{"id":"df96121f-cbd5-4fad-8944-fd4cdc6d509f","arxiv_id":"2412.01164","paper_version":1,"verdict":"REJECT","confidence":"HIGH","novelty_score":3.0,"correctness_risk":"high","formal_verification":"none","parameter_count":6,"one_line_summary":"An f(Q,C) gravity model with an assumed transit Hubble law is fitted to H(z), supernova, and BAO data, but the fit leaves the model's own parameters unconstrained and unstated.","lead":"This paper fits a predefined form of the Hubble parameter to cosmological data inside an f(Q,C) modified gravity model and then reads off the dark energy behavior. It claims the model matches observations, but key model parameters are never reported and the reported predictions are built into the assumed Hubble law.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The MCMC constrains only H0,b1,b2; α,a1,a2 never enter the likelihood, so the reported ω, transition, and SEC behavior are consequences of the assumed H(z) ansatz, not of f(Q,C) gravity.","rationale":"The reader's weakest assumption identifies the hand-picked Hubble parametrization as the source of the headline results. My stress-test agrees with that assessment and sharpens it: the problem is not merely that H(z) is assumed, but that the f(Q,C) parameters are completely absent from the likelihood, so the model is never actually constrained. The MCMC fit of H0,b1,b2 may be a valid kinematic exercise, and the paper's plots of energy density and pressure do follow from the given formulas, but those formulas are evaluated with unstated choices for α and a1. The central claim of observational viability for f(Q,C) gravity therefore lacks support. I also note the data-availability statement contradicts the stated use of H(z), SN, and BAO data, and the squared sound speed is found negative, reinforcing doubts about physical viability. No independent support, such as machine-checked derivations or released code, offsets these issues. Since the reader already recommended REJECT, my conclusion leaves that verdict unchanged.","tokens_in":14539,"tokens_out":7010,"duration_ms":60781,"concrete_test":"Vary α (and a1) over a grid while keeping H0,b1,b2 at the reported best fit, and recompute χ2 in Eq. (20). If Δχ2 ≡ 0 for all α, then no f(Q,C) parameter is tested by the data; the same fit would be obtained for any theory that produces the same H(z). Alternatively, add α to the MCMC with a flat prior and check whether its posterior is visibly flat.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that the f(Q,C) model is observationally viable, but the MCMC likelihood in Eq. (20) contains only the kinematic Hubble expression Eq. (14). The gravity-model parameters α, a1, and a2 do not appear in χ2, so the fit cannot constrain or validate the f(Q,C) action. The later physical outputs—transition redshift, ω(z) near −1, and SEC violation—are obtained by inserting the fitted H(z) into Eqs. (10)–(13); they are algebraic consequences of the chosen transit ansatz, not independent predictions of f(Q,C) gravity. Even if the a2 terms cancel for the stated boundary-term convention, the reported conclusions would be unchanged if the same H(z) were used in ΛCDM or any other theory with identical kinematics. Thus the paper supports only the weaker statement that the parametric Hubble law fits the data; it does not test the modified-gravity framework.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript studies f(Q,C) modified gravity with the specific model f(Q,C) = a1 Q^α + a2 C in a flat FLRW universe. A transit Hubble parametrization H(z) = b0 (b1 + (1+z)^b2) is proposed, and the parameters H0, b1, b2 are fitted to a combination of H(z), Type Ia supernova, and uncorrelated BAO data using MCMC, yielding H0 = 64.51, b1 = 1.543, b2 = 1.141. The fitted H(z) is then substituted into the field equations to compute the energy density, pressure, equation of state, (ω−ω′) plane, squared sound speed, and energy conditions. On this basis the paper concludes that the f(Q,C) model can replicate late-time accelerated expansion and dark-energy-like behavior, including ω near −1 and SEC violation.","tokens_in":14818,"tokens_out":5800,"duration_ms":49728,"significance":"If the central claim were valid, the paper would