stated as an equation: the display reads 'MG(r)/r^2 (rho+pr)e^{(xi-eta)/2} + p'_r - 2Delta/r ,' with no '=0', and the text then refers to 'Equation (??)'. The missing equation and broken cross-reference prevent verification of the force-balance calculation. This is a load-bearing part of the equilibrium claim and must be corrected.","section":"Section 3.5"},{"comment":"The constants a,b,c are fixed by matching to the observed mass and radius of each star, and the subsequent checks are performed on the same fitted solution. Describing these checks as 'predictions' (abstract, Section 5) overstates their status; they are internal consistency tests of the ansatz. The conclusions should be rephrased accordingly.","section":"Section 2 (Table 1, Eq. (40)) and Section 5"}],"minor_comments":[{"comment":"The line 'The variation of Eq.(45) yields' refers to an equation number that does not exist; the intended reference is likely Eq. (21).","section":"Section 2"},{"comment":"The TOV expression is missing a right-hand side ('=0') and the cross-reference 'Equation (??)' is broken.","section":"Section 3.5"},{"comment":"The sentence 'the difference between ust and ust' should read 'the difference |u_t^2 - u_r^2|' or similar.","section":"Section 4.1"},{"comment":"The notation f(Q,T) and f (Q, T) is used inconsistently; please standardize.","section":"Throughout"},{"comment":"The colors mentioned in the text (gray, pink, green, brown) are not visible in a grayscale rendering; the caption should identify the curves explicitly.","section":"Figure 1"},{"comment":"The bibliographic details of entries [66] and [67] appear to overlap (both Eur. Phys. J. C 83 (2023) 1088); please verify these references.","section":"References"}],"recommendation":"reject","confidential_remarks":"The manuscript is internally inconsistent at the level of its central equations, so the rejection is technical rather than a disagreement with the f(Q,T) program. The paper is an ansatz-based application in a crowded literature, and the algebraic error is decisive. I would not recommend resubmission unless the authors fully re-derive the field equations and redo all figures and stability tests."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's the bottom line: this is a by-the-numbers f(Q,T) compact-star paper, and the central claim—that the four stars are viable and stable—does not survive contact with the field equations.\n\nWhat the paper does well: it follows the standard recipe completely. It writes down the f(Q,T) action, chooses the linear model f = hQ + kT, uses a Tolman ansatz, matches to the Schwarzschild exterior, and runs the usual battery of checks: energy conditions, TOV equilibrium, causality via sound speeds, adiabatic index. The figures are clean and the qualitative behavior is plausible. If the equations were right, this would be a serviceable application of the method.\n\nThe problem is that the equations are not right. Equations (35)-(37) are presented as the explicit field equations for f = hQ + kT, but they cannot follow from the generic system (31)-(33). With f_QQ = 0 and f_Q = h, the system is linear in ρ, p_r, p_t, and the only fluid coupling is through kT and f_T terms, so h appears only in the geometric source terms. It cannot appear in any denominator. The denominator 2h^2 + k - 1 in (35) is therefore impossible, and the different denominator 2k^2 + k - 1 in (36)-(37) is a red flag that something was copied or typed incorrectly. No derivation is given, and every figure and conclusion depends on these formulas. On top of that, the printed EoS parameters ω_r and ω_t are identical, and the adiabatic indices Γ_r and Γ_t are identical, even though the model is explicitly anisotropic and the paper claims p_t > p_r. That is a copy-paste error, not a physical result. The matching condition has a factor-of-2 typo (derivative of the exterior metric should be 2m/R^2, not m/R^2), though the constants they solve for are actually consistent with the correct condition.\n\nNone of this is rescued by the parameter choice: h=2, k=3 are chosen by hand, and no uncertainty or sensitivity analysis is given. The stability analysis is applied to the same constructed solution, so it is not an independent prediction.