{"id":"ba84df50-b6bc-4bd7-b55b-8c68b0743b8e","arxiv_id":"2506.06399","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":5,"one_line_summary":"An exponential Om(z) parameterization fitted to CC+BAO+Pantheon+ data gives late-time acceleration parameters but becomes unphysical at high redshift, and the f(T,T_G) gravity parameters are not actually fitted.","lead":"The paper fits a new exponential formula for the Om(z) cosmic diagnostic to supernova, galaxy, and baryon-acoustic-oscillation data, reporting a Hubble constant near 73 km/s/Mpc and a deceleration-to-acceleration transition near redshift 0.5. The model, however, becomes unphysical at high redshift, and the modified-gravity parameters it claims to test are actually fixed by hand rather than constrained by the data.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Best-fit parameters make H(z)^2 negative at z ≳ 11, so the 'well-behaved at all redshifts' claim and all high-redshift derived quantities are internally invalid.","rationale":"The reader's weakest_assumption identifies exactly the high-redshift breakdown of the exponential Om(z) ansatz: for the best-fit values α = -0.148 and β = 0.369, Om(z) becomes negative at z ≈ 10.6, and H(z)^2 becomes negative at z ≈ 11. This is not a minor technicality; it undermines the paper's central claim that the model is 'well-behaved at all redshifts' and that its derived quantities (deceleration parameter, EoS, energy conditions, statefinder, cosmic age) describe the full expansion history. The observational data used (CC up to z ~ 2.4, Pantheon+ up to z ~ 2.26) do not probe this high-redshift region, so the fit cannot detect the breakdown, and the paper provides no goodness-of-fit or model-comparison statistics that might reveal tension. The theoretical inconsistency is sufficient by itself to reject the paper's central conclusion. The arbitrary fixing of γ = 0.05 is a secondary concern, but the high-redshift sign change of H^2 is the most load-bearing issue, and it agrees with the reader's verdict. Since my analysis confirms rather than changes the reader's REJECT decision, the verdict remains unchanged.","tokens_in":16223,"tokens_out":4981,"duration_ms":47840,"concrete_test":"Evaluate Eq. (25) at z = 20 with the reported best-fit α = -0.148, β = 0.369: H(20)^2/H0^2 = (-0.148 e^{20/21} + 0.369)(21^3 - 1) + 1 ≈ -0.0028 × 9259 + 1 ≈ -24.9 < 0. A negative value directly falsifies the claim that the model is well-behaved at all redshifts. To verify that this is not a harmless boundary effect, re-run the MCMC with a hard prior requiring H(z)^2 > 0 for all z ∈ [0, 1100]; if the best-fit region then changes substantially or the fit becomes unacceptably poor, the model cannot simultaneously match the data and remain physically real.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that the exponential Om(z) parameterization is robust and well-behaved at all redshifts fails on the paper's own equations. With Eq. (21), Om(z) = α e^{z/(1+z)} + β. Inserting the CC+BAO+Pantheon+ best fit (α = -0.148, β = 0.369) gives Om(z) → α e + β ≈ -0.033 < 0 as z → ∞, and Om(z) = 0 at z ≈ 10.6. In Eq. (25), H(z)^2/H0^2 = Om(z)[(1+z)^3 - 1] + 1; for z ≳ 11 the negative Om multiplied by the cubic term makes H(z)^2 negative, so the model has no real expansion history in the early universe. The paper invokes this H(z) to compute q(z), ρ, p, ω, energy conditions, statefinder parameters and the cosmic age integral (Eq. 49) up to arbitrarily high redshift; those results are therefore unphysical or defined only over a truncated range. Section 4 explicitly asserts that the z/(1+z) form 'remains well-behaved at all redshifts from z=0 to high redshift z→∞', which is contradicted by the best-fit parameters reported in Section 5. The age estimates and the transition/statefinder results depend on integrals or derivatives that enter the broken region, so the claim of 'stable and physically realistic behavior across all epochs' is unsupported. Additionally, the statement in Section 4 that negative α produces an increasing Om(z) is backwards: d Om/dz = α e^{z/(1+z)}/(1+z)^2 is negative for α < 0, so Om(z) decreases with z, contrary to the phantom-like interpretation given. The gravity parameter γ is also fixed to 0.05 rather than fitted, so the energy-condition and EoS results are not constrained by the data. The single most load-bearing issue is the high-redshift breakdown: it invalidates the model as a complete cosmological description no matter how well the low-z fit looks.