{"id":"b1c2147a-9d32-4c71-9664-4c2469b7b421","arxiv_id":"2412.19852","paper_version":3,"verdict":"REJECT","confidence":"HIGH","novelty_score":3.0,"correctness_risk":"high","formal_verification":"none","parameter_count":7,"one_line_summary":"A logarithmic q(z) ansatz fitted to OHD and Pantheon+SH0ES in f(Q,C)=gamma1 Q^2 + gamma2 C claims zt about 0.98 and 0.76, but C is dynamically irrelevant and Table I's q0 contradicts the reported q(z=0).","lead":"This paper fits a logarithmic formula for the cosmic deceleration parameter to Hubble and supernova data inside f(Q,C) modified gravity. The fit claims a deceleration-to-acceleration transition, but the boundary term C drops out of the chosen action, the reported parameter table contradicts the claimed present-day deceleration, and the 'predictions' are refits of the assumed parameterization.","discovery_kind":"incremental","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Reported acceleration and transition redshifts cannot be reproduced from the stated q(z) fit: Table I gives q(0)≈+4.6, contradicting Table II's q0≈−0.28.","rationale":"The reader correctly identified that the q(z) ansatz is imposed rather than derived and that γ2 C is a boundary term. I agree these undermine the modified-gravity interpretation. However, the most load-bearing concern is more basic and purely internal: the claimed fits and derived quantities are mutually inconsistent. The paper presents q0 as a fitted parameter in Eq. (27) and Table I (q0=3.53), yet also reports a current deceleration parameter q0≈−0.28 in Table II. Direct substitution shows the two cannot both follow from the same formula. This is not a matter of model choice or external consensus; it means the published H(z), q(z), zt, and EoS results are not reproducible from the stated equations and parameters. Until this is corrected, the paper's central claim cannot be evaluated. The reader's verdict of rejection is therefore appropriate, and my assessment does not change it.","tokens_in":17131,"tokens_out":5983,"duration_ms":55454,"concrete_test":"Recompute q(0) by inserting the Table I central values into Eq. (27) and independently re-derive Eq. (36) from Eq. (25); evaluate Eq. (36) at z=0. If either result is positive while Table II reports q0≈−0.28 and Fig. 5 shows a negative present-day q, then the published data products do not follow from the stated model. Optionally, rerun the MCMC with H(z) from Eq. (30) and verify whether the posterior peak reproduces the Table II transition redshifts.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The decisive problem is internal consistency. With the Table I best fits (q0=3.53, q1=−1.151, α=1.863, β=1.58), Eq. (27) gives q(0)=q0+q1(ln α−β)=3.53+(−1.151)(0.622−1.58)=4.63, a strongly decelerating present epoch. Even the paper's own rewritten expression, Eq. (36), evaluated at z=0 with the same numbers, gives approximately q(0)=+2.7, not the Table II value q0≈−0.28 and not the negative current q shown in Fig. 5. The bullet after Eq. (27) also misstates the z=0 limit, dropping the 1/(1+z) factor. Consequently, the plotted q(z), the claimed transition redshifts zt≈0.98 and 0.76, and the quoted present EoS are not consequences of the stated parameterization with the stated fitted parameters. Since every headline result depends on this q(z), the central claim is unsupported as written. The paper itself concedes the q(z) choice is 'somewhat arbitrary' (Section VII), but the internal contradiction is independent of that judgement. Separately, f(Q,C)=γ1 Q^n+γ2 C has f_C=γ2=constant, so γ2 enters only through a total derivative; no γ2 appears in Eqs. (37)–(38), so the boundary term C does no dynamical work in the reported analysis.