provide an observational constraint on a specific f(Q,C) gravity model, which would be of interest to the modified-gravity community. However, the analysis does not actually test the f(Q,C) action: the MCMC likelihood in Eq. (20) contains no dependence on the gravity parameters α, a1, or a2, so it constrains only the kinematic Hubble ansatz. The derived physical quantities in Figs. 2–7 are algebraic consequences of substituting that same H(z) into the model equations, and the key conclusion (ω near −1, SEC violation, transition redshift) is an artifact of the assumed H(z) form rather than a prediction of the gravitational theory. The manuscript does have some strengths: it uses standard datasets, reports best-fit values with uncertainties, and clearly explains the geometric motivations for f(Q,C) gravity. Nevertheless, the central claim in the abstract and conclusion is not supported by the analysis as presented.","major_comments":[{"comment":"The MCMC likelihood in Eq. (20) is constructed from χ²_H(z), χ²_SN, and χ²_unCorBAO, all of which depend only on H(z) through Eq. (14) and the standard distance formulas (16)–(19). The f(Q,C) model parameters α, a1, and a2 from Eq. (7) do not appear in any of these terms. Therefore the best-fit values reported in §III.E constrain only a kinematic Hubble law, not the gravitational theory. The subsequent physical outputs, including the transition redshift, ω close to −1, and SEC violation, are obtained by inserting the fitted H(z) into Eqs. (8)–(13); they are consequences of the chosen transit ansatz and would be the same for any theory with identical kinematics. This undermines the paper's central claim that the f(Q,C) model is observationally viable.","section":"§III.D–III.E, Eq. (20)"},{"comment":"The passage from the general field equations (5)–(6) to the model-specific expressions (8)–(9) is not derived. For f = a1 Q^α + a2 C, equation (5) contains contributions from f_C = a2 and the boundary term C, yet these disappear without justification in Eq. (8). Moreover, the resulting ρ and p still depend on α and a1, but the paper never states the numerical values of α and a1 used for the figures. Consequently, Figures 2–7 have no specified parameter values or units and cannot be reproduced from the information given.","section":"§II, Eqs. (8)–(9)"},{"comment":"The equation of state in Eq. (10) is independent of a1 but depends explicitly on α. Since α is not reported anywhere in the manuscript, the quantitative claims about ω(z) remaining near −1, the magnitudes of ρ and p, and the energy-condition violations are not checkable. The figures must have been generated with some implicit choice of α (and a1), but without those values the curves are not reproducible. This is a load-bearing problem because the conclusion that the model 'successfully describes' cosmic evolution rests on these plots.","section":"§IV, Eq. (10) and Figs. 2–7"},{"comment":"The data availability statement says 'No data was used for the research described in the article,' but Section III explicitly employs 57 H(z) points, the Pantheon Type Ia supernova sample, and 17 uncorrelated BAO points. This is a direct contradiction that must be corrected to list the actual datasets and their sources.","section":"Data Availability, p. 9"}],"minor_comments":[{"comment":"The definitions of Q and C for the FLRW metric are not provided, so a reader cannot verify the substitution that leads to Eqs. (8)–(9); please give explicit expressions for Q and C in this geometry.","section":"§II, Eqs. (5)–(6)"},{"comment":"Figures 5 and 6 are mislabeled. Figure 5 is described in the text as the (ω−ω′) plane, but its caption reads 'The behavior of squared velocity of sound'; Figure 6, which actually shows the squared sound speed, has a caption that also references the same quantity. The captions should be swapped.","section":"Figure captions"},{"comment":"The MCMC implementation is not described: no priors, chain lengths, burn-in, or convergence diagnostics are reported, so the 1σ and 2σ contours in Figure 1 cannot be independently verified.","section":"§III.D–III.E"},{"comment":"There are many typographical and grammatical errors, including repeated phrases in figure descriptions, inconsistent