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes an exponential parameterization of the Om(z) diagnostic, Om(z) = α e^{z/(1+z)} + β, within the f(T,T_G) = T + γ√T_G + δ√T gravity model. The authors invert the standard Om diagnostic to reconstruct H(z), fit α, β, and H0 to 31 cosmic chronometer, 26 BAO, and 1701 Pantheon+ data points using MCMC, and then derive q(z), the effective equation of state, energy conditions, statefinder parameters, and the cosmic age. The reported best-fit results include H0 ≈ 73.3 km/s/Mpc, z_tr ≈ 0.48–0.54, q0 ≈ −0.34, ω0 ≈ −0.33, and an age of 13.28–13.87 Gyr, leading the authors to claim the model is observationally supported and well-behaved at all redshifts.","tokens_in":16602,"tokens_out":7706,"duration_ms":75000,"significance":"If the reconstructed expansion history and the derived cosmological parameters were reliable, the paper would add a useful example to the literature on Om(z) parameterizations in modified gravity. The use of 31 CC + 26 BAO + 1701 Pantheon+ points is a reasonable dataset combination, and the paper presents the field-equation algebra explicitly, which aids reproducibility of the derivation. However, the central claims are undermined by an internal inconsistency in the high-redshift regime, an error in the interpretation of the fitted parameters, and an ad hoc treatment of the modified-gravity parameters. The presently stated conclusions therefore do not provide a dependable test of the f(T,T_G) framework.","major_comments":[{"comment":"The claim that the exponential Om(z) form 'remains well-behaved at all redshifts from z=0 to high redshift z→∞' is contradicted by the paper's own best-fit values. With α = −0.148 and β = 0.369 (the CC+BAO+Pantheon+ case), Om(z) = α e^{z/(1+z)} + β vanishes at z ≈ 10.6 and becomes negative for larger z. Since H(z)^2/H0^2 = Om(z)[(1+z)^3 − 1] + 1, H(z)^2 becomes negative for z ≳ 11, so H(z) is imaginary in the early universe. Every quantity derived from H(z), including q(z) in Eq. (39), ρ and p in Eqs. (40)–(41), the energy conditions in Eqs. (43)–(45), the statefinder parameters, and the age integral in Eq. (49), is therefore not defined on the full redshift range used to support the claimed 'stable and physically realistic behavior across all epochs'.","section":"§4, Eqs. (21), (25)"},{"comment":"The phantom-like interpretation of the best fit is based on an incorrect derivative. The text states that a negative α produces an increasing Om(z), but dOm/dz = α e^{z/(1+z)}/(1+z)^2, which is negative for α < 0. Hence the best-fit parameter set gives a decreasing Om(z), not an increasing one. The claimed phantom behavior and the related discussion in Sections 5.2 and 6.4 need to be revised accordingly.","section":"§4, Eq. (21)"},{"comment":"The observational analysis does not actually constrain the f(T,T_G) model. The reconstructed H(z) comes entirely from the Om(z) ansatz (Eqs. 21 and 25), and the MCMC fit in Section 5 involves only H0, α, and β; the gravity parameters γ and δ do not enter the likelihood. The field equations of f(T,T_G) are used only after the fit, with γ fixed to 0.05, to compute ρ, p, the EoS, and the energy conditions. Consequently, the claimed agreement with CC+BAO+Pantheon+ data is a statement about the kinematic Om(z) parameterization, not about f(T,T_G) gravity; the modified-gravity part of the model is not tested by the data.","section":"§2–3, 5"},{"comment":"The energy-density, pressure, EoS, and energy-condition results are presented for γ = 0.05 with no explanation of how this value was chosen and no propagation of the MCMC uncertainties. Since γ is a free parameter in the action, the statement that the model 'satisfies NEC and DEC' is not a result of the observational fit; it is conditional on an arbitrary choice of γ. A joint fit over γ (or a demonstration of insensitivity to γ) is needed before these claims can be regarded as a test of the model.","section":"§6.2–6.3, §7, Eqs. (40)–(45)"}],"minor_comments":[{"comment":"The BAO chi-square uses the notation σYi; this should read σ(Y_i) or σ_i. In addition, the manuscript does not itemize the 26 BAO data points or the exact covariance information, making the analysis difficult to reproduce.","section":"§5.1.1, Eq. (34)"},{"comment":"The caption contains a typo: 'CC+ABO' should be 'CC+BAO'. The caption also refers to 'Pantheon+SHOES' while the text and abstract refer to the Pantheon+ dataset; the nomenclature should be unified.","section":"Fig. 3 caption"},{"comment":"The text states that Om(z) 'starts near 0.05 