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes a logarithmic ansatz for the deceleration parameter, q(z)=q0+q1[ln(alpha+z)/(1+z)-beta], and uses it to close the FLRW equations of f(Q,C)=gamma1 Q^n + gamma2 C gravity. It fits the parameters (H0, q0, q1, alpha, beta) to 31 OHD points and 1701 Pantheon+SH0ES points via MCMC, reports best fits in Table I, and then derives H(z), the deceleration parameter, effective dark-energy density and pressure, the equation of state, statefinder diagnostics, and the Om diagnostic. The headline results are a deceleration-to-acceleration transition at zt about 0.98 (OHD) and 0.76 (Pantheon+SH0ES), with current deceleration q0 about -0.28 and -0.25 and current EoS about -0.55 and -0.70 for the two datasets.","tokens_in":17436,"tokens_out":12821,"duration_ms":105166,"significance":"If the results were correct, the paper would demonstrate that a nonmetricity-based modified gravity can reproduce late-time cosmic acceleration without scalar fields or an explicit cosmological constant. The paper includes an MCMC analysis, compares with LambdaCDM, and uses standard diagnostics such as statefinder and Om, which are appropriate tools for this kind of study. However, the central quantitative claim is not reproducible from the stated equations and fitted parameters, and the chosen action makes the boundary term C dynamically inert. As it stands, the paper does not support its conclusions.","major_comments":[{"comment":"The reported fits are internally inconsistent. Substituting the Table I best-fit values (q0=3.53, q1=-1.151, alpha=1.863, beta=1.58) into Eq. (27) at z=0 gives q(0)=3.53+(-1.151)(ln 1.863 - 1.58)=+4.63, a strongly decelerating present epoch. Even the paper's own rewritten expression, Eq. (36), evaluated at z=0 with the same numbers gives approximately +2.7. Both are positive, contradicting Table II, which reports q0 about -0.28, and Fig. 5, which shows negative q at low redshift. Consequently, the claimed transition redshifts zt about 0.98 and 0.76, the negative current EoS, and all the derived conclusions in Section V are not consequences of the stated parameterization with the stated fitted parameters.","section":"Section III, Eq. (27); Table I vs. Table II and Fig. 5"},{"comment":"The derivation connecting the ansatz Eq. (27) to the Hubble solution is not correct as printed. Integrating H'/H=(1+q)/(1+z) with q given by Eq. (27) yields a factor ((alpha+z)/(1+z))^{-q1/(alpha-1)} in H(z), whereas Eq. (28) and Eq. (30) have the opposite sign in the exponent, ((alpha+z)/(1+z))^{q1/(alpha-1)}. The subsequent expression for q(z) in Eq. (36) does not reduce to Eq. (27) when the relation q=-1+(1+z)H'/H is used, and it gives a positive q(0) numerically, as noted above. The stated limiting condition after Eq. (27), q(0)=q0+q1 log(alpha-beta), is also wrong; the correct limit is q0+q1(ln alpha - beta). These are load-bearing algebraic errors, not presentation issues.","section":"Section III, Eqs. (25)-(30) and Eq. (36)"},{"comment":"With the chosen action f(Q,C)=gamma1 Q^n + gamma2 C, one has f_C=gamma2, a constant, so all terms involving derivatives of f_C vanish, and the gamma2 C contribution cancels identically in the effective dark-energy density and pressure. This is visible in Eqs. (37)-(38), where gamma2 does not appear at all. The analysis is therefore dynamically an f(Q) model, not an f(Q,C) model; the title, abstract, and conclusions overstate the role of the boundary term C in producing the reported cosmic dynamics.","section":"Section II, Eq. (31); Eqs. (23)-(24) and Eqs. (37)-(38)"},{"comment":"The q(z) ansatz is imposed ad hoc rather than derived from the f(Q,C) field equations, and Section VII concedes that the choice is 'somewhat arbitrary.' As a result, the transition redshift, the current deceleration, and the EoS are re-expressions of the parameters fitted to the same Hubble and supernova data, not independent predictions of the gravity theory. The data agreement validates the ansatz, but it does not provide evidence for f(Q,C) gravity unless the theory is shown to single out this expansion history or to produce it dynamically.","section":"Section III and Section VII"}],"minor_comments":[{"comment":"The quantity labeled q0 in Table II is the derived current value of the deceleration parameter, not the fitted parameter q0 of Eq. (27). Rename it q(0) or q_cur to avoid the direct contradiction with Table I.","section":"Table II"},{"comment":"The text says the r-s trajectory converges to the LambdaCDM point (0,1), while the same section earlier correctly identifies LambdaCDM as (r=1, s=0). One of these statements is a typo and should be corrected.","section":"Section V.D"},{"comment":"The MCMC