{"id":"13603914-a144-46e1-98ed-1316c9abb95e","arxiv_id":"2505.18285","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":2.0,"correctness_risk":"high","formal_verification":"none","parameter_count":2,"one_line_summary":"A review-style preprint that restates an R+F(T,G) modified gravity framework but provides no derivation, data, or reproducible numerical analysis.","lead":"This paper reviews a proposed 'Einstein-Gauss-Bonnet-Myrzakulov' gravity that combines curvature, torsion, and a Gauss-Bonnet term, claiming it can explain cosmic acceleration and other physics. The text does not actually derive the field equations or provide numerical results, so the main claims are unsupported.","discovery_kind":"review","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central field equations are never derived: G is undefined in the Weitzenböck framework, the variation of action (11) is not computed, and Eqs. (30)-(35) are imported effective-fluid expressions that even fail to match Eq. (25) and are dimensionally inconsistent in Eq. (33).","rationale":"The paper's stated purpose is to construct a self-consistent derivation of the field equations in R+F(T,G) gravity and thereby demonstrate robustness. That requires a well-defined G, an explicit variation of (11), and a resulting set of equations. None of these are present. I checked the natural places: §IV gives a 'generalized Gauss-Bonnet' Eq. (9) that is never invoked; §V-A gives schematic variations only; §VII asserts (30)-(35). The two versions of the field equations (Eq. (25) versus Eqs. (30)-(35)) are not mutually consistent, since (25) lacks any F_G contribution. The dimensional problem in (33) is a further internal indication that the equations were assembled rather than derived. Each of the paper's downstream claims—statefinder curves, phase-space attractors, black-hole thermodynamics, neutron-star mass-radius—is a consequence of these equations, so the missing derivation is the single most load-bearing weakness. This is not a disagreement with consensus; it is a failure of internal support. The reader's REJECT verdict is therefore unchanged.","tokens_in":22040,"tokens_out":7113,"duration_ms":58708,"concrete_test":"Re-derive the field equations from action (11) for F(T,G)=αT+βG on the flat FLRW tetrad of §VI, first defining G explicitly (e.g., the torsion-GB invariant of ref. [48] or the standard curvature GB term) and performing the vielbein variation by hand or with a computer algebra system. Check whether the resulting Friedmann equations reproduce (30)-(35), whether any definition makes G nonzero on that tetrad, and whether Eq. (33) becomes dimensionally homogeneous. If the equations differ, the central construction has a hidden assumption.","verdict_should_be":"UNCHANGED","load_bearing_attack":"To support 'robustness of the EGBMG framework,' the paper must show that action (11), S = ∫ d^4x √-g [R + F(T,G)], yields Eqs. (19), (25), and (30)-(35). This is the load-bearing step, and it is absent. G is never defined in the Weitzenböck/vielbein geometry: §IV-A proposes a different object, L_GB^(T) = R^2 - 4R_μν R^μν + R_μναβ R^μναβ + T in Eq. (9), which is not used in (11). §V-A's variational principle stops at generic Euler-Lagrange statements (13)-(15); no δF/δe or δF/δΓ computation is shown. The cosmological equations then appear as assertions: (30)-(31) are standard Friedmann forms with undetermined ρ_torsion, p_torsion, ρ_GB, p_GB, and (32)-(35) are written down with f(T)/f(G)-style effective-fluid expressions, with no derivation from (11). Eq. (25), which is supposed to be the same field equations, contains no F_G term at all, so the paper offers two inconsistent versions of its central equations. Eq. (33) adds \\dot{T} F_T with dimension L^-3 to terms of dimension L^-2, which cannot come from a four-dimensional variational principle without an additional H factor. Since every subsequent statefinder, black-hole, and neutron-star plot rests on these equations, the central claim is unsupported.