at higher redshifts and approaches approximately 0.36 as z → −1', while the figure axis extends to z = −1, where the combination z/(1+z) is singular. The redshift range of the plot and the interpretation of the limiting behavior should be clarified.","section":"§6.4 and Fig. 6"},{"comment":"The parameter δ in f(T,T_G) = T + γ√T_G + δ√T does not appear in the reconstructed ρ and p or in any of the derived observables. If δ cancels in the FLRW background, this should be stated explicitly; if it does not, the expressions in Eqs. (40)–(41) are incomplete. As written, the paper advertises a two-parameter modification but effectively analyzes only the γ√T_G term.","section":"§3 and §6.2, Eqs. (20), (40)–(41)"}],"recommendation":"reject","confidential_remarks":"The manuscript does not provide the MCMC chains, code, or a full BAO data table, so the numerical results cannot be independently verified. The high-redshift breakdown of H(z)^2 < 0 for the reported best fit is a decisive internal inconsistency that, together with the ad hoc fixing of γ, undermines the central claims. I see no straightforward revision within the paper's current scope that would preserve the stated conclusions."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe short version: this is a new exponential Om(z) parameterization (α e^{z/(1+z)} + β) fitted to CC+BAO+Pantheon+ data within an f(T,TG) = T + γ√TG + δ√T model. The fit itself is fine at low redshift, and the parameterization is genuinely new in the cited Om(z) literature. But the best-fit parameters (α ≈ -0.148, β ≈ 0.369) make Om(z) cross zero at z ≈ 10.6, so H(z)^2 goes negative for z ≳ 11. That kills the paper's repeated claim that the model is 'well-behaved at all redshifts' and invalidates the age integral and all derived high-z quantities.\n\nWhat the paper does well: it runs a standard MCMC with 31 CC, 26 BAO, and 1701 Pantheon+ points, reports parameter ranges, and computes the usual diagnostics. The low-z phenomenology—transition redshift ~0.5, q0 ~ -0.33, H0 near local measurements—is consistent with what you'd expect from any flexible parameterization fit to this data. The exponential form is reasonably motivated as a saturating deviation from ΛCDM.\n\nThe soft spots are not subtle. First, the high-redshift breakdown is a load-bearing flaw: any quantity that depends on H(z) beyond z≈11 is imaginary or meaningless. Second, the paper claims a negative α produces an increasing Om(z), but dOm/dz = α e^{z/(1+z)}/(1+z)^2, so with α<0 the function decreases. Their phantom interpretation is literally backwards. Third, γ is set to 0.05 by hand, δ never appears in the density/pressure expressions, and no fit or error propagation for the gravity parameters is given, so the f(T,TG) results are unconstrained. Fourth, there is no goodness-of-fit statistic or model comparison, and the derived parameters (q0, ω0, ztr, age) are direct functions of the fitted α, β, H0—they are not independent predictions. The statefinder section also contradicts itself: it says the trajectory passes through the ΛCDM point while reporting r0 = 0.5956.\n\nWho is this for? A reader interested in yet another Om(z) parameterization might glance at the low-z fit, but the paper's central claim of a robust, physically viable model fails on its own equations. I would not send this to a referee in its current form; it needs a major revision that restricts the model's valid redshift range, fixes the monotonicity error, and actually constrains or marginalizes over γ. If those are fixed, a modest empirical paper could emerge, but as written this deserves rejection.","headline":"New exponential Om(z) parameterization fit to standard datasets, but the best-fit parameters make H(z)^2 negative at z≳11, contradicting the paper's central 'well-behaved at all redshifts' claim.","tokens_in":17190,"tokens_out":4189,"would_cite":false,"duration_ms":40878,"reading_group":"no","serious_thinker":"no","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["83F05","83D05"],"pacs":["98.80.