{"id":"7b375175-4237-4596-af2a-41daf98fcad3","arxiv_id":"2509.02641","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":3.0,"correctness_risk":"high","formal_verification":"none","parameter_count":6,"one_line_summary":"The authors assert that an anisotropic Krori-Barua model in f(Q,T) gravity describes pulsar SAX J1748.9-2021, but misspecified parameters and unphysical densities leave the assertion unsupported.","lead":"A study applies an exotic modified gravity (f(Q,T)) to pulsar SAX J1748.9-2021 and claims the resulting star model is stable and consistent with observations. The claim is not supported: the model's parameters are partly hidden and its central density is wildly larger than that of any known neutron star.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Metric constant a=-2 is incompatible with the Schwarzschild junction conditions: at r=R it gives e^-2=0.135 while (1-2M/R)^-1>1, so the interior never matches the exterior; the viability claim rests on an invalid boundary.","rationale":"I read the paper as claiming a stable anisotropic KB star in f(Q,T)=ζQ+ηT gravity, matched to an exterior Schwarzschild metric via junction conditions and consistent with SAX J1748.9-2021. The reader's REJECT verdict is well supported. Among the listed concerns (unreported η, hand-assigned constants, mass mismatch), I judge the boundary mismatch to be the single most load-bearing because it is a direct contradiction between Eqs. (34)-(35) and the value a=-2 adopted in Section 4.1. It does not depend on any free parameter or numerical code, and it is robust to all quoted observational uncertainties in M and R. If a is not meant to satisfy the junction condition, then the paper's statement that junction conditions fix the constants is false and the exterior matching is absent. The proposed one-line substitution settles the issue. Since this reinforces the existing REJECT verdict rather than changing it, I keep the reader's verdict unchanged.","tokens_in":34187,"tokens_out":9985,"duration_ms":106330,"concrete_test":"Evaluate the boundary condition Eq. (35) with the paper's constants: a=-2 gives e^{β(R)}=e^{-2}=0.1353. Since u=2M/R is positive and <1 for any physical star, the Schwarzschild g_rr component is (1-u)^{-1}>1; the two cannot match. For the quoted SAX J1748.9-2021 values (M≈1.81 M⊙, R≈13.4 km in geometric units, u≈0.399), the required β(R) is ≈0.51, not -2. Equivalently, solve a=-ln(1-u) for any M,R in the observed ranges and compare with -2; the mismatch persists for all of them.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The most load-bearing flaw is internal: the chosen KB constant a=-2 cannot satisfy the junction conditions that the paper says determine the constants. Section 3.2 (Eqs. 34-35) requires β(R)=-ln(1-u) with u=2GM/(c^2R). For any physical stellar mass, 0<u<1, so β(R)>0. Section 4.1 sets a=-2, hence β(R)=-2. Then e^{β(R)}=e^{-2}≈0.135, whereas the Schwarzschild g_rr component is (1-u)^{-1}>1. Equivalently, solving -ln(1-u)=-2 gives u=1-e^2<0, which is unphysical. Thus g_rr is discontinuous at r=R and the interior KB metric is not matched to the exterior Schwarzschild metric. Every subsequent energy-condition, causality, adiabatic-index, TOV, and compactness check is performed on an interior solution that has not been attached to the exterior spacetime. This failure is independent of the also-unstated coupling η and of the ζ scan, and it is directly checkable from the paper's own equations.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper constructs an anisotropic stellar model in f(Q,T)=ζQ+ηT gravity using the Krori-Barua metric ansatz, and attempts to validate it against observations of the pulsar SAX J1748.9-2021. The authors derive field equations from the action, match the interior to a Schwarzschild exterior via junction conditions, and then check a battery of physical criteria: energy conditions, causality, adiabatic index, TOV equilibrium, Zeldovich condition, redshift, and compactness. The central claim is that the model configuration is physically viable and stable and that it reproduces the observed pulsar.","tokens_in":34450,"tokens_out":5681,"duration_ms":61411,"significance":"If the central claim were sound, the