description is incomplete: the priors, burn-in length, and convergence diagnostics are not stated, and the text interchangeably says chi-square minimization and Bayesian sampling. Please report the effective chi-square or a comparable goodness-of-fit statistic for each dataset.","section":"Section IV"},{"comment":"The treatment of the cosmic chronometer data should specify whether the 31 H(z) points are treated as independent or with a covariance matrix; the distinction can affect the derived uncertainties in Table I.","section":"Section IV.A"},{"comment":"References [38] and [39] are identical, and the caption of Fig. 3 contains the typo 'Pantheon + SHE0ES.' These should be cleaned up in a revision.","section":"References and figures"}],"recommendation":"reject","confidential_remarks":"The internal inconsistency between the fitted parameters and the reported q(z) behavior is decisive: the central claim of a deceleration-acceleration transition cannot be reproduced from the paper's own equations and numbers. The boundary-term issue compounds the problem, since the action used is effectively f(Q). A corrected derivation and a complete refit would be needed before the manuscript could be reconsidered; even then, the authors would need to address the circularity of imposing the expansion history by hand."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short answer: the reader is right, and the stress-test note lands. I checked Eq. (27) with Table I: q(0)=3.53−1.151(ln 1.863 −1.58)=+4.63. Table II says q0≈−0.28. Both cannot be true. The plots and transition redshifts are not reproducible from the stated fit. That alone sinks the central claim.\n\nWhat is actually here: a standard kinematic fit. The logarithmic ansatz is a variation of divergence-free q(z) forms already in refs. [45,59]. It is not derived from the f(Q,C) field equations. The gravity side is even weaker: f_C=γ2 is constant, so γ2 cancels out of Eqs. (23)–(24), and the model is effectively f(Q)=γ1 Q^2 with γ1=0.235 and n=2 chosen by hand. The C-sector claims in the abstract and conclusions do no dynamical work. The paper's own Section VII concedes the q(z) is “somewhat arbitrary,” which is honest but does not rescue the inconsistency.\n\nCredit where it is due: the numerical machinery is standard, the authors compare with ΛCDM, run MCMC, and report contour plots. The diagnostics (statefinder, Om) are routine. The tables are clear. This is not a fabricated paper; it is a real but flawed fit.\n\nSoft spots in proportion: the internal inconsistency is the main problem. Secondary is circularity—zt, q0, and ω0 are functions of the fitted parameters, not independent predictions. Also there is no released code or data, so the fits are not externally reproducible as shipped.\n\nWho this is for: a reader looking for one more q(z) parameterization applied to modified gravity might skim it, but they would quickly find that the C term does nothing and the headline numbers contradict each other. Not a serious contribution as written.\n\nRecommendation: desk reject. If the authors fixed the Table I/II contradiction and reframed the paper as a pure kinematic fit without the f(Q,C) packaging, it could be a modest contribution. As written, it is not ready for referee time.","headline":"Internal inconsistency in the reported q0 and transition redshift undermines an otherwise standard kinematic fit; the f(Q,C) label adds nothing because the linear C term drops out.","tokens_in":18050,"tokens_out":2444,"would_cite":false,"duration_ms":20624,"reading_group":"no","serious_thinker":"no","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper claims that a logarithmic deceleration parameter in $f(Q,C)$ gravity can reproduce the observed cosmic expansion with a single geometric dark-energy fluid, transitioning from deceleration to acceleration near $z\\approx0.8$.","keywords":["f(Q,C) gravity","dark energy","deceleration parameter","logarithmic parameterization","nonmetricity","transition redshift","observational Hubble data","Pantheon+SH0ES"],"falsifier":"Apply a model-independent reconstruction of $H(z)$ from the same OHD and Pantheon+SH0ES data and read off the deceleration parameter $q(z)=-1+(1+z)H'(z)/H(z)$. If