{"id":"65fbd226-4d29-4dd4-bc13-3f13254bf0cc","arxiv_id":"2411.17754","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":2.0,"correctness_risk":"high","formal_verification":"none","parameter_count":5,"one_line_summary":"The paper claims three parameterized dark energy equations of state in f(Q,C) gravity fit expansion data and support a deceleration-to-acceleration transition, but the modified gravity parameters themselves are not constrained.","lead":"The paper fits three assumed redshift-dependent forms of the dark energy equation of state, combined with a modified gravity model, to Hubble, BAO, and supernova data. It reports that the fitted models transition from deceleration to acceleration and show quintessence-like or near-Lambda-CDM behavior.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The f(Q,C) parameter β cancels identically from the background equations (§3, Eqs. 19–20), so the MCMC fits only an imposed EoS ansatz; the paper's claim that the data support f(Q,C) gravity is not actually tested.","rationale":"The paper aims to constrain f(Q,C) parameters and to validate the framework against Hubble, BAO and Pantheon data. What must be true for the central claim is that the theory's parameters enter the observables being fitted. In Section 3, for the linear ansatz f(Q,C)=αQ+βC, β cancels identically from κρ and κp, and α cancels from ω=p/ρ. The resulting H(z) fits are exactly those of a one-component perfect fluid with an imposed ω(z); hence the observational constraints are constraints on the EoS parameterization, not on f(Q,C) gravity. This is the most load-bearing concern because even if every numerical result in the paper were correct, the analysis would not test the title's model. It is an internal algebraic fact, so no external consensus is needed. The reader's weakest assumption about the single-fluid ansatz is adjacent, but the sharper diagnosis is the exact cancellation of the theory parameters from the background equations. The additional internal inconsistencies identified by the reader reinforce the rejection but are secondary. I would keep the reader's REJECT verdict; the rating does not change.","tokens_in":28228,"tokens_out":11831,"duration_ms":116946,"concrete_test":"Compute the β-dependent terms in Eqs. (16)–(17) explicitly for f=αQ+βC. If they do not vanish, the paper's Eqs. (19)–(20) are wrong and my concern fails. If they vanish as expected, run the Model 5.1 MCMC with β included as a free parameter with a broad prior (e.g., uniform in [-10,10]) and plot its marginalized posterior; a posterior identical to the prior and Δχ²≈0 relative to any fixed β demonstrates that the data carry no information about the f(Q,C) parameter. If the posterior is flat, the central claim of the paper is unsupported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Using f(Q,C)=αQ+βC with Q=-6H² and C=6(3H²+Ḣ), the derivatives f_Q=α and f_C=β are constants, so all terms containing ḟ_Q, ḟ_C and ¨f_C in Eqs. (16)–(17) vanish. The β-dependent parts of f/2 and (9H²+3Ḣ)f_C cancel, leaving κρ=3αH² and κp=-3αH²-2αḢ (Eqs. 19–20). Since α scales both ρ and p, the EoS ω=p/ρ is independent of both α and β. Therefore the Hubble parameter in Eqs. (33), (35), (37) is obtained solely from the hand-chosen ω(z) through Eq. (21); the MCMC constrains only H0, ω0, ω1. The α=0.5 chosen in §6 is arbitrary and cancels from all diagnostics. Consequently, the data neither distinguish nor constrain the f(Q,C) model, and the abstract's conclusion that the results 'support f(Q,C) gravity as a viable framework' does not follow from the analysis: any theory sharing the same background would give identical fits, q0, ztr, statefinders and sound speeds. This is an internal algebraic feature of the model, not a disagreement with external consensus. Secondary inconsistencies (Eq. 40 disagrees with q=0.5+1.5ω(z); Fig. 16 shows c_s²>1 while text claims 0<c_s²<1; SEC inequalities are written ≥0 while interpreted as negative) support rejection but are not the primary issue.