{"id":"d3f12014-acb0-4206-9a8b-1663cfdb5c80","arxiv_id":"2505.01661","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"This work obtains H0 around 72.9 to 73.1 km/s/Mpc and a sound horizon around 137 to 138 Mpc from combined DESI, H0LiCOW, and Pantheon data, in tension with Planck.","lead":"Using DESI galaxy surveys, gravitational lens time delays, and Pantheon supernovae, this paper estimates the universe's expansion rate and the sound horizon without fixing a dark energy model. It finds a Hubble constant near 73 km/s/Mpc, matching the local SH0ES measurement and disagreeing with the Planck early-universe value.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Taylor and Padé truncation errors at DESI high-z BAO are not tested; their mutual agreement does not bound shared bias, so the lensing-anchored H0 and rd calibration may shift.","rationale":"The strongest claim is the model-independent measurement of H0 and rd from late-time data. The most load-bearing link in that argument is the mapping between the absolute lensing distances, which are anchored near z < 0.8, and the DESI BAO observables at z up to 4.2. That mapping is provided entirely by the truncated cosmographic expansions. The paper does several things well: it uses the full H0LiCOW posterior distributions rather than Gaussian approximations, it marginalizes the supernova absolute magnitude, it runs a standard MCMC analysis, and it reports a DIC comparison between the two expansions. None of these, however, bounds the truncation error of a fourth-order Taylor series or a (2,1) Padé approximant at z > 1. The two approximants are not independent checks because both are derived from the same low-redshift Taylor coefficients. The reader identified this concern, including the unreported Omega_k dependence. I agree that the verdict should remain conditional: the paper is a reasonable analysis, but the headline uncertainties do not yet include the dominant model-approximation systematic. A redshift-cut rerun is a direct, feasible test of whether that systematic actually moves H0 or rd. If it does not, the central claim is substantially strengthened.","tokens_in":14393,"tokens_out":13328,"duration_ms":142588,"concrete_test":"Rerun the joint DESI + 4D_d + 6D_Dt + SN analysis with DESI BAO restricted to effective redshifts z_eff <= 1.5, excluding all Lyman-alpha and high-z quasar bins, keeping the lensing and supernova data unchanged, for both Taylor and Padé cosmography. If the median H0 shifts by more than about 1.8 km/s/Mpc or rd shifts by more than about 3.5 Mpc relative to the full-data result, the headline values depend on untested high-redshift extrapolation and the central claim should be downgraded. If the results are stable, the low-z anchors dominate and the truncation concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that H0 = 72.9 ± 1.8 km/s/Mpc and rd = 138.2 Mpc are model-independent rests on the accuracy of the fourth-order Taylor series (Eqs. 2-3) and the Padé (2,1) form (Eq. 7) over the full DESI BAO redshift range, including Lyman-alpha bins with effective redshifts up to about 4.2. Both are low-redshift expansions calibrated at z = 0; at z > 1 their truncation error is not quantified. The paper itself acknowledges Taylor convergence problems at z > 1 in Section 2.2 and recommends using Padé instead, yet it still reports the Taylor result as a headline value. Agreement between Taylor and Padé at the 0.2 km/s/Mpc level is therefore not a robustness check: both are built from the same low-z Taylor coefficients and can fail in the same direction at high z. In addition, the curvature parameter Omega_k appears explicitly in Eqs. (3)-(4) but is never fitted or reported, which is effectively an unstated flatness assumption. If D_M/rd and D_H/rd at z > 1.5 are systematically mispredicted, the absolute calibration provided by the lensing distances propagates into shifted H0 and rd values. No residual check, convergence test, or higher-order comparison is shown.