the reconstructed curve does not cross zero between $z\\approx0.7$ and $z\\approx1.0$, or if it deviates from Eq. (27) by more than the reported uncertainties at $z>2$, the assumed logarithmic parameterization is falsified independently of the $f(Q,C)$ action.","tokens_in":16824,"feed_emoji":"🌌","tokens_out":13360,"duration_ms":105805,"temperature":0.7,"pith_summary":"The paper tries to establish that one chosen logarithmic formula for the deceleration parameter, $q(z)=q_0+q_1[\\ln(\\alpha+z)/(1+z)-\\beta]$, can serve as the expansion history of a universe governed by $f(Q,C)$ gravity with action $f(Q,C)=\\gamma_1Q^n+\\gamma_2C$. The model is fitted to 31 cosmic-chronometer Hubble points and 1701 Pantheon+SH0ES supernovae, yielding $H_0\\approx70\\ \\mathrm{km\\,s^{-1}\\,Mpc^{-1}}$ and a smooth deceleration-to-acceleration crossover at $z_t\\approx0.98$ (OHD) and $z_t\\approx0.76$ (Pantheon+SH0ES). If the claim holds, late-time acceleration arises from geometry alone: the nonmetricity sector acts as an effective dark-energy fluid whose equation of state remains in the quintessence window, so no cosmological constant or scalar field is needed. The paper openly notes that the logarithmic choice is somewhat arbitrary and is used to close the system, so the gravitational theory is tested only through this assumed history.","feed_headline":"A log formula fits cosmic expansion with transition near z=0.8","feed_subtitle":"Nonmetricity-based modified gravity reproduces Hubble and supernova data without a dark energy fluid.","key_machinery":"The load-bearing object is the logarithmic deceleration parameterization in Eq. (27), $q(z)=q_0+q_1[\\ln(\\alpha+z)/(1+z)-\\beta]$, which is integrated through the kinematic relation $q(z)=-1+(1+z)H'(z)/H(z)$ to give the Hubble solution in Eq. (30). That Hubble solution is then put into the modified Friedmann equations of $f(Q,C)$ gravity, whose effective dark-energy density and pressure are given by Eqs. (23)--(24). The action $f(Q,C)=\\gamma_1Q^n+\\gamma_2C$ with integer $n>1$ supplies the geometric reinterpretation of the fluid, while the logarithmic factor is what makes the transition smooth and keeps $q(z)$ finite at high redshift.","core_discovery":"The paper's central claim is that nonmetricity-modified gravity can reproduce the observed transition from a decelerating to an accelerating universe without exotic matter. Starting from the action $f(Q,C)=\\gamma_1Q^n+\\gamma_2C$ with $n=2$ and $\\gamma_1=0.235$, the Friedmann-like equations produce an effective dark-energy density and pressure; inserting the logarithmic ansatz gives a Hubble rate that tracks the data. The best fits place the current deceleration parameter at $q_0\\approx-0.28$ (OHD) and $q_0\\approx-0.26$ (Pantheon+SH0ES), with equation-of-state parameters $\\omega_0\\approx-0.55$ and $\\omega_0\\approx-0.70$, all in the quintessence regime. The transition redshifts are $z_t\\approx0.98$ and $z_t\\approx0.76$ respectively, and the statefinder and $Om(z)$ diagnostics behave consistently with a quintessence-like dark energy that approaches the $\\Lambda$CDM point.","pith_inferences":["Because $\\gamma_2$ multiplies the boundary term $C$ and cancels from the explicit density and pressure in Eqs. (37)--(38), the fits presented here effectively test the $f(Q)=\\gamma_1Q^2$ sector; the advertised $f(Q,C)$ framework is not yet distinguished from plain $f(Q)$ by these data.","The same logarithmic ansatz could be fitted in general relativity with a purely phenomenological dark-energy fluid; if the goodness of fit is statistically indistinguishable, the data do not select nonmetricity gravity over a direct parameterization of dark energy.","A sharper test would add BAO and CMB distance priors or growth data, since the model's $H(z)$ rises steeply at high redshift and the two datasets already disagree on the transition redshift by roughly 0.2."],"forward_implications":["If the central claim is right, cosmic acceleration can be obtained from nonmetricity geometry alone, removing the need for a cosmological constant or scalar-field dark energy.","The model predicts that acceleration began recently, with a transition redshift between about 0.76 and 0.98 