{"id":"e753075d-4674-465c-b992-99f1d32bcbd3","arxiv_id":"2607.04596","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":4.5,"correctness_risk":"low","formal_verification":"none","parameter_count":1,"one_line_summary":"In f(Q)=Q+ξQ² gravity with realistic EOSs, negative ξ increases neutron-star maximum masses while positive ξ decreases them, with exterior spacetime remaining Schwarzschild.","lead":"This paper models neutron stars in a quadratic f(Q) gravity theory using four realistic nuclear equations of state. Negative values of the free parameter ξ raise maximum masses above General Relativity, offering a possible route to very heavy neutron stars.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.5","headline":"No significant objection identified","rationale":"The paper is a careful, incremental extension of the authors’ earlier polytropic study. The strongest claim is narrowly technical (sign of ξ controls the shift in maximum M_S for four realistic EOSs while exterior geometry remains Schwarzschild) and is supported by the derived equations and the displayed sequences. The reader’s identification of the covariant-formulation premise is accurate, yet that premise is an external theoretical choice, not an internal inconsistency; once accepted, the numerics follow. No stronger load-bearing concern (e.g., algebraic error in the TOV reduction, failure of vacuum matching, or contradiction with the perfect-fluid conservation law) appears in the text. Therefore the CONDITIONAL verdict with high confidence remains appropriate; no adjustment is required.","tokens_in":13049,"tokens_out":464,"duration_ms":4252,"concrete_test":"Independently re-integrate the first-order system (Eqs. 12–14) for the SLy EOS at ξ = -1 (in r_gs^{2} units) with a standard adaptive Runge–Kutta solver and the same central-density grid used for Fig. 3; if the resulting maximum M_S differs from the published curve by more than ~2 %, a numerical or transcription error is present.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The reader’s weakest_assumption correctly flags that the entire phenomenology rests on the covariant formulation remaining dynamically non-trivial for stellar interiors (Zhao 2022). Within the paper itself, however, that framework is applied consistently: the modified TOV system (Eqs. 12–14), the algebraic expression for Q (Eq. 15), and the vacuum recovery of Schwarzschild (Eq. 18) are derived without internal contradiction. The numerical claim—that negative ξ systematically raises M_S for FPS, SLy, ENG and MPA1—follows directly from those equations and is displayed in Figs. 2–5. No derivation error, circularity, or hidden inconsistency undermines the strongest claim as stated. The free parameter ξ and the limited stability check (only M_S < M_0) are acknowledged limitations, not load-bearing flaws in the argument.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The paper studies static, spherically symmetric neutron stars in the quadratic model f(Q)=Q+ξQ^{2} of covariant symmetric teleparallel gravity. Starting from the covariant field equations, the authors derive a closed first-order system for the metric derivatives A' and B (Eqs. 12–14) together with an algebraic expression for the nonmetricity scalar Q (Eq. 15). They integrate the system for four realistic EOSs (FPS, SLy, ENG, MPA1) and five values of the free parameter ξ (in units of r_gs^{2}), producing mass–radius and mass–central-density sequences. The principal claim is that negative ξ systematically raises the maximum gravitational mass M_S relative to GR while positive ξ lowers it; the exterior geometry remains exactly Schwarzschild. Profiles of Q(r), A(r) and B(r) are also shown for maximum-mass configurations.","tokens_in":13179,"tokens_out":1028,"duration_ms":8307,"significance":"If the numerical results hold under the covariant formulation, the work supplies a concrete, observationally relevant extension of the authors’ earlier polytropic study: realistic EOSs can support maximum masses above the GR limit for negative ξ, offering a possible geometric interpretation of the heaviest known pulsars and of the secondary component of GW190814. The analytic recovery of the Schwarzschild exterior (Eq. 18) and the explicit algebraic form of Q (Eq. 15) are clean technical strengths that make the model falsifiable by future mass–radius measurements. The paper therefore contributes a usable benchmark for strong-field tests of f(Q) gravity.","major_comments":[{"comment":"Section 4 and Figs. 2–5: the sequences are plotted only for M_S; the companion