paper would provide a concrete example of a stable anisotropic pulsar in f(Q,T) gravity constrained by real observational data, which would be a useful contribution to the modified-gravity stellar structure literature. The paper has some strengths: the field equations are derived from a variational principle, the junction-condition formalism is invoked explicitly, and the set of checks (energy conditions, causality, TOV, adiabatic index, Buchdahl) is extensive. However, the numerical implementation contains multiple load-bearing inconsistencies that invalidate the claim, as detailed in the major comments. The manuscript is not suitable for publication in its present form.","major_comments":[{"comment":"The junction condition for the radial metric potential is e^{β(R)}=(1-2GM/R)^{-1}. The paper sets a=-2 in Eq. (31), so e^{β(R)}=e^{-2}≈0.135. For any physical star, 0<2M/R<1, hence (1-2M/R)^{-1}>1. The two sides can never match; solving gives 2M/R=1-e^2<0, which is unphysical. Thus the interior KB spacetime is not matched to the exterior Schwarzschild spacetime at r=R, and every subsequent physical check is performed on an interior solution that has not been embedded in an exterior geometry.","section":"Section 3.2, Eq. (34) and Section 4.1"},{"comment":"The mass function shown in Figure 3 reaches M≈3 M_⊙ already in the plotted range r≈8 km for ζ=1.08. The observed mass of SAX J1748.9-2021 is M=1.81±0.3 M_⊙ with R=11.7±1.7 km. The paper never quotes M(R) at R=13.4 km, and the plot does not extend to the stellar surface. The model therefore does not reproduce the observed mass-radius point, undermining the headline claim that the model is validated by the pulsar's observations.","section":"Section 4.1 and Figure 3"},{"comment":"The central density is reported as ρ_core≈8.93×10^27 g/cm³ (for ζ=1.08), which is about 10^13 times the nuclear saturation density (≈2.8×10^14 g/cm³). The boundary density is also quoted as ≈5.69×10^27 g/cm³. An object with these densities is not a neutron star or pulsar in any standard equation-of-state picture. The identification of this configuration as a pulsar is therefore physically unsupported, and the paper's own numbers contradict its interpretation.","section":"Section 4.1, Table 2"},{"comment":"The model function is f(Q,T)=ζQ+ηT, and all field-equation expressions depend on both ζ and η. The paper fixes ζ=1, 1.04, 1.08, but never assigns a numerical value to η anywhere, including in Table 2 and the figures. The quantitative results are therefore not reproducible. In addition, the constants A1=2, a1=0, a=-2 and R=13.4 km are stated by hand; R=13.4 km is explicitly chosen because lower values 'led to deviations from the expected behavior' rather than being derived from the junction conditions or matched to the observed mass and radius. This circular selection of parameters means the checks are performed on a fine-tuned configuration rather than a predictive model.","section":"Eq. (27) and Section 4.1"}],"minor_comments":[{"comment":"The text states that at the boundary ρI is 5.69×10^27 g/cm³, 'which is about 1.8 times the core density.' For ζ=1.08, the ratio is 5.69/8.93≈0.64, not 1.8. In Section 5, the same symbol ρI is used for the surface density in the linear EoS and given as 5.4×10^14 g/cm³, a discrepancy of 13 orders of magnitude with the boundary density quoted in Section 4.1.","section":"Section 4.1"},{"comment":"The Zeldovich condition is quoted for the ratio P(0)/ρ(0), and the paper reports Pr(0)/ρ(0)=-0.0842. A negative central radial pressure is inconsistent with the positive core pressure listed in Table 2; the sign suggests an algebraic error or an inconsistent choice of parameters in the limits.","section":"Section 4.4"},{"comment":"The caption of the second panel lists ζ=2, 2.02, 2.04 for P_r, while the text and the other panels use ζ=1, 1.04, 1.08. This is a clear caption inconsistency.","section":"Figure 1"},{"comment":"The torsion tensor is written as T^λ_{ξ̺} = 1/2(hatΓ^λ_{ξ̺} - hatΓ^λ_{ξ̺}); the second term should be hatΓ^λ_{̺ξ}. Also, Eq. (32) writes 'dθ + sin^2θ dφ^2' instead of 'dθ^2 + sin^2θ dφ^2'.","section":"Eq. (5)"},{"comment":"The heading 'Casuality Condition' is a typo for 'Causality Condition'.","section":"Appendix