-k","98.80.Es","04.50.Kd"],"model":"deepseek-v4-flash","headline":"An exponential Om(z) diagnostic in modified teleparallel gravity fits the combined CC, BAO, and Pantheon+ datasets and yields a Hubble constant in line with local distance-ladder measurements.","keywords":["modified teleparallel gravity","f(T,T_G) gravity","Om(z) diagnostic","exponential parameterization","dark energy","late-time cosmic acceleration","observational constraints","Hubble constant tension"],"falsifier":"A reliable measurement of $H(z)$ at a redshift above about 10.6 would falsify the all-redshift claim, because the best-fit model makes $H(z)^2$ negative there. Even without new data, evaluating the reconstructed $H(z)$ at $z=10.6$ with $\\alpha=-0.148$ and $\\beta=0.369$ gives a negative square, contradicting the paper's statement that the model is well-behaved at all redshifts.","tokens_in":15954,"feed_emoji":"🌌","tokens_out":11668,"duration_ms":114615,"temperature":0.7,"pith_summary":"The paper tries to establish that a two-parameter exponential form of the $Om(z)$ diagnostic, $Om(z)=\\alpha e^{z/(1+z)}+\\beta$, can describe the late-time acceleration of the universe when the gravity sector is the square-root teleparallel model $f(T,T_G)=T+\\gamma\\sqrt{T_G}+\\delta\\sqrt{T}$. A sympathetic reader would care because the model fits 31 cosmic-chronometer, 26 BAO, and 1701 Pantheon+ supernova points with just two extra parameters, and it returns a Hubble constant near the local distance-ladder value, offering one route toward the Hubble tension. The same fit produces a transition redshift and present deceleration and equation-of-state values close to those inferred in standard cosmology, so the model is a viable alternative to a cosmological constant. It also predicts a universe age of about 13.3–13.9 Gyr and satisfies the null and dominant energy conditions while violating the strong energy condition at late times.","feed_headline":"Exponential Om(z) diagnostic yields H0 in line with local measurements","feed_subtitle":"An exponential Om(z) form in f(T,T_G) gravity reproduces late-time acceleration and a local-value Hubble constant.","key_machinery":"The central object is the exponential $Om(z)$ diagnostic, $Om(z)=\\alpha e^{z/(1+z)}+\\beta$, whose inversion through the definition $Om(z)=((H/H_0)^2-1)/((1+z)^3-1)$ produces the model Hubble function $H(z)=H_0\\sqrt{(\\alpha e^{z/(1+z)}+\\beta)[(1+z)^3-1]+1}$. This Hubble function is fed into the modified Friedmann equations of $f(T,T_G)=T+\\gamma\\sqrt{T_G}+\\delta\\sqrt{T}$ (with $\\gamma=0.05$ used for the derived plots), which turn it into predictions for the deceleration parameter, energy density and pressure, equation of state, energy conditions, statefinder pair, and cosmic age. The diagnostic carries the argument by converting a model-independent ratio of Hubble rates into a parameterized expansion history that can be fit directly to CC, BAO, and Pantheon+ data.","core_discovery":"The paper's central claim is that the exponential diagnostic $Om(z)=\\alpha e^{z/(1+z)}+\\beta$, combined with the modified teleparallel gravity model $f(T,T_G)=T+\\gamma\\sqrt{T_G}+\\delta\\sqrt{T}$, accounts for the observed late-time expansion history. With the combined CC+BAO+Pantheon+ dataset the best-fit parameters $\\alpha=-0.148$, $\\beta=0.369$ yield $H_0\\approx73.3$ km/s/Mpc with a 1$\\sigma$ range of about 68.5–77.4, a deceleration-to-acceleration transition at $z_{tr}\\approx0.48$–$0.54$, present $q_0\\approx-0.32$ to $-0.34$ and $\\omega_0\\approx-0.33$, and a cosmic age of about 13.3–13.9 Gyr. The model satisfies the null and dominant energy conditions, violates the strong energy condition at late times, and its statefinder trajectory passes through the $\\Lambda$CDM point $(r,s)=(1,0)$. The authors take these results to show that the exponential $Om(z)$ form is a viable, data-consistent description of dark energy evolution within this modified gravity framework.","pith_inferences":["Read as a full-history model, the best-fit form fails at high redshift: $\\alpha e^{z/(1+z)}+\\beta$ changes sign near $z\\approx10.6$, making the reconstructed expansion rate imaginary. That suggests the exponential diagnostic should be treated as a late-time parameterization rather than a complete description of the early universe.","Because $\\gamma$ is set to 0.05 by hand for the energy-condition and equation-of-state plots, those conclusions are conditional on that choice; a joint fit of $\\gamma$ with $\\alpha$ and $\\beta$ would test whether the NEC and DEC results survive.","Since the paper compares against $\\Lambda$CDM but not against other two-parameter dark-energy forms, a model comparison on the same data would show whether the exponential shape itself is preferred or merely adequate.","The negative $\\alpha$ produces an $Om(z)$ that grows with redshift, which the paper links to phantom-like dark energy; a derived check of whether this growth leads to a future singularity would extend the model's predictions beyond the current