mass M obtained by integrating the energy density is never shown, even though the text repeatedly notes that M_S \neq M in general and that regions with M_S > M_0 appear. Without a quantitative comparison of the two mass definitions (or a clear statement that only M_S is observationally relevant), the claim that negative ξ produces “more massive configurations” remains ambiguous for observers who measure gravitational mass via orbital dynamics or gravitational waves.","section":null},{"comment":"Section 4.1: stability is assessed solely by the inequality M_S < M_0. No radial-perturbation analysis, no turning-point criterion applied to the M_S(ρ_c) curves, and no discussion of the adiabatic index are provided. Because the paper’s central phenomenological claim concerns the maximum mass, a minimal stability check (e.g., the sign of dM_S/dρ_c along each sequence) is required before the higher-mass configurations can be regarded as viable neutron-star models.","section":null}],"minor_comments":[{"comment":"Abstract and Introduction: the phrase “a family of f(Q) gravity models” is used, yet only the single quadratic model is studied; rephrase for precision.","section":null},{"comment":"Equation (12): the lengthy expression for A'' would benefit from a short intermediate derivation or a reference to the corresponding equation in the polytropic companion paper, so that readers can verify the algebra without reconstructing every term.","section":null},{"comment":"Figures 2–5: the shaded or labelled regions where M_S > M_0 are mentioned in the captions but are not visually distinct in the text description; a clearer legend or hatching would help.","section":null},{"comment":"Section 4.2: the statement that “the more negative (positive) ξ is, the greater (smaller) the magnitude of Q” is illustrated only for SLy; a single additional panel for a stiffer EOS (e.g., MPA1) would strengthen the claim that the Q-profile behaviour is universal.","section":null},{"comment":"References: a few recent observational papers on massive pulsars (e.g., the latest NICER radius measurements) are missing and would better anchor the comparison with current constraints.","section":null}],"recommendation":"minor_revision","confidential_remarks":"The manuscript is a natural and well-executed sequel to the authors’ own polytropic study (arXiv:2407.08884). The technical overlap is legitimate, but the journal may wish to confirm that the numerical code and the realistic-EOS tables are sufficiently independent of that earlier work. No other ethical or scope concerns."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"This is a straightforward numerical extension of the authors’ own 2026 Nucl. Phys. B paper. They keep the same quadratic model f(Q)=Q+ξQ² and the same covariant TOV system, swap polytropes for FPS, SLy, ENG and MPA1, and recompute the sequences. That is exactly what one expects next, and they execute it cleanly.\n\nWhat is new is the concrete mass–radius and mass–central-density curves for those four EOSs (Figs. 2–5). Negative ξ systematically lifts M_S relative to GR; positive ξ lowers it. The exterior remains exactly Schwarzschild (Eq. 18), Q vanishes outside the star, and they monitor the M_S < M_0 condition. The reduction to a first-order system for A′ and B is careful, and the analytic expression for Q (Eq. 15) is useful. No derivation error or circularity shows up.\n\nSoft spots are real but proportionate. ξ is free and unconstrained by other data; the range they scan is chosen for illustration. Stability is checked only via M_S < M_0; there is no radial-oscillation analysis. Code and tabulated sequences are not released. The whole phenomenology rests on the covariant formulation remaining non-trivial for stellar interiors (Zhao 2022), which they state clearly and apply consistently. None of these are load-bearing flaws in the calculation itself.\n\nThe paper is for people already working on f(Q) or modified-gravity compact stars who want realistic-EOS numbers rather than polytropes. It is not a foundational advance, but it is solid enough that a serious editor should send it to referees rather than desk-reject. I would cite the sequences if I needed a realistic-EOS benchmark in this model; I would not bring it to reading group unless we were already deep in f(Q) stellar structure.","headline":"Clean incremental extension of the authors’ own polytropic f(Q) work to four realistic EOSs; negative ξ raises maximum masses while vacuum stays Schwarzschild.","tokens_in":13841,"tokens_out":471,"would_cite":true,"duration_ms":3990,"reading_group":"no","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"Negative