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper claims to constrain the parameters of f(Q,C)=αQ+βC gravity using three redshift-dependent dark-energy equation-of-state parameterizations against Hubble, Hubble+BAO, and Hubble+BAO+Pantheon datasets, and to derive deceleration parameters, energy conditions, statefinder diagnostics, and sound speeds from the fits. The central conclusion, stated in the abstract, is that the observational results 'support f(Q,C) gravity as a viable framework for describing diverse dark energy dynamics.' The manuscript derives the background field equations, integrates the Hubble parameter for each EoS ansatz, performs a standard MCMC likelihood analysis, and presents contour plots, error bars, and a battery of cosmological diagnostics.","tokens_in":28582,"tokens_out":5465,"duration_ms":48916,"significance":"If the analysis were a genuine test of f(Q,C) gravity, the paper would provide useful observational constraints on a modified-gravity model and a comparison of three dark-energy parameterizations. The paper has some strengths: the H(z) integrals in Eqs. (33), (35), and (37) are standard and, as algebraic exercises, are carried out correctly; the MCMC pipeline is conventional; and the use of three data combinations allows a check of parameter stability. However, the central inference is not supported because, as the paper's own equations show, the free parameters α and β of f(Q,C) cancel from the background dynamics, so the fits constrain only the hand-chosen EoS parameters and H0. Consequently, the paper does not test f(Q,C) gravity; it tests phenomenological EoS forms in a background that is indistinguishable from GR with a perfect fluid. This is a load-bearing problem that cannot be repaired by a local correction.","major_comments":[{"comment":"The background field equations for f(Q,C)=αQ+βC reduce to κρ=3αH² and κp=-3αH²-2αḢ. The resulting EoS, ω=p/ρ=-1-(2/3)Ḣ/H², is independent of both α and β, and α merely rescales the effective gravitational constant. Therefore the Hubble parameter in Eqs. (33), (35), and (37) is determined solely by the assumed ω(z) and H0; the MCMC fits constrain only H0, ω0, and ω1. The choice α=0.5 made in Section 6.2 is arbitrary and cancels from all diagnostics. Because of this degeneracy, the abstract's statement that the findings 'support f(Q,C) gravity as a viable framework' does not follow from the analysis: any theory with the same background fluid would produce identical fits, transition redshifts, statefinders, and sound speeds. The paper's observational analysis is thus not a test of f(Q,C) gravity.","section":"Section 3, Eqs. (19)-(21)"},{"comment":"The deceleration parameter for Model 5.3 is inconsistent with the standard relation q=0.5+1.5ω(z). Inserting ω=ω0+ω1z²/(1+z²) gives q(z)=0.5+1.5ω0+1.5ω1z²/(1+z²), whereas Eq. (40) contains the terms 3ω1z(1+z)/(4(1+z²)) and -3ω1/(4(1+z²)), which do not reduce to the required quadratic-in-z² form. Differentiating ln H from Eq. (37) yields a constant prefactor of 3(2+2ω0+ω1)/2, not 3(2+2ω0+ω1)/4 as written, and a last term proportional to (1+z)/(1+z²). This error propagates into the q0 and ztr values reported in Section 6.1 and Figure 7(c).","section":"Section 5.3, Eq. (40)"},{"comment":"The present-day EoS values quoted in the text do not match the MCMC best-fit values in the tables. For Model 5.1, Table 4 lists ω0≈-0.588 to -0.590, while Section 6.3 reports ω0=-0.635, -0.657, and -0.675. For Model 5.2, Table 5 lists ω0≈-0.650 to -0.654, while the text reports -0.9630, -0.9016, and -0.8401. For Model 5.3, Table 6 lists ω0≈-0.569 to -0.571, while the text reports -0.6214, -0.5396, and -0.52345. Because ω0 and ω1 are the only physically meaningful free parameters in the fits, these inconsistencies affect every subsequently derived diagnostic, including the deceleration parameter, statefinders, and sound speed.","section":"Section 6.3 and Tables 4-6"},{"comment":"The SEC inequalities are written as ρ+3p≥0 for Models 5.1, 5.2, and 5.3, but the surrounding text and Figures 11-13 state that the SEC is negative at all redshifts. For an accelerating universe the SEC should be violated, i.e., ρ+3p<0, and the figures indeed plot negative values. The equations as written contradict the interpretation and the plotted results, so the energy-condition analysis is internally inconsistent.","section":"Section 6.4, Eqs. (47)-(55)"},{"comment":"The text claims all models satisfy 0<c_s²<1, but Figure 16(b) for Model 5.2 appears to show sound speed values orders of magnitude larger than 1; the axis labels are corrupted, and the plotted