epoch."],"forward_implications":["The combined CC, BAO, and Pantheon+ data can be described by a two-parameter exponential $Om(z)$ diagnostic, so the present data do not require a cosmological constant if modified teleparallel gravity is allowed.","The best-fit $H_0$ of about 73.3 km/s/Mpc sits closer to local distance-ladder values than to the early-universe Planck value, giving a concrete path toward easing the Hubble tension.","The predicted transition redshift $z_{tr}\\approx0.48$–$0.54$ and present deceleration $q_0\\approx-0.32$ place the onset of acceleration at roughly the epoch inferred in $\\Lambda$CDM.","The model's statefinder trajectory passes through the $\\Lambda$CDM point $(r,s)=(1,0)$, so the modified-gravity model is observationally close to $\\Lambda$CDM while allowing evolving dark energy.","The age estimate of 13.3–13.9 Gyr is consistent with globular-cluster and Planck age bounds, so the model does not require a revision of cosmic chronology."],"supporting_citations":[{"why":"Defines the $Om(z)$ diagnostic as a ratio of Hubble rates, which the paper inverts to build its Hubble function.","marker":"[27]"},{"why":"Links the slope of $Om(z)$ to the dark-energy equation of state, which the paper uses to interpret the negative best-fit $\\alpha$ as phantom-like behaviour.","marker":"[29]"},{"why":"Supplies the differential-age method that turns galaxy ages into cosmic-chronometer $H(z)$ measurements.","marker":"[52]"},{"why":"Supplies the 31 cosmic-chronometer data points used in the MCMC fit.","marker":"[54]"},{"why":"Supplies the DESI baryon-acoustic-oscillation measurements used in the MCMC fit.","marker":"[55]"},{"why":"Supplies the 1701 Pantheon+ supernova light curves used in the MCMC fit.","marker":"[59]-[62]"},{"why":"Supplies the drag-epoch sound-horizon calculation used to convert BAO distances into observable ratios.","marker":"[58]"},{"why":"Supplies the local distance-ladder $H_0$ measurement that the paper compares its result to.","marker":"[63]"}],"fun_headline_variants":["Exponential Om(z) diagnostic reproduces local H0 value","Modified gravity with exponential Om(z) matches local H0","Late-time acceleration from exponential Om(z) in f(T,TG) gravity","Exponential Om(z) diagnostic in f(T,TG) gravity yields H0","New exponential Om(z) form ties cosmic expansion to local H0"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the exponential expansion formula used for $Om(z)$ is valid at every redshift, so the reconstructed expansion rate squared stays positive; at the paper's best-fit parameters the factor $\\alpha e^{z/(1+z)}+\\beta$ crosses zero near $z\\approx10.6$, which would make the expansion rate imaginary there.","fun_headline_variants_meta":{"raw":{"variants":["Exponential Om(z) diagnostic reproduces local H0 value","Modified gravity with exponential Om(z) matches local H0","Late-time acceleration from exponential Om(z) in f(T,TG) gravity","Exponential Om(z) diagnostic in f(T,TG) gravity yields H0","New exponential Om(z) form ties cosmic expansion to local H0"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000823,"raw_usage":{"total_tokens":3676,"prompt_tokens":1098,"completion_tokens":2578,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":714,"completion_tokens_details":{"reasoning_tokens":2485}},"tokens_in":714,"tokens_out":2578,"duration_ms":17964,"temperature":1.0,"reasoning_tokens":2485,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T10:15:14.991222+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A reliable measurement of $H(z)$ at a redshift above about 10.6 would falsify the all-redshift claim, because the best-fit model makes $H(z)^2$ negative there. Even without new data, evaluating the reconstructed $H(z)$ at $z=10.6$ with $\\alpha=-0.148$ and $\\beta=0.369$ gives a negative square, contradicting the paper's statement that the model is well-behaved at all redshifts.","supporting_citations":[{"cited_title":"Sahni, A","cited_arxiv_id":null,"evidence_quote":"Defines the $Om(z)$ diagnostic as a ratio of Hubble rates, which the paper inverts to build its Hubble function."},{"cited_title":"Zunckel, C","cited_arxiv_id":null,"evidence_quote":"Links the slope of $Om(z)$ to the dark-energy equation of state, which the paper uses to interpret the negative best-fit $\\alpha$ as phantom-like behaviour."},{"cited_title":"Eisenstein, et al., Astrophys","cited_arxiv_id":null,"evidence_quote":"Supplies the drag-epoch sound-horizon calculation used to convert BAO distances into observable ratios."}],"review_version":1}