\n\nFor whom is this paper? Someone collecting yet another example in the f(Q,T) stellar catalogue might find it useful, but only after the algebra is corrected. As submitted, the load-bearing derivation is broken, so I would desk-reject rather than send it to referees. The authors can redo the algebra and resubmit.","headline":"A routine f(Q,T) compact-star paper whose explicit field equations are algebraically impossible, so the central stability claim is unverified.","tokens_in":17431,"tokens_out":8003,"would_cite":false,"duration_ms":69992,"reading_group":"no","serious_thinker":"no","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["97.10.Cv","04.50.Kd","97.60.Jd","04.20.Jb"],"model":"deepseek-v4-flash","headline":"The paper argues that four known compact stars can be modeled as stable anisotropic spheres in f(Q,T) gravity, with matter that satisfies every energy condition and stability test.","keywords":["compact stars","anisotropic fluid spheres","f(Q,T) gravity","non-metricity","energy conditions","sound speed stability","adiabatic index","stellar equilibrium"],"falsifier":"Re-derive the explicit density and pressure formulas from the general field equations by direct substitution of $f=hQ+kT$; the printed equations give density a denominator $2h^2+k-1$ while both pressures carry $2k^2+k-1$, so a single correct substitution should settle whether the system is consistent.","tokens_in":16344,"feed_emoji":"⭐","tokens_out":11490,"duration_ms":103520,"temperature":0.7,"pith_summary":"This paper tries to establish that four observed compact stars—Vela X-1, 4U 1608-52, PSR J1903+327, and PSR J1614-2230—can be described as anisotropic fluid spheres in $f(Q,T)$ gravity, an extended theory in which gravity is carried by non-metricity and coupled to the trace of the energy-momentum tensor. Using a linear model $f(Q,T)=hQ+kT$ and a prescribed metric ansatz, the authors derive explicit density and pressure profiles, fix the free constants by matching the interior metric to the exterior spacetime at the stellar surface, and then check the standard physical criteria. They report that the energy conditions hold, the forces in the stellar equilibrium condition balance, the sound speeds are causal, and the adiabatic index exceeds the stability bound, so the stars are physically viable and stable. A sympathetic reader would care because this is evidence that a non-metricity-based modification of general relativity can accommodate realistic neutron-star masses and radii without exotic matter.","feed_headline":"Four compact stars pass every stability test in f(Q,T) gravity","feed_subtitle":"Energy conditions, force balance, causality, and adiabatic index all hold for the four stars.","key_machinery":"The central object is the linear model $f(Q,T)=hQ+kT$, where $Q$ is non-metricity (the failure of the connection to preserve the metric tensor) and $T$ is the trace of the energy-momentum tensor. From the variational field equations, the paper writes explicit density and pressure formulas in terms of the metric functions $\\xi(r)$ and $\\eta(r)$; substituting the ansatz turns those formulas into closed expressions for $\\rho$, $p_r$, and $p_t$. Surface matching conditions fix the three constants from each star's observed mass and radius, and the resulting profiles are then fed into the energy conditions, equilibrium, sound-speed, and adiabatic-index tests. The load-bearing device is therefore the linear $f(Q,T)$ model together with this specific metric ansatz: it is what converts a complicated modified-gravity system into testable stellar profiles.","core_discovery":"On the paper's own terms, the central discovery is that the chosen metric ansatz with the constants fixed by the junction conditions produces anisotropic compact-star solutions in $f(Q,T)$ gravity whose matter variables are regular and decreasing, satisfy the null, weak, strong, and dominant energy conditions, obey the equilibrium condition, and lie within the causality and adiabatic-index stability windows. The density and both pressures peak at the center and fall toward the boundary; tangential pressure exceeds radial pressure, so the anisotropy is positive and repulsive. The mass function rises monotonically, and the compactness and surface redshift stay below the standard bounds. The conclusion is stated as unconditional: the proposed compact stars in the $f(Q,T)$ framework are physically viable and stable.","pith_inferences":["If the field