curves are not in the claimed range. As written, the figure contradicts the causality/stability conclusion, and the typesetting artifacts make the quantitative claim impossible to verify.","section":"Section 6.6, Figure 16"}],"minor_comments":[{"comment":"The abstract states that the Pantheon sample contains 1408 data points, whereas Section 4.4 and Table 3 state 1048; the discrepancy should be reconciled.","section":"Abstract and Section 4.4"},{"comment":"The axis labels in Figure 16 contain obvious typesetting artifacts (e.g., '3 4 3', '7 4 3', 'G F H'), rendering the figure unintelligible; it should be regenerated with proper mathematical notation.","section":"Figure 16"},{"comment":"Eq. (25) defines χ²_BAO using D_obs and D_th, but the text calls D_th a theoretical distance modulus, while Table 2 lists H(z) values; the notation needs to be clarified so the reader can identify which quantity is actually compared.","section":"Section 4.2"},{"comment":"In the caption of Figure 7(b), the value '-303 842' appears to be a typo for '-0.3842'.","section":"Section 6.1, Figure 7(b)"},{"comment":"The sentence 'The values from Model 5.2 show a strong negative trend, suggesting a more pronounced dark energy component that could hint at phantom behavior' is not supported by the reported ω0 values, which are all greater than -1; this should be reworded.","section":"Section 6.3"}],"recommendation":"reject","confidential_remarks":"The core problem is not a stylistic issue but a conceptual one: the f(Q,C) parameters do not enter the background dynamics, so the entire observational analysis is an EoS-parameterization exercise in GR-like form. The secondary inconsistencies (Eq. (40), the table/text mismatches, the SEC sign errors, and the corrupted Figure 16) further reduce confidence in the quantitative results. Even a major revision would require either a genuinely non-linear f(Q,C) model or a complete reframing of the paper's claims, which seems outside the manuscript's current scope."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper's center does not hold: under the chosen linear f(Q,C)=alpha Q + beta C, both f_Q and f_C are constants, so every derivative term in the field equations dies, and the beta terms cancel identically. The background equations reduce to kappa rho = 3 alpha H^2 and kappa p = -3 alpha H^2 - 2 alpha Hdot, which means the equation of state is independent of both alpha and beta. The Hubble solutions in Section 5 are therefore nothing more than the standard single-fluid solutions for the three EoS parameterizations, and the MCMC fits only H0, omega0, omega1. The abstract's claim that the results support f(Q,C) gravity as a viable framework is not supported by the analysis. What the paper does well is routine: the dataset assembly (H(z), BAO, Pantheon) is standard, the MCMC setup is plausible, and the integrations of the three EoS forms are correct as far as I checked. If the work were reframed as a fit of known EoS parameterizations, it would be a modest but acceptable exercise. The soft spots are serious. Equation (40) for Model 5.3 disagrees with the correct relation q = 0.5 + 1.5 omega(z). The SEC inequalities in Section 6.4 are written with greater-than-or-equal signs while the text and figures interpret them as negative. Figure 16 shows c_s^2 greater than 1 for most redshifts, contradicting the claim that 0 < c_s^2 < 1. The quoted q0 and ztr values are inconsistent with the fitted omega0 values in Table 6. These are not cosmetic issues; they suggest the diagnostics were not checked against the model's own equations. This paper is for readers who want to see a standard dark-energy EoS fit in a modified-gravity costume. It does not deserve referee time in its current form because the central claim is untestable with the given setup. I recommend desk rejection, with encouragement to the authors to either drop the f(Q,C) framing or actually test a model where the new term affects the background.","headline":"The f(Q,C) parameters cancel out of the background equations, so the paper constrains only the imposed EoS ansatz, not the gravity model.","tokens_in":784,"tokens_out":1782,"would_cite":false,"duration_ms":55458,"reading_group":"no","serious_thinker":"no","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["83D05","83F05"],"pacs":["04.50.Kd","95.36.