punctuation, and an incorrect year for reference [7] (2023 for what is a 2013 release); careful proofreading is needed.","section":"Throughout"},{"comment":"The distance modulus in Eq. (16) uses µ0, and the luminosity distance in Eq. (17) uses c/H0, but the treatment of the absolute magnitude nuisance parameter and the covariance matrix in χ²_SN is not explained; please clarify whether the standard Pantheon likelihood with marginalization over the absolute magnitude is used.","section":"§III.B, Eqs. (16)–(18)"}],"recommendation":"reject","confidential_remarks":"The paper is a typical 'parametrize H(z), fit, and derive physical quantities' cosmology study, but the connection to f(Q,C) gravity is purely algebraic because the likelihood does not involve the gravity parameters. Even a careful revision that reports α, a1, derives the a2 cancellation, and corrects the data availability statement would not fix the central issue: the fit constrains only the kinematic Hubble ansatz, not the modified-gravity action. The editor may wish to consider whether a purely kinematic fit with derived quantities, presented as a test of f(Q,C) gravity, is within the journal's scope as it currently stands."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You can trust the reader's report. The central problem is real: Eq. (20) for chi^2 contains only the Hubble ansatz (14) with parameters H0, b1, b2. The f(Q,C) parameters alpha, a1, and a2 never appear in the likelihood, so the MCMC cannot constrain or validate the gravity model. When the paper later reports omega near -1, SEC violation, and transition redshift, it is just plugging the fitted H(z) into Eqs. (10)-(13). Those outputs are properties of the chosen H(z), not of f(Q,C) gravity. The stress-test note has it right.\n\nWhat is new here is thin but not zero: a combined H(z)+Pantheon+BAO likelihood applied to a model and ansatz that, as the paper itself cites, already appeared in refs. [77], [79], [81], and [83]. The MCMC pipeline is standard, and the authors are transparent about borrowing the ansatz from prior work. This could have been a reasonable exercise in fitting a parametric H(z).\n\nThe soft spots are stacked. Equations (8)-(9) depend on alpha and a1, but neither is reported or fitted, so the plotted rho and p have no stated parameters or units. The boundary-term parameter a2 disappears between Eq. (7) and Eq. (8) without an explanation; maybe it cancels for this model, but the paper should say so. The data availability statement says \"No data was used\" while the text claims 57 H(z) points, Pantheon SN, and BAO data. That is a plain contradiction. And the word \"transit\" is doing too much work: the ansatz is chosen because it transitions from deceleration to acceleration, then the paper reports that it transitions. That is not a prediction.\n\nFor a serious referee: I would not send this out. The load-bearing flaw is not fixable by revision—if the gravity parameters do not enter the fit, the paper is not testing f(Q,C). A rewritten version that drops the gravity framing and presents the kinematic fit plus effective diagnostics might be acceptable for a modest journal, but the current manuscript would waste a referee's time.\n\nCredit where due: the paper is clearly written and honest about its borrowings. It is just not doing what it claims.","headline":"The paper is a kinematic fit wearing a modified-gravity costume: alpha, a1, and a2 never enter the likelihood, so the f(Q,C) conclusions do not follow from the data.","tokens_in":15296,"tokens_out":3746,"would_cite":false,"duration_ms":32250,"reading_group":"no","serious_thinker":"no","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["83D05","83F05"],"pacs":["98.80.