A"},{"comment":"The text quotes the cracking condition as 0≤|v_t²−v_r²|≤1, but then reports −0.79<v_t²−v_r²<−0.37. This is fine for the absolute value, but the phrasing is confusing and should be clarified.","section":"Section 4.6"}],"recommendation":"reject","confidential_remarks":"The paper is a routine application of the Krori-Barua ansatz in f(Q,T) gravity, but it contains fundamental numerical inconsistencies: the chosen metric constant a=-2 cannot satisfy the junction conditions, the mass-radius output does not match the claimed pulsar observations, and the central density is unphysically large for a neutron star. These are not merely presentational; they invalidate the central claim. The refereeing process has not uncovered any mitigating contribution that would justify a major revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is the same f(Q,T)=ζQ+ηT model, Krori-Barua ansatz, and the same stability checklist as the authors' earlier papers, applied to a different pulsar. The only new thing is the input mass and radius, so the scientific increment is small.\n\nFair credit: the paper does derive the field equations from an action, writes out analytic expressions for density, pressures, anisotropy, sound speeds, and runs the standard battery of checks: energy conditions, causality, adiabatic index, TOV, Zeldovich, Buchdahl. The algebra is heavy and the presentation is clear. If you need a worked example of the mechanics of f(Q,T) stellar models, this is readable.\n\nBut the central claim fails on the paper's own equations. Section 3.2 states the matching condition β(R) = -ln(1-u) with u>0, so β(R) must be positive. Section 4.1 sets a=-2, so β(R)=-2 and e^{β(R)}=0.135, while the Schwarzschild g_rr is (1-u)^{-1}>1. The interior and exterior do not match. Every subsequent check is applied to a solution that is not attached to the exterior spacetime. This is a load-bearing flaw, not a typo.\n\nOther problems pile up. The central density is ~10^27-10^28 g/cm^3, about 10^13 times nuclear saturation, so calling this a neutron star is not credible. The mass function plotted to 8 km already exceeds the observed 1.81 M⊙. The Zeldovich ratio Pr(0)/ρ(0) is reported as -0.0842, contradicting the positive central radial pressure in Table 2. The coupling η is never assigned a numerical value, so the plots cannot be reproduced. The claimed uncertainty analysis is mentioned but no error propagation is shown. The paper's own conclusion concedes ζ and η lack direct observational constraints.\n\nThe authors deserve credit for laying out the algebra and checking many criteria, but the junction mismatch and the density scale mean the paper does not establish a physical model of SAX J1748.9-2021. It is a parameter-fitting exercise inside their own framework.\n\nI would desk-reject. The internal contradiction is decisive and the paper does not warrant referee time. If the authors fixed the junction conditions and reported η, the exercise might become a useful reference for f(Q,T) stellar modeling, but as it stands it is not citable.","headline":"Routine re-scan of the authors' own f(Q,T) star program, with a fatal junction-condition mismatch that invalidates the whole viability claim.","tokens_in":34997,"tokens_out":3286,"would_cite":false,"duration_ms":35898,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["97.60.Gb","04.50.Kd","97.10.-q"],"model":"deepseek-v4-flash","headline":"The paper argues that the observed mass and radius of pulsar SAX J1748.9-2021 support a stable anisotropic stellar model in f(Q,T) gravity, where the action couples non-metricity to the trace of the energy-momentum tensor.","keywords":["pulsar","f(Q,T) gravity","non-metricity","anisotropic matter","Krori-Barua ansatz","stellar stability","energy conditions","SAX J1748.9-2021"],"falsifier":"Compute the total mass from the paper's own density integral M(R)=4π∫_0^R χ^2ρ(χ)dχ at R=13.4 km with ζ=1.08; the observed mass is 1.81±0.3 M⊙, yet the paper never reports this value. If the integrated mass falls outside that band—or if re-running with R=10 km, or with any stated value of η different from the implicit one, makes Pr(R)≠0 or drives v_t^2−v_r^2 out of [−1,0]—the stability claim is