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes a modified gravity theory, 'Einstein-Gauss-Bonnet-Myrzakulov gravity', with action S = ∫ d^4x √−g [R+F(T,G)] in Weitzenböck spacetime. It claims to derive the field equations for this theory and then use them to study Friedmann cosmology, statefinder diagnostics, black-hole and compact-object solutions, phase-space dynamics, solar-system constraints, and neutron-star mass-radius relations. The stated goal is to demonstrate the robustness of the R+F(T,G) framework. In practice the paper is largely a review of existing F(R,T), f(T), and f(G) literature, and the derivations that would support the new claims are only sketched or entirely absent. The manuscript asserts in Section XV that the field equations have been derived and investigated, but the actual variation is never carried out and the central equations are mutually inconsistent.","tokens_in":22449,"tokens_out":9420,"duration_ms":72308,"significance":"The paper identifies a genuinely open problem: hybrid theories containing both torsion and Gauss-Bonnet terms require a careful variational derivation, and a correct set of field equations would be useful for cosmology and compact-object physics. The literature survey may also help readers locate related work. However, the manuscript does not solve the problem it poses. No machine-checked derivation, reproducible code, or parameter-free prediction is provided, and several of the displayed equations are internally inconsistent. The qualitative plots of statefinder parameters, potentials, and mass-radius curves are not tied to the stated field equations in any checkable way. If the central derivation were supplied and corrected, the framework might be of interest, but as it stands the paper's central claim of robustness is not established.","major_comments":[{"comment":"The central field equations are asserted, not derived. The variational principle is stated only in the generic Euler–Lagrange forms (13)–(15); no variation of the vielbein or connection is actually computed, and the terms δF/δe and δF/δΓ are never evaluated. The symbol G in the action (11) is never defined in the Weitzenböck geometry used in the paper: Eq. (9) defines a different object, L_GB^(T) = R^2 −4R_μνR^μν + R_μναβR^μναβ + T, which is not the G of Eq. (11). The closing paragraph of §V.B asserts that the field equations have been derived, but no derivation appears in the text. Since Eqs. (19), (25), and (29)–(35) are the foundation of every subsequent plot and solution, this is a load-bearing gap.","section":"§V.A, Eqs. (11)–(19)"},{"comment":"The paper presents incompatible versions of the field equations from the same action. Eq. (19) includes a Gauss–Bonnet stress tensor T^(G)_μν, while Eq. (25), also labelled as the field equations of the R+F(T,G) action, contains no F_G term at all and instead has a term 1/2[F(T,G)−T]g_μν. Eq. (29) is yet another form with separate torsion and Gauss–Bonnet tensors. The paper never reconciles these expressions; a single action should yield a single set of field equations. This inconsistency directly undermines the claim that the field equations have been derived.","section":"§VI, Eq. (25) versus §V.A, Eq. (19)"},{"comment":"The effective torsion and Gauss-Bonnet energy densities and pressures are imported from f(T) and f(G) cosmology without being derived from the two-variable action (11). Eq. (33) contains the term 2 RT F_T, which has dimension L^{-3} if T ~ H^2 and F has the same dimension as R; the adjacent terms have dimension L^{-2}, so the equation is dimensionally inconsistent as written. A correct variation of F(T,G) would also generate mixed F_TG terms and RG contributions, none of which appear. Consequently the modified Friedmann equations (30)–(31) are not justified.","section":"§VII.A, Eqs. (32)–(35)"},{"comment":"The dust solution is internally inconsistent. The paper sets the acceleration equation RH + H^2 + k/a^2 = 0 and then states that the Hubble parameter follows H ∼ a^{−3/2}. For k=0, H = C a^{−3/2} implies RH = −(3/2)H^2, hence RH + H^2 = −(1/2)H^2, which is not zero. The quoted scaling is the solution of RH = −(3/2)H^2, not of RH = −H^2. The claimed dust solution is therefore not a solution of the displayed equation.","section":"§VII.B, Eq. (37) and following text"},{"comment":"The solar-system consistency claim is not