equations are correct, the linear $f(Q,T)$ model with the chosen parameters becomes a tunable extension of general relativity; scanning $h$ and $k$ against a larger catalog of neutron stars could map which modifications are compatible with observation.","The same ansatz could be inverted to extract an approximate equation of state $\\rho(p_r)$ from each fitted star, something the paper does not do; a derived equation of state would connect the model to nuclear-matter predictions.","Treating $k$ as a free parameter rather than fixing it ahead of the plots would test how strongly the viability conclusion depends on the matter coupling."],"forward_implications":["Vela X-1, 4U 1608-52, PSR J1903+327, and PSR J1614-2230 can each be fitted by the same two-function ansatz with constants determined from their observed mass and radius.","The matter in these fits is ordinary: all four energy conditions hold throughout the interior.","The configurations are in hydrostatic equilibrium: the gravitational, hydrostatic, and anisotropic forces sum to zero at every radius.","The models are causally stable and resist radial collapse: sound speeds lie in $[0,1]$, their difference obeys the cracking condition, and the adiabatic index stays above $4/3$.","Compactness and surface redshift respect the standard bounds, so the stars are neither too compact nor produce unphysically large redshift."],"supporting_citations":[{"why":"Supplies the $f(Q,T)$ gravity action and the field equations that the paper starts from.","marker":"[4]"},{"why":"Motivates the linear model $f(Q,T)=hQ+kT$ and the parameter values used in the plots.","marker":"[94]"},{"why":"Supplies the metric ansatz for the interior spacetime of the stars.","marker":"[95]"},{"why":"Provides Vela X-1's observed mass and radius used in Table 1.","marker":"[96]"},{"why":"Provides 4U 1608-52's observed mass and radius used in Table 1.","marker":"[97]"},{"why":"Provides PSR J1903+327's observed mass and radius used in Table 1.","marker":"[98]"},{"why":"Provides PSR J1614-2230's observed mass and radius used in Table 1.","marker":"[99]"},{"why":"Supplies the equilibrium condition that the paper uses to test force balance.","marker":"[102]"},{"why":"Supplies the sound-speed range and cracking condition used for causality stability.","marker":"[103]"},{"why":"Supplies the adiabatic-index bound used to test stability against collapse.","marker":"[104]"}],"fun_headline_variants":["Anisotropic stars pass every test in f(Q,T) gravity","Stable compact stars emerge in extended teleparallel gravity","f(Q,T) theory yields physically viable anisotropic spheres","Compact stars remain stable under f(Q,T) modifications"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The entire analysis rests on the unshown algebra that turns the general $f(Q,T)$ field equations into the explicit density and pressure formulas; if those formulas are wrong, every graph and stability conclusion built on them fails.","fun_headline_variants_meta":{"raw":{"variants":["Anisotropic stars pass every test in f(Q,T) gravity","Stable compact stars emerge in extended teleparallel gravity","f(Q,T) theory yields physically viable anisotropic spheres","Compact stars remain stable under f(Q,T) modifications"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000154,"raw_usage":{"total_tokens":1149,"prompt_tokens":821,"completion_tokens":328,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":437,"completion_tokens_details":{"reasoning_tokens":262}},"tokens_in":437,"tokens_out":328,"duration_ms":4049,"temperature":1.0,"reasoning_tokens":262,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T05:07:01.241721+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-derive the explicit density and pressure formulas from the general field equations by direct substitution of $f=hQ+kT$; the printed equations give density a denominator $2h^2+k-1$ while both pressures carry $2k^2+k-1$, so a single correct substitution should settle whether the system is consistent.","supporting_citations":[{"cited_title":"and Koivisto, T.: J","cited_arxiv_id":null,"evidence_quote":"Motivates the linear model $f(Q,T)=hQ+kT$ and the parameter values used in the plots."},{"cited_title":"et al.: Astrophys","cited_arxiv_id":null,"evidence_quote":"Provides Vela X-1's observed mass and radius used in Table 1."}],"review_version":1}