+x","98.80.-k"],"model":"deepseek-v4-flash","headline":"A linear f(Q,C) gravity model with three dark energy equations of state fits Hubble, BAO, and supernova data and supports late-time cosmic acceleration.","keywords":["f(Q,C) gravity","non-metricity","dark energy","equation of state parameterization","observational constraints","deceleration parameter","statefinder diagnostics","energy conditions"],"falsifier":"Measure $H(z)$ at several redshifts between $0.4$ and $1.2$ with errors below about 2 percent and compare the deceleration-to-acceleration transition redshift $z_{\\rm tr}$: the models predict $z_{\\rm tr}\\approx0.54$--$0.99$, so observing a transition outside this range, or none at all, would rule out these parameterizations.","tokens_in":27942,"feed_emoji":"🌌","tokens_out":6191,"duration_ms":91808,"temperature":0.7,"pith_summary":"This paper tests whether a specific modified gravity theory, $f(Q,C)$ gravity with the linear action $f(Q,C)=\\alpha Q+\\beta C$, can describe late-time cosmic acceleration. The authors impose three redshift-dependent forms for the dark energy equation of state, integrate them through the field equations to get explicit Hubble functions $H(z)$, and fit the free parameters against Hubble, BAO, and Pantheon supernova data. All three parameterizations fit the data, yield a deceleration-to-acceleration transition at redshifts near $0.5$--$1.0$, and satisfy the usual energy-condition and stability checks while predicting a positive energy density and negative pressure. The paper concludes that $f(Q,C)$ gravity is a viable framework for diverse dark energy dynamics.","feed_headline":"f(Q,C) gravity matches cosmic acceleration data","feed_subtitle":"Three dark-energy equation-of-state forms all pass Hubble, BAO, and supernova tests.","key_machinery":"The central object is the linear Lagrangian $f(Q,C)=\\alpha Q+\\beta C$, which reduces the $f(Q,C)$ field equations in a flat FRW universe to $\\kappa\\rho=3\\alpha H^2$ and $\\kappa p=-3\\alpha H^2-2\\alpha \\dot H$, giving the equation-of-state identity $\\omega=-1-\\frac{2}{3}\\frac{\\dot H}{H^2}$. Substituting the three parameterized $\\omega(z)$ forms into this identity and integrating yields closed-form Hubble functions $H(z)$ (equations 33, 35, and 37), from which the deceleration parameter, energy density, pressure, energy conditions, statefinder parameters, and sound speed are all derived.","core_discovery":"The central claim is that the linear $f(Q,C)=\\alpha Q+\\beta C$ model, combined with any of three parameterized dark energy equations of state ($\\omega=\\omega_0+\\omega_1 z$, $\\omega=\\omega_0+\\omega_1 z(1+z)/(1+z^2)$, and $\\omega=\\omega_0+\\omega_1 z^2/(1+z^2)$), reproduces the observed expansion history. With best-fit parameters, the deceleration parameter crosses from positive to negative at low redshift, the energy density is positive while the pressure is negative, the NEC, WEC, and DEC hold while the SEC is violated, and the sound speed lies between 0 and 1. The statefinder diagnostics place the first two parameterizations in the quintessence region of the $\\{r,s\\}$ plane and the third near the $\\Lambda$CDM fixed point, supporting $f(Q,C)$ gravity as a viable dark energy framework.","pith_inferences":["The three EoS forms are assumed rather than derived from the action, so the viability claim attaches to the parameterized one-fluid cosmologies; a different EoS history could change the conclusions.","Adding growth-rate data or explicitly including radiation and baryonic matter would test whether the single-fluid simplification hides tension with CMB-era observations.","The near-$\\Lambda$CDM behavior of Model 3 suggests the framework may mimic a cosmological constant at the background level; checking the growth index would distinguish this from a true constant."],"forward_implications":["The model predicts a deceleration-to-acceleration transition at $z_{\\rm tr}\\approx0.54$--$0.99$ depending on the parameterization and dataset, a directly testable signature.","The fitted $H_0\\approx67.4$--$67.9$ km/s/Mpc sits close to the value from CMB measurements, so the model does not aggravate the Hubble tension.","Models 1 and 2 describe dark energy as quintessence-like with a time-varying equation of state, while Model 