a test of the theory. The text states that the parameters α, β, n, m 'can be tuned to ensure agreement' with the inverse-square law, and Fig. 6 shows a potential for one arbitrary parameter choice (α=0.1, β=0.05, n=m=2). No derivation of the modified Newtonian potential from the field equations is given, no comparison with actual data such as perihelion precession or Shapiro delay is performed, and no bounds are reported. A parameter that is freely tuned to force agreement cannot support the claimed compatibility with local gravity constraints.","section":"§XIII, Figs. 5–6"},{"comment":"The neutron-star mass-radius prediction is not supported by any calculation in the manuscript. The text asserts qualitatively that F(T,G) gravity changes the mass-radius relation and that the green curve accommodates PSR J0740+6620, but no Tolman–Oppenheimer–Volkoff equations for this theory, no equation of state, and no numerical scheme for the stellar-structure problem are given. The claim that the theory can explain high-mass neutron stars is therefore unsubstantiated.","section":"§XIV.C, Fig. 7"}],"minor_comments":[{"comment":"Equation (17) uses the same symbol T_μν for both the matter energy-momentum tensor and the torsional contribution; distinct notations such as T^(m)_μν and T^(tor)_μν should be used throughout.","section":"§V.A.4, Eq. (17)"},{"comment":"The abstract reads 'Einstein-Gauss-Bonnet-Myrzakulov $R = F(T, G)$ gravity', but the action used in the paper is R + F(T,G); the equals sign appears to be a typo and should be corrected.","section":"Abstract"},{"comment":"The variable z = f_G/H^4 is introduced as a dimensionless dynamical variable, but with the dimensions used elsewhere in the paper (F has dimension L^{-2}, G has dimension L^{-4}), f_G has dimension L^2 and H^4 has dimension L^{-4}, so z is not dimensionless.","section":"§XII, phase-space variables"},{"comment":"The numerical plots are not reproducible: the specific functions F(T,G), parameter values, initial conditions, and metric functions that define 'Model A', 'Model B', the modified potential, and the mass-radius curves are not specified.","section":"Figures 1–3, 6, 7"},{"comment":"The statement that the Gauss-Bonnet term is a total divergence in four dimensions and 'does not affect the equations of motion in 4D' needs qualification, since a nonlinear f(G) or a coupled F(T,G) is nontrivial even in four dimensions.","section":"§IV"}],"recommendation":"reject","confidential_remarks":"I concur with the reader's assessment: the central derivation is absent, the Gauss-Bonnet object entering the action is undefined, and the few displayed equations that would carry the paper are mutually inconsistent. These are not cosmetic defects; they would require a completely new derivation of the field equations and a rebuilt numerical analysis. I do not see a path to a sound paper within a normal revision cycle."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this paper has no new derivation, no new quantitative result, and its central field equations are asserted in two mutually inconsistent forms. It reads as a survey of the authors' own earlier work plus a set of sketches. I would not send it to a referee.\n\nWhat is actually there: the paper does gather a useful bibliography on f(T), f(T,TG), and Myrzakulov F(R,T) models, and it makes the reasonable point that a combined R+F(T,G) action is a natural next step. The statefinder definitions are standard. The figures, though qualitative, do illustrate what a torsion–Gauss-Bonnet coupling might do to H(z) and the statefinder pair. That is about the extent of the value.\n\nWhere it falls apart: the field equations are never derived from action (11). A generic variational principle is stated, then Eqs. (19), (25), (30)-(35) appear as assertions. G is never defined in the Weitzenböck framework; Eq. (9) proposes a different object that is not used in (11). Eq. (25) contains no F_G term at all, so the paper offers two inconsistent versions of its central equations. Eq. (33) adds \\dot{T} F_T, which has dimension L^{-3}, to terms of dimension L^{-2}; that cannot come from a four-dimensional variation. The dust solution in Sec. VII.B sets the acceleration equation to zero while claiming H ~ a^{-3/2}; for dust the acceleration equation is not zero. The solar-system consistency check is an explicit parameter-tuning exercise: α, β, n, m are chosen so the potential decays, so it proves nothing. No equation of state or TOV calculation supports the neutron star mass-radius plot. The numerical section lists generic methods but describes no implementation, convergence tests, or data. These are not minor blemishes; the load-bearing equations are unsupported.