falsified for that parameter set.","tokens_in":34031,"feed_emoji":"🌟","tokens_out":9325,"duration_ms":86553,"temperature":0.7,"pith_summary":"The paper tries to show that observations of the pulsar SAX J1748.9-2021 are compatible with a specific modified theory of gravity whose action depends on both non-metricity Q and the trace T of the energy-momentum tensor. It adopts the non-singular Krori-Barua metric for the star's interior, matches it to a Schwarzschild exterior, and inserts the pulsar's observed mass and radius into the resulting anisotropic fluid model. The authors report that density and pressures peak at the core and fall outward, radial pressure vanishes at the surface, and the configuration satisfies energy conditions, causality (0.44 < v_r^2 < 0.50, 0.40 < v_t^2 < 0.46), the adiabatic index, the Zeldovich condition, TOV equilibrium, and the Buchdahl bound. If correct, the result would establish a stable anisotropic stellar configuration in f(Q,T) gravity consistent with this pulsar's data, extending modified-gravity tests to strong-field compact objects.","feed_headline":"Pulsar SAX J1748.9-2021 fits stable modified-gravity star model","feed_subtitle":"A non-singular anisotropic stellar model passes causality, energy, equilibrium, and compactness for three ζ values.","key_machinery":"The load-bearing object is the Krori-Barua ansatz for the interior metric potentials, α(r)=A1(r/R)^2+a1 and β(r)=a(r/R)^2, inserted into the f(Q,T)=ζQ+ηT field equations. This ansatz gives non-singular analytic expressions for energy density, radial and tangential pressures, and their derivatives, which then feed every stability criterion: sound speeds come from dP/dρ, the adiabatic index from (ρ+P)v^2/P, TOV balance from the gradient forces, and compactness from M(r)/r. The Schwarzschild matching at r=R is presented as the way to fix the constants, and the observed mass-radius of SAX J1748.9-2021 is the empirical anchor for the numerical evaluation.","core_discovery":"The central claim is that the anisotropic solution built from the Krori-Barua potentials with A1=2, a1=0, a=-2 and R=13.4 km, in the model f(Q,T)=ζQ+ηT with ζ=1, 1.04 and 1.08, is a physically viable and stable representation of the pulsar SAX J1748.9-2021. The solution is obtained by solving the f(Q,T) field equations for an anisotropic fluid and matching to the Schwarzschild exterior; the constants, however, are fixed by hand in Section 4.1 rather than derived from the junction conditions. The paper then checks a standard battery of criteria—energy conditions, sound speeds, cracking, adiabatic index, Zeldovich condition, TOV force balance, equation-of-state parameters, redshift, and compac","pith_inferences":["Editorial inference: A direct test the paper leaves implicit is to compute the total mass M(R)=4π∫χ^2ρ(χ)dχ at R=13.4 km for each ζ and compare with the observed 1.81±0.3 M⊙; the paper never reports this number, so agreement with the pulsar's mass is unverified.","Editorial inference: Because η is never assigned a value in Eq. (27) or in Section 4.1, every plotted quantity is actually a one-parameter family; whether the stability windows survive across a range of η is an open question.","Editorial inference: The statement that lower R=10 km 'led to deviations' suggests the model's viability is radius-sensitive; a systematic scan over the observed 1σ range R=11.7±1.7 km would show whether the stability is robust or a contrived choice.","Editorial inference: The same construction could be applied to other pulsars with measured mass-radius pairs to see whether the chosen constants generalize or need retuning, which would test the theory's predictive power beyond a single object."],"forward_implications":["If the claim holds, f(Q,T) gravity with f=ζQ+ηT admits stable anisotropic compact-star solutions at nuclear densities, not just cosmological solutions.","The reported sound-speed ranges 0.44 < v_r^2 < 0.50 and 0.40 < v_t^2 < 0.46 provide concrete, testable equation-of-state slopes for the star's interior.","The mass function increases monotonically and compactness stays below 4/9, so the solution would evade gravitational collapse under the Buchdahl criterion.","The TOV equilibrium with four force