3 behaves nearly like $\\Lambda$CDM, so the framework accommodates a spectrum of dark energy behaviors.","All three parameterizations satisfy the sound-speed stability condition $0<c_s^2<1$, meaning dark energy perturbations do not grow uncontrollably.","The energy conditions are satisfied except for the SEC, which is violated, matching the standard requirement for accelerated expansion."],"supporting_citations":[{"why":"establishes the f(Q,C) gravity action and field equations used throughout the paper.","marker":"[14]"},{"why":"provides the symmetric teleparallel / f(Q) foundation that f(Q,C) extends.","marker":"[12]"},{"why":"supplies the linear EoS parameterization ω=ω0+ω1z used as Model 1.","marker":"[51]"},{"why":"supplies the Model 2 EoS parameterization ω=ω0+ω1z(1+z)/(1+z²).","marker":"[56]"},{"why":"supplies the Model 3 EoS parameterization ω=ω0+ω1z²/(1+z²).","marker":"[58]"},{"why":"provides the CMB-based H0 value used to check consistency of the fitted Hubble constant.","marker":"[53]"},{"why":"is the Pantheon supernova dataset that enters the joint likelihood.","marker":"[49]"},{"why":"supplies the cosmic-chronometer H(z) data used for the first dataset.","marker":"[21]"},{"why":"defines the statefinder pair {r,s} used to classify dark energy behavior.","marker":"[63]"}],"fun_headline_variants":["f(Q,C) gravity: three dark energy EoS all pass cosmic tests","Linear f(Q,C) model matches Hubble, BAO, and supernova data","f(Q,C) gravity: deceleration to acceleration matches data","Statefinder shows f(Q,C) mimics quintessence or LambdaCDM"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the universe's total energy content behaves as a single perfect fluid whose equation of state is exactly one of the three adopted redshift parameterizations, with no separate matter or radiation density parameter; if the real universe needs a multi-component energy budget, or if these EoS forms are not the correct effective description of $f(Q,C)$ gravity, the fitted parameters are not predictions of the theory.","fun_headline_variants_meta":{"raw":{"variants":["f(Q,C) gravity: three dark energy EoS all pass cosmic tests","Linear f(Q,C) model matches Hubble, BAO, and supernova data","f(Q,C) gravity: deceleration to acceleration matches data","Statefinder shows f(Q,C) mimics quintessence or LambdaCDM"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000713,"raw_usage":{"total_tokens":3223,"prompt_tokens":977,"completion_tokens":2246,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":593,"completion_tokens_details":{"reasoning_tokens":2165}},"tokens_in":593,"tokens_out":2246,"duration_ms":18184,"temperature":1.0,"reasoning_tokens":2165,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T20:45:07.862367+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure $H(z)$ at several redshifts between $0.4$ and $1.2$ with errors below about 2 percent and compare the deceleration-to-acceleration transition redshift $z_{\\rm tr}$: the models predict $z_{\\rm tr}\\approx0.54$--$0.99$, so observing a transition outside this range, or none at all, would rule out these parameterizations.","supporting_citations":[{"cited_title":"Statefinder—A new geometrical diagnost ic of dark energy","cited_arxiv_id":null,"evidence_quote":"defines the statefinder pair {r,s} used to classify dark energy behavior."},{"cited_title":"Coincident gener al relativity","cited_arxiv_id":null,"evidence_quote":"provides the symmetric teleparallel / f(Q) foundation that f(Q,C) extends."},{"cited_title":"Probing dark energy: Methods an d strategies","cited_arxiv_id":null,"evidence_quote":"supplies the linear EoS parameterization ω=ω0+ω1z used as Model 1."},{"cited_title":"Probing the time depende nce of dark energy","cited_arxiv_id":null,"evidence_quote":"supplies the Model 2 EoS parameterization ω=ω0+ω1z(1+z)/(1+z²)."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"supplies the Model 3 EoS parameterization ω=ω0+ω1z²/(1+z²)."},{"cited_title":"Planck 2018 Results. VI . Cosmological Parameters","cited_arxiv_id":null,"evidence_quote":"provides the CMB-based H0 value used to check consistency of the fitted Hubble constant."},{"cited_title":"K., Tiwari, D","cited_arxiv_id":null,"evidence_quote":"supplies the cosmic-chronometer H(z) data used for the first dataset."}],"review_version":1}