\n\nWho gets value from this? A graduate student wanting a quick tour of the literature might skim the reference list, but not the physics. This paper claims to demonstrate the robustness of the EGBMG framework; it demonstrates nothing of the sort. My recommendation: desk reject.","headline":"Review-style preprint with no derivation, inconsistent central equations, and qualitative plots; not suitable for peer review.","tokens_in":22946,"tokens_out":2102,"would_cite":false,"duration_ms":17367,"reading_group":"no","serious_thinker":"no","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["04.50.Kd"],"model":"deepseek-v4-flash","headline":"This paper claims that the R+F(T,G) action forms a viable modified gravity in Weitzenböck spacetime, with torsion–Gauss-Bonnet corrections driving cosmic acceleration, altering black-hole thermodynamics, and raising the neutron-star mass…","keywords":["modified gravity","teleparallel gravity","torsion scalar","Gauss-Bonnet term","dark energy","statefinder diagnostics","neutron stars","Weitzenböck spacetime"],"falsifier":"The decisive check is a direct calculation: take the action $S=\\int d^4x\\sqrt{-g}\\,[R+F(T,G)]$ and perform the full variation with respect to the vielbein and the connection in Weitzenböck spacetime. If the resulting equations contain cross-terms involving $\\partial^2F/\\partial T\\partial G$, or differ from Eqs. (19), (25), and (30)-(35), then the paper's equations are not the equations of its own action. On the observational side, the mass-radius curve predicts a maximum neutron-star mass above the general-relativistic bound, so a precise measurement of a neutron star that exceeds the predicted curve, or a tidal-deformability measurement that contradicts it, would settle the astrophysical claim.","tokens_in":21817,"feed_emoji":"🌌","tokens_out":20032,"duration_ms":178295,"temperature":0.7,"pith_summary":"The paper aims to establish that an action of the form $S=\\int d^4x\\sqrt{-g}\\,[R+F(T,G)]$, with $R$ the Ricci curvature scalar, $T$ the torsion scalar of teleparallel gravity, and $G$ the Gauss-Bonnet term (a quadratic curvature invariant), defines a consistent modified theory of gravity in Weitzenböck (teleparallel) spacetime. It claims that the field equations contain explicit effective energy densities and pressures from both torsion and the Gauss-Bonnet term, and that these geometric contributions can drive early-time inflation and late-time cosmic acceleration without a cosmological constant. The same framework is then applied to statefinder diagnostics, black-hole horizons, Solar System limits, and neutron-star mass-radius relations. A sympathetic reader would care because, if the framework holds, one geometric mechanism would simultaneously address dark energy and predict heavier neutron stars than general relativity allows.","feed_headline":"Torsion-Gauss-Bonnet gravity claims cosmic speed-up","feed_subtitle":"One action joining curvature, torsion, and Gauss-Bonnet aims to replace the cosmological constant and raise neutron-star mass limits.","key_machinery":"The load-bearing object is the arbitrary function $F(T,G)$ in the action. The paper treats $T$ and $G$ as independent geometric scalars on a Weitzenböck (teleparallel) spacetime, varies the action with respect to the vielbein (the local frame field) and the connection, and packages the result as effective torsion and Gauss-Bonnet fluids in the modified Friedmann equations. This machinery generates the paper's concrete predictions: dynamical-system variables $x=\\dot{H}/H^2$, $y=f_T/H^2$, $z=f_G/H^4$ for stability analysis, a statefinder pair $(r,s)$ built from third and second derivatives of