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper combines DESI BAO measurements, six time-delay distances and four deflector angular-diameter distances from the H0LiCOW sample, and the Pantheon SNe Ia sample, using a fourth-order Taylor expansion and a Padé (2,1) approximant for the distance-redshift relation. The authors report H0 = 72.9 ± 1.8 km/s/Mpc and rd = 138.2 ± 3.9/3.3 Mpc for the Taylor cosmography, and H0 = 73.1 ± 1.8 km/s/Mpc and rd = 137.0 ± 3.7/3.2 Mpc for the Padé cosmography, concluding that these late-time values favor a larger H0 and a smaller rd than Planck flat-ΛCDM while agreeing with SH0ES.","tokens_in":14739,"tokens_out":7708,"duration_ms":82858,"significance":"If the result holds, the paper provides a useful late-time, cosmographic calibration of H0 and rd that is independent of early-universe physics and of a specific dark-energy model. The analysis is a direct likelihood fit to public data, uses a standard MCMC approach, and its full-data results are qualitatively consistent with earlier work by Wojtak & Agnello (2019) and with the H0LiCOW analyses. The main value is in showing that the DESI BAO + lensing + SNe combination can anchor an absolute distance scale without a CMB prior. However, the strength of the conclusion depends on the fidelity of the two low-order distance approximants over the full redshift range, and on the treatment of curvature, neither of which is adequately tested in the manuscript.","major_comments":[{"comment":"The curvature parameter Ω_k appears explicitly in the distance expansion at third and fourth order in z, yet it is absent from the list of fitted parameters and is never reported in Table 1. Setting Ω_k = 0 is an unstated flatness assumption, and it conflicts with the paper's claim of model independence. Because the DESI BAO data include high-redshift Lyman-alpha bins, a nonzero Ω_k would change the model predictions for D_M/rd and D_H/rd and would propagate into the inferred H0 and rd. Please either fit Ω_k with a prior, or explicitly state the flat assumption and demonstrate insensitivity by repeating the analysis for fixed Ω_k values such as ±0.01 or by adding a geometric curvature probe.","section":"Section 2.1, Eqs. (3)-(4), Table 1"},{"comment":"The central calibration uses the fourth-order Taylor expansion and the Padé (2,1) approximant out to the highest DESI BAO redshifts, including Lyman-alpha bins with effective redshifts above 2, while Section 2.2 itself concedes that the Taylor series has convergence problems for z > 1. No truncation-error estimate, residual plot, or higher-order comparison is provided. The agreement between the Taylor and Padé results at the ~0.2 km/s/Mpc level is not a sufficient robustness check, because both approximants are constructed from the same low-order Taylor coefficients and can share a common high-z bias. Please add quantitative convergence tests, for example a Padé (3,2) or (2,2) fit, or a repeat of the analysis with the BAO data truncated at z < 1.5, together with residuals as a function of redshift.","section":"Section 2.2, Eqs. (2), (3), (7), Table 1"},{"comment":"The Pantheon χ² in Eq. (19) sums only the diagonal variance σ²_μ,SN. The Pantheon release includes a full covariance matrix with systematic contributions, and standard analyses use the inverse covariance matrix. Restricting to the diagonal underestimates the SNe uncertainties and can bias the inferred q0, j0, and s0, which enter the distance model and therefore the calibration of H0 and rd. Please use the full Pantheon covariance matrix, or clearly justify the diagonal-only approximation and quantify its effect on the reported parameters.","section":"Section 3.3, Eq. (19)"}],"minor_comments":[{"comment":"The redshift coverage is described inconsistently: Section 3.1 states DESI BAO spans 0.1 < z < 4.2, while Section 2.2 and the conclusion refer to data extending to z ≈ 2.3. Please state the effective redshifts of the highest DESI bins (e.g., the Lyman-alpha effective redshift) consistently throughout.","section":"Section 2.2 and Section 5"},{"comment":"The DIC definition contains an algebraic typo: DIC = D(θbar) + 2p_D = Dbar + p_D, not D(θbar) + p_D. Additionally, 'deending' should read 'depending'.","section":"Section 4, Eq. (21)"},{"comment":"The paper reports the Taylor-series value as a headline result in the abstract and conclusion even though it recommends using the Padé approximation and discarding the Taylor expansion in future analyses; please state explicitly which of the two results is considered fiducial.","section":"Section 4 and Table 1"},{"comment":"Several references are duplicated in the bibliography, including Jee et al. 2019, Liao et al. 2020, Poulin et al. 2019, and Wojtak & Agnello 2019; these should be merged.","section":"References"},{"comment":"There are minor typographical errors, including 'Supernavae' in the Section 3.3 title, 'Talor' after Eq. (8), and 'constraining chances' in Section 4; these should be corrected.","section":"Throughout"}],"recommendation":"major_revision","confidential_remarks":"The paper is a straightforward data combination with moderate novelty, but the analysis is clean and the datasets are public. The main risk is the overstatement of model independence: the treatment of Ω_k and the lack of convergence tests are fixable within the scope of a revision. I do not see grounds for rejection, but the authors should be required to add the requested tests and to temper the 'model-independent' language."