depending on the dataset.","The equation of state stays in the quintessence interval $-1<\\omega<-1/3$ and does not cross the phantom divide, so the future evolution approaches a de Sitter-like regime.","The statefinder trajectory ends at the $\\Lambda$CDM point and $Om(z)$ has a negative slope, giving two diagnostics that distinguish this geometric dark-energy fluid from phantom models."],"supporting_citations":[{"why":"Supplies the derivation of the f(Q,C) field equations whose cosmological reduction gives the Friedmann-like equations used here.","marker":"[50]"},{"why":"Provides the 31 cosmic-chronometer Hubble data points used in the OHD chi-square fit.","marker":"[62]"},{"why":"Provides the Pantheon+SH0ES sample and its covariance matrix used in the supernova fit.","marker":"[68]"},{"why":"Justifies the nonlinear functional form of f(Q,C) and motivates the power-law nonmetricity choice.","marker":"[26]"},{"why":"Gives a precedent nonlinear f(Q,C) model that motivates the specific action adopted here.","marker":"[27]"},{"why":"Provides the divergence-free parameterization logic on which the logarithmic q(z) ansatz is built.","marker":"[59]"}],"fun_headline_variants":["Log deceleration in f(Q,C) gravity fits cosmic data","Cosmic acceleration without dark energy via log f(Q,C) model","Log deceleration parameter in f(Q,C) explains cosmic transition","Log deceleration in f(Q,C) fits supernovae and Hubble data","Transition from deceleration to acceleration in log f(Q,C) model"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the true expansion history really is the assumed logarithmic curve $q(z)=q_0+q_1[\\ln(\\alpha+z)/(1+z)-\\beta]$; the gravity theory only reinterprets that imposed history, so if the curve is wrong the fitted transition redshifts and equation of state carry no predictive weight.","fun_headline_variants_meta":{"raw":{"variants":["Log deceleration in f(Q,C) gravity fits cosmic data","Cosmic acceleration without dark energy via log f(Q,C) model","Log deceleration parameter in f(Q,C) explains cosmic transition","Log deceleration in f(Q,C) fits supernovae and Hubble data","Transition from deceleration to acceleration in log f(Q,C) model"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001088,"raw_usage":{"total_tokens":4555,"prompt_tokens":962,"completion_tokens":3593,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":578,"completion_tokens_details":{"reasoning_tokens":3512}},"tokens_in":578,"tokens_out":3593,"duration_ms":24032,"temperature":1.0,"reasoning_tokens":3512,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T04:19:00.727378+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Apply a model-independent reconstruction of $H(z)$ from the same OHD and Pantheon+SH0ES data and read off the deceleration parameter $q(z)=-1+(1+z)H'(z)/H(z)$. If the reconstructed curve does not cross zero between $z\\approx0.7$ and $z\\approx1.0$, or if it deviates from Eq. (27) by more than the reported uncertainties at $z>2$, the assumed logarithmic parameterization is falsified independently of the $f(Q,C)$ action.","supporting_citations":[{"cited_title":"Constraining model parameters in f(Q,C) gravity: Observational analysis and geometric diagnostics","cited_arxiv_id":"2411.17754","evidence_quote":"Supplies the derivation of the f(Q,C) field equations whose cosmological reduction gives the Friedmann-like equations used here."},{"cited_title":"Singirikonda and S","cited_arxiv_id":null,"evidence_quote":"Provides the 31 cosmic-chronometer Hubble data points used in the OHD chi-square fit."},{"cited_title":"Scolnic, D","cited_arxiv_id":null,"evidence_quote":"Provides the Pantheon+SH0ES sample and its covariance matrix used in the supernova fit."},{"cited_title":"Samaddar, S","cited_arxiv_id":null,"evidence_quote":"Justifies the nonlinear functional form of f(Q,C) and motivates the power-law nonmetricity choice."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives a precedent nonlinear f(Q,C) model that motivates the specific action adopted here."},{"cited_title":"Al Mamon and S","cited_arxiv_id":null,"evidence_quote":"Provides the divergence-free parameterization logic on which the logarithmic q(z) ansatz is built."}],"review_version":1}