contributions (anisotropic, gravitational, hydrostatic, and the f(Q,T) correction) implies that the modified gravity contributes a stabilizing force balance inside the star."],"supporting_citations":[{"why":"Supplies the Krori-Barua metric potentials α(r)=A1(r/R)^2+a1, β(r)=a(r/R)^2 used to build the interior solution.","marker":"[53]"},{"why":"Provides the observational mass M=1.81±0.3 M⊙ and radius R=11.7±1.7 km of SAX J1748.9-2021 that anchor all numerical evaluations.","marker":"[55]"},{"why":"Introduces the f(Q,T) gravity framework whose field equations the paper solves for the anisotropic star.","marker":"[20]"},{"why":"Gives the specific linear model f(Q,T)=ζQ+ηT that the analysis adopts.","marker":"[51]"},{"why":"Previous f(R,T)-gravity treatment of the same pulsar, used as the comparison result the paper's stability claims align with.","marker":"[47]"},{"why":"States that positive anisotropy indicates stability, the criterion behind the paper's anisotropy plot.","marker":"[54]"},{"why":"Supplies the cracking condition 0≤|v_t^2−v_r^2|≤1 used to certify stability from the sound-speed split.","marker":"[62]"},{"why":"States the Buchdahl compactness bound u<4/9 that the mass-radius plot must respect.","marker":"[71]"}],"fun_headline_variants":["Pulsar SAX J1748.9-2021 supports f(Q,T) gravity star model","SAX J1748.9-2021 fits stable anisotropic star in f(Q,T) gravity","Pulsar data validate f(Q,T) gravity anisotropic model","f(Q,T) gravity passes pulsar SAX J1748.9-2021 checks"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"The stability conclusion rests on hand-picked values—A1=2, a1=0, a=-2, R=13.4 km, and an unstated η—that are fixed in Section 4.1 rather than derived from the junction conditions or from matching the pulsar's observed mass and radius.","fun_headline_variants_meta":{"raw":{"variants":["Pulsar SAX J1748.9-2021 supports f(Q,T) gravity star model","SAX J1748.9-2021 fits stable anisotropic star in f(Q,T) gravity","Pulsar data validate f(Q,T) gravity anisotropic model","f(Q,T) gravity passes pulsar SAX J1748.9-2021 checks"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001023,"raw_usage":{"total_tokens":4161,"prompt_tokens":763,"completion_tokens":3398,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":507,"completion_tokens_details":{"reasoning_tokens":3303}},"tokens_in":507,"tokens_out":3398,"duration_ms":24357,"temperature":1.0,"reasoning_tokens":3303,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T12:04:00.066056+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the total mass from the paper's own density integral M(R)=4π∫_0^R χ^2ρ(χ)dχ at R=13.4 km with ζ=1.08; the observed mass is 1.81±0.3 M⊙, yet the paper never reports this value. If the integrated mass falls outside that band—or if re-running with R=10 km, or with any stated value of η different from the implicit one, makes Pr(R)≠0 or drives v_t^2−v_r^2 out of [−1,0]—the stability claim is falsified for that parameter set.","supporting_citations":[{"cited_title":"and Barua, J.: J","cited_arxiv_id":null,"evidence_quote":"Supplies the Krori-Barua metric potentials α(r)=A1(r/R)^2+a1, β(r)=a(r/R)^2 used to build the interior solution."},{"cited_title":"and Psaltis, D.: Astrophys","cited_arxiv_id":null,"evidence_quote":"Provides the observational mass M=1.81±0.3 M⊙ and radius R=11.7±1.7 km of SAX J1748.9-2021 that anchor all numerical evaluations."},{"cited_title":"et al.: Eur","cited_arxiv_id":null,"evidence_quote":"Introduces the f(Q,T) gravity framework whose field equations the paper solves for the anisotropic star."},{"cited_title":"et al.: Eur Phys","cited_arxiv_id":null,"evidence_quote":"Gives the specific linear model f(Q,T)=ζQ+ηT that the analysis adopts."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Previous f(R,T)-gravity treatment of the same pulsar, used as the comparison result the paper's stability claims align with."},{"cited_title":"et al.: Eur Phys","cited_arxiv_id":null,"evidence_quote":"States that positive anisotropy indicates stability, the criterion behind the paper's anisotropy plot."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"States the Buchdahl compactness bound u<4/9 that the mass-radius plot must respect."}],"review_version":1}