-k","04.50.Kd"],"model":"deepseek-v4-flash","headline":"This paper claims that the $f(Q,C)$ gravity model $f=a_1Q^{\\alpha}+a_2C$, fitted to Hubble, supernova, and BAO data through a transit Hubble parametrization, is observationally viable and reproduces late-time accelerated expansion.","keywords":["f(Q,C) gravity","dark energy","FLRW cosmology","transit Hubble parameter","energy conditions","Markov Chain Monte Carlo","modified gravity","equation of state"],"falsifier":"Take the same $f(Q,C)$ field equations and fit them to the same Hubble, supernova, and BAO data without assuming the transit form, for example by reconstructing $H(z)$ non-parametrically or with a different parametrization; if the reconstructed history does not show $\\omega$ near $-1$ and strong-energy-condition violation, the paper's dark-energy conclusions are artifacts of the chosen ansatz.","tokens_in":14360,"feed_emoji":"🌌","tokens_out":10023,"duration_ms":78159,"temperature":0.7,"pith_summary":"The paper claims that a modified gravity theory built from the non-metricity scalar $Q$ and its boundary term $C$, with action $f(Q,C)=a_1Q^{\\alpha}+a_2C$, can act as a geometric source of dark energy in a flat FLRW universe. By imposing the transit Hubble parametrization $H(z)=H_0(b_1+(1+z)^{b_2})/(1+b_1)$ and fitting to 57 Hubble-parameter measurements, standard-candle distance moduli, and 17 uncorrelated baryon acoustic oscillation points, the authors obtain best-fit parameters $H_0=64.51$, $b_1=1.543$, $b_2=1.141$. With these parameters the equation-of-state parameter stays close to $-1$ throughout and approaches $-1$ in the future, the universe transitions from deceleration to acceleration, and the strong energy condition is violated. The paper reads these results as evidence that $f(Q,C)$ gravity offers a viable alternative to a cosmological constant.","feed_headline":"Modified gravity model reproduces dark-energy acceleration","feed_subtitle":"Fitted to Hubble, supernova, and BAO data, it keeps the equation of state near -1 and breaks the strong energy condition.","key_machinery":"The load-bearing object is the action $f(Q,C)=a_1Q^{\\alpha}+a_2C$, where $Q$ is the non-metricity scalar and $C$ is the boundary term connecting non-metricity to curvature; this choice reduces the FLRW field equations to algebraic expressions for density $\\rho$ and pressure $p$ that depend only on $H$ and $\\dot H$. The expansion history is then supplied by the assumed transit Hubble parametrization $H(z)=H_0(b_1+(1+z)^{b_2})/(1+b_1)$, which is what produces the smooth deceleration-to-acceleration transition. The MCMC fit of the three free parameters to the combined $H(z)$, standard-candle, and BAO datasets fixes the numbers from which $\\omega$, the $\\omega$-$\\omega'$ plane, sound speed, and energy conditions are evaluated.","core_discovery":"The central claim is that the field equations of $f(Q,C)$ gravity, once specialized to the linear-in-$C$ power-law model and combined with the transit Hubble ansatz, yield an energy density and isotropic pressure whose late-time behavior matches the observed accelerated expansion. The fitted equation-of-state parameter is nearly $-1$ at all epochs and asymptotically reaches $-1$ in the future, the deceleration-to-acceleration transition occurs at a redshift consistent with current data, and the strong energy condition is violated while the null and dominant energy conditions hold. The authors conclude that the model can describe early deceleration, present acceleration, and a future de Sitter-like phase, and that it passes basic background-level tests against Hubble, supernova, and BAO data.","pith_inferences":["A direct test not performed in the paper would be to fit $f(Q,C)$ gravity without imposing the transit Hubble ansatz; the fact that all conclusions are computed from that ansatz means the model's apparent success is not yet separated from the choice of background.","The best-fit $H_0=64.51$ sits below local distance-ladder measurements; if this pattern persists in a model-independent reconstruction, the $f(Q,C)$ framework could have something to say about the Hubble tension, though the paper does not explore that.","The negative squared sound speed suggests that a full linear-perturbation analysis is needed before claiming the model is viable on structure-formation scales; the paper's conclusions are background-level only."],"forward_implications":["The fitted $f(Q,C)$ model can reproduce late-time acceleration with $\\omega$ near $-1$, offering a geometric alternative to a bare cosmological constant.","The best-fit transition redshift is consistent with current observations, so the model can be used to date the onset of cosmic acceleration.","Because