the scale factor, and the mass-radius relation obtained by solving the hydrostatic-equilibrium equations with the same effective densities.","core_discovery":"On its own terms, the central claim is that the Einstein–Gauss–Bonnet framework described by $S=\\int d^4x\\sqrt{-g}\\,[R+F(T,G)]$ yields the modified Einstein equations $G_{\\mu\\nu}=\\kappa\\left(T^{\\rm matter}_{\\mu\\nu}+T^{\\rm torsion}_{\\mu\\nu}+T^{(G)}_{\\mu\\nu}\\right)$ (Eq. (19)), and that under the Friedmann-Robertson-Walker cosmological ansatz these reduce to the Friedmann system Eqs. (30)-(35) with $\\rho_{\\rm torsion}=\\tfrac12(TF_T-F)$, $p_{\\rm torsion}=\\tfrac12(TF_T-F+2\\dot{T}F_T)$, $\\rho_{\\rm GB}=\\tfrac12(GF_G-F)$, and $p_{\\rm GB}=\\tfrac12(GF_G-F+2\\dot{G}F_G)$. The paper further claims that numerical integration of these equations produces a Hubble history starting from $H_0=70$ km/s/Mpc, statefinder tracks $(r,s)$ that leave the $\\Lambda$CDM point $(1,0)$, black-hole horizon functions $A(r)$ and $B(r)$ with torsion-dependent temperatures, a Newtonian limit that survives Solar System tests, and a neutron-star mass-radius curve whose maximum mass exceeds the general-relativistic limit, consistent with observed high-mass pulsars.","pith_inferences":["Editorial inference: a full variation of the action would likely produce explicit cross-coupling terms from $\\partial^2F/\\partial T\\partial G$; computing them and testing whether they are small would settle whether the paper's effective-fluid split is the right leading-order description.","Editorial inference: the statefinder tracks in Figs. 1 and 2 could be converted directly into a fitting statistic against model-independent reconstructions of $H(z)$ from supernova and baryon acoustic oscillation data, turning the qualitative deviations into a quantitative viability test.","Editorial inference: because the theory is claimed to raise the maximum neutron-star mass, the same framework should predict the tidal deformability of neutron stars; a future gravitational-wave event could discriminate $F(T,G)$ gravity from general relativity even without resolving the mass-radius curve.","Editorial inference: the paper's special-case limits suggest a direct consistency check, namely verifying that sending $F(T,G)$ to $f(T)$, $f(G)$, or $f(R)$ reproduces those known equations term by term."],"forward_implications":["If the field equations (19) and (30)-(35) are correct, torsion and Gauss-Bonnet form an effective dark-energy fluid, so cosmic acceleration can arise without introducing a cosmological constant by hand.","The statefinder parameters $(r,s)$ evolve away from $\\Lambda$CDM's fixed point $(1,0)$ in a redshift-dependent way, giving high-precision cosmic surveys a geometric signature that distinguishes this theory from standard cosmology.","With $F(T,G)=\\alpha T^n+\\beta G^m$ and parameters such as $\\alpha=0.1$, $\\beta=0.05$, $n=m=2$, the modified potential returns to the Newtonian $1/r$ form at Solar System scales, so the theory can satisfy local gravity constraints.","The torsion-dependent horizon functions $A(r)$ and $B(r)$ change Hawking temperatures and horizon structure, producing testable modifications in black-hole observations.","The mass-radius relation predicted for neutron stars allows larger maximum masses than general relativity, offering an explanation for observed pulsars that appear to exceed the standard limit."],"supporting_citations":[{"why":"Introduces the F(R,T) gravity model whose action and curvature-torsion signatures the paper takes as its starting framework.","marker":"[3]"},{"why":"Supplies the metric-affine f(R,T) treatment that treats metric and connection independently, the approach the paper says it extends to F(T,G).","marker":"[46]"},{"why":"Develops the vielbein formalism in Weitzenböck spacetime that the paper uses to describe torsion dynamics.","marker":"[47]"},{"why":"Provides the teleparallel equivalent of Gauss-Bonnet gravity and its modified equations, the main source for the torsion-Gauss-Bonnet coupling structure.","marker":"[48]"},{"why":"Establishes f(G) gravity as a candidate for dark energy, the precedent for adding a function of the Gauss-Bonnet term