quadratic corrections to nonmetricity raise neutron-star maximum masses while the exterior remains Schwarzschild.","keywords":["f(Q) gravity","symmetric teleparallel gravity","neutron stars","mass-radius relation","nonmetricity scalar","realistic equations of state","modified TOV equations"],"falsifier":"A precise mass–radius measurement of a neutron star whose equation of state is independently known (for example from simultaneous NICER and gravitational-wave data) that lies outside every mass–radius sequence generated by the model for any |ξ| of order a few r_gs² would rule out the claimed effect.","tokens_in":13908,"feed_emoji":"⭐","tokens_out":651,"duration_ms":6121,"temperature":0.7,"pith_summary":"This paper asks whether a simple quadratic extension of symmetric teleparallel gravity can ease the tension between ordinary nuclear equations of state and the heaviest observed neutron stars. Working in the covariant formulation of f(Q) gravity, the authors replace the nonmetricity scalar Q by Q + ξQ² and derive the corresponding stellar-structure equations for four realistic equations of state (FPS, SLy, ENG, MPA1). Numerical sequences show that negative values of the free parameter ξ systematically increase the maximum gravitational mass relative to General Relativity, while positive ξ lowers it; the vacuum exterior remains exactly the Schwarzschild geometry. The nonmetricity itself vanishes at the centre and outside the star, peaking in magnitude only in the high-density interior. If the pattern holds, quadratic f(Q) gravity supplies a concrete geometric mechanism that can accommodate multi-solar-mass compact objects without inventing exotic matter.","feed_headline":"Negative ξ raises neutron-star maximum masses","feed_subtitle":"Quadratic f(Q) gravity lifts M_max above GR while the exterior stays Schwarzschild","key_machinery":"The modified Tolman–Oppenheimer–Volkoff system obtained from the covariant field equations of f(Q) = Q + ξQ², closed by the first-order relation that determines A′ + B′ and by the algebraic expression for the nonmetricity scalar Q(r) ≤ 0 that vanishes both at the centre and outside the star.","core_discovery":"For the model f(Q) = Q + ξQ² and the realistic equations of state FPS, SLy, ENG and MPA1, negative values of ξ (measured in units of the solar gravitational radius squared) raise the maximum gravitational mass M_S above the General-Relativity value obtained with the same equation of state, while positive ξ lowers it; the exterior geometry is identical to Schwarzschild and all deviations are confined to the stellar interior.","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["Negative ξ lifts neutron-star M_max above GR values","f(Q)=Q+ξQ²: negative ξ raises max masses for FPS SLy ENG MPA1","Quadratic f(Q) boosts neutron-star limits when ξ is negative","Negative ξ in f(Q) gravity supports heavier neutron stars","Interior-only f(Q) effects: negative ξ elevates M_max"],"cache_read_input_tokens":128,"weakest_assumption_plain":"The whole construction stands or falls with the covariant formulation that keeps a non-vanishing connection; if that formulation is not the correct one for stellar interiors, the quadratic term becomes dynamically trivial and the mass shifts disappear.","fun_headline_variants_meta":{"raw":{"variants":["Negative ξ lifts neutron-star M_max above GR values","f(Q)=Q+ξQ²: negative ξ raises max masses for FPS SLy ENG MPA1","Quadratic f(Q) boosts neutron-star limits when ξ is negative","Negative ξ in f(Q) gravity supports heavier neutron stars","Interior-only f(Q) effects: negative ξ elevates M_max"]},"model":"grok-4.5","effort":"low","cost_usd":0.003538,"raw_usage":{"total_tokens":1149,"prompt_tokens":743,"num_sources_used":0,"completion_tokens":106,"cost_in_usd_ticks":35380000,"prompt_tokens_details":{"text_tokens":743,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":300,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":743,"tokens_out":106,"duration_ms":4137,"temperature":1.0,"reasoning_tokens":300,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-11T16:39:36.974957+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"A precise mass–radius measurement of a neutron star whose equation of state is independently known (for example from simultaneous NICER and gravitational-wave data) that lies outside every mass–radius sequence generated by the model for any |ξ| of order a few r_gs² would rule out the claimed effect.","supporting_citations":[],"review_version":1}