the strong energy condition is violated while the null and dominant conditions hold, $f(Q,C)$ gravity provides a mechanism for repulsive gravitational behavior without exotic matter.","The model passes basic background-level tests against $H(z)$, Type Ia supernova, and BAO data, making it a candidate for further perturbation-level study.","The persistently negative squared sound speed implies the model is perturbatively unstable; the paper acknowledges this and links it to non-standard structure formation."],"supporting_citations":[{"why":"sets up $f(Q,C)$ gravity and its cosmological signatures, the framework the paper tests.","marker":"[73]"},{"why":"supplies the cosmological dynamics of $f(Q,C)$ gravity, especially the boundary-term effects the paper relies on.","marker":"[74]"},{"why":"provides stability analysis and cosmological applications for $f(Q,C)$ gravity that the paper draws on for its stability discussion.","marker":"[75]"},{"why":"introduces the specific power-law-plus-boundary model $f=a_1Q^{\\alpha}+a_2C$ used in the field equations.","marker":"[83]"},{"why":"presents a prior observationally constrained flat FLRW $f(Q,C)$ dark-energy model, providing the template for this analysis.","marker":"[81]"},{"why":"gives another observationally constrained $f(Q,C)$ dark-energy model that supports the same model choice.","marker":"[77]"}],"fun_headline_variants":["f(Q,C) gravity fits cosmic acceleration data","Modified f(Q,C) gravity matches dark energy","f(Q,C) model: EoS near -1, data constrained","Dark energy from f(Q,C) gravity passes data","f(Q,C) gravity predicts late-time acceleration"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"Every headline result is computed from the hand-picked Hubble form $H(z)=H_0(b_1+(1+z)^{b_2})/(1+b_1)$; if that assumed expansion history is not the real one, the near-$-1$ equation of state, the transition redshift, and the energy-condition behavior are not predictions of $f(Q,C)$ gravity itself.","fun_headline_variants_meta":{"raw":{"variants":["f(Q,C) gravity fits cosmic acceleration data","Modified f(Q,C) gravity matches dark energy","f(Q,C) model: EoS near -1, data constrained","Dark energy from f(Q,C) gravity passes data","f(Q,C) gravity predicts late-time acceleration"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000542,"raw_usage":{"total_tokens":2557,"prompt_tokens":866,"completion_tokens":1691,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":482,"completion_tokens_details":{"reasoning_tokens":1614}},"tokens_in":482,"tokens_out":1691,"duration_ms":12306,"temperature":1.0,"reasoning_tokens":1614,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T04:39:13.840547+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take the same $f(Q,C)$ field equations and fit them to the same Hubble, supernova, and BAO data without assuming the transit form, for example by reconstructing $H(z)$ non-parametrically or with a different parametrization; if the reconstructed history does not show $\\omega$ near $-1$ and strong-energy-condition violation, the paper's dark-energy conclusions are artifacts of the chosen ansatz.","supporting_citations":[{"cited_title":"Capozziello, A","cited_arxiv_id":null,"evidence_quote":"sets up $f(Q,C)$ gravity and its cosmological signatures, the framework the paper tests."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"supplies the cosmological dynamics of $f(Q,C)$ gravity, especially the boundary-term effects the paper relies on."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"provides stability analysis and cosmological applications for $f(Q,C)$ gravity that the paper draws on for its stability discussion."},{"cited_title":"Capozziello, V","cited_arxiv_id":null,"evidence_quote":"introduces the specific power-law-plus-boundary model $f=a_1Q^{\\alpha}+a_2C$ used in the field equations."},{"cited_title":"Zhao and Y","cited_arxiv_id":null,"evidence_quote":"presents a prior observationally constrained flat FLRW $f(Q,C)$ dark-energy model, providing the template for this analysis."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"gives another observationally constrained $f(Q,C)$ dark-energy model that supports the same model choice."}],"review_version":1}