to the action.","marker":"[49]"},{"why":"Cited as the work behind black-hole physics and stability analysis of modified gravity models in the paper's discussion of f(G) gravity.","marker":"[50]"},{"why":"Gives the high-mass neutron star measurement that the F(T,G) mass-radius relation is claimed to accommodate.","marker":"[51]"},{"why":"Provides the binary neutron star gravitational-wave event that the paper uses as a testing ground for its astrophysical predictions.","marker":"[52]"}],"fun_headline_variants":["Torsion + Gauss-Bonnet: new gravity model for dark energy","One action unites curvature, torsion, Gauss-Bonnet to drive cosmos","Heavier neutron stars predicted by torsion-Gauss-Bonnet gravity","Torsion-Gauss-Bonnet gravity: new route to cosmic acceleration","Modified gravity model challenges Lambda-CDM with torsion and Gauss-Bonnet"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole framework rests on the assumption that a single spacetime can carry a well-defined torsion scalar $T$ and an independent Gauss-Bonnet term $G$, and that varying the action with respect to the frame and connection really produces the field equations written in the paper; if either geometric quantity is ill-defined or the variation yields different terms, the predicted cosmology and neutron-star results do not follow.","fun_headline_variants_meta":{"raw":{"variants":["Torsion + Gauss-Bonnet: new gravity model for dark energy","One action unites curvature, torsion, Gauss-Bonnet to drive cosmos","Heavier neutron stars predicted by torsion-Gauss-Bonnet gravity","Torsion-Gauss-Bonnet gravity: new route to cosmic acceleration","Modified gravity model challenges Lambda-CDM with torsion and Gauss-Bonnet"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000813,"raw_usage":{"total_tokens":3630,"prompt_tokens":1075,"completion_tokens":2555,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":691,"completion_tokens_details":{"reasoning_tokens":2457}},"tokens_in":691,"tokens_out":2555,"duration_ms":19650,"temperature":1.0,"reasoning_tokens":2457,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T14:33:29.046218+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"The decisive check is a direct calculation: take the action $S=\\int d^4x\\sqrt{-g}\\,[R+F(T,G)]$ and perform the full variation with respect to the vielbein and the connection in Weitzenböck spacetime. If the resulting equations contain cross-terms involving $\\partial^2F/\\partial T\\partial G$, or differ from Eqs. (19), (25), and (30)-(35), then the paper's equations are not the equations of its own action. On the observational side, the mass-radius curve predicts a maximum neutron-star mass above the general-relativistic bound, so a precise measurement of a neutron star that exceeds the predicted curve, or a tidal-deformability measurement that contradicts it, would settle the astrophysical claim.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduces the F(R,T) gravity model whose action and curvature-torsion signatures the paper takes as its starting framework."},{"cited_title":"Cosmological Study in Myrzakulov $F(R, T)$ Quasi-dilaton Massive Gravity","cited_arxiv_id":"2309.09230","evidence_quote":"Supplies the metric-affine f(R,T) treatment that treats metric and connection independently, the approach the paper says it extends to F(T,G)."},{"cited_title":"Dynamical system analysis of Myrzakulov gravity","cited_arxiv_id":"2202.10871","evidence_quote":"Develops the vielbein formalism in Weitzenböck spacetime that the paper uses to describe torsion dynamics."},{"cited_title":"Metric-Affine Myrzakulov Gravity Theories","cited_arxiv_id":"2108.00957","evidence_quote":"Provides the teleparallel equivalent of Gauss-Bonnet gravity and its modified equations, the main source for the torsion-Gauss-Bonnet coupling structure."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Cited as the work behind black-hole physics and stability analysis of modified gravity models in the paper's discussion of f(G) gravity."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the high-mass neutron star measurement that the F(T,G) mass-radius relation is claimed to accommodate."}],"review_version":1}