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nQuick take: this is a competent, incremental late-time combination. The new piece is just the dataset combination—DESI DR1 BAO, six H0LiCOW time-delay distances, four deflector angular diameter distances, and Pantheon SNe—fitted with fourth-order Taylor and Padé (2,1) cosmographies. That exact combination hasn't been published, and the resulting H0 around 73 and rd around 137–138 Mpc are consistent with SH0ES and prior late-time analyses. The lensing KDE treatment of correlated posteriors is a nice touch, and the DIC comparison is honest about the fact that neither expansion wins consistently.\n\nBut the paper overstates model-independence. Two concrete issues. First, Omega_k appears in Eqs. (3)–(4) but is never fitted or reported; the analysis silently assumes flatness. That is exactly the kind of model dependence the title claims to avoid. Second, the Taylor series is a fourth-order expansion around z=0, and the data extend to z~4.2 through DESI Lyman-alpha BAO. The authors themselves note Taylor convergence problems at z>1 and recommend Padé, yet they still present the Taylor value as a headline. Agreement between Taylor and Padé does not bound shared truncation bias, since the Padé (2,1) coefficients come from the same low-z Taylor expansion. No convergence test, higher-order comparison, or residual check is shown. If the high-z distance ratios are mispredicted, the lensing anchor propagates that into H0 and rd, and the reported error bars likely understate this systematic.\n\nMinor point: the Pantheon likelihood in Eq. (19) appears to use only diagonal errors; the full Pantheon covariance includes systematics. If they used the full covariance, the text should say so.\n\nSo the paper is fine as a dataset re-analysis, and the numbers are plausible, but I would not call the constraints model-independent. The authors are straight about the Taylor issue and the literature coverage is adequate. It deserves a serious referee, not a desk reject. The referee should ask for a treatment of Omega_k, a truncation-error estimate for the high-z BAO, and a clarification of the SNe covariance. Those fixes would make this a useful incremental contribution.","headline":"A competent incremental combination of DESI BAO, H0LiCOW lensing, and Pantheon gives H0~73 and rd~138, but the 'model-independent' label is oversold given the silent flatness assumption and untested high-z expansion.","tokens_in":15227,"tokens_out":3582,"would_cite":false,"duration_ms":36108,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["85A40","83F05"],"pacs":["98.80.-k","98.80.Es"],"model":"deepseek-v4-flash","headline":"This paper claims that model-independent late-universe data—DESI BAO, time-delay lenses, and Pantheon SNe—yield H0 ≈ 73 km/s/Mpc and rd ≈ 137–138 Mpc, favoring the SH0ES value over Planck flat-ΛCDM.","keywords":["Hubble constant","sound horizon","cosmography","baryon acoustic oscillations","time-delay lensing","type Ia supernovae","Hubble tension","Padé approximation"],"falsifier":"Redo the joint fit with spatial curvature Ω_k included as a free parameter and with a higher-order approximation such as Padé (3,2) or a fifth-order Taylor series; if the inferred H0 shifts by more than about 2 km/s/Mpc or rd by more than about 4 Mpc relative to the quoted errors, the reported values are artifacts of the truncation and the fixed flatness assumption.","tokens_in":14210,"feed_emoji":"🔭","tokens_out":8389,"duration_ms":68846,"temperature":0.7,"pith_summary":"This paper tries to measure the Hubble constant H0 and the sound horizon rd without assuming a cosmological model like ΛCDM. It combines DESI baryon acoustic oscillation data with six time-delay lensing distances and four deflector angular diameter distances from H0LiCOW, plus the Pantheon supernovae sample. Two flexible distance-redshift approximations are used: a fourth-order Taylor series and a Padé (2,1) rational function. Both give H0 ≈ 72.9–73.1 km/s/Mpc and rd ≈ 137–138 Mpc. Those values support the higher H0 measured by the SH0ES distance ladder and a smaller sound horizon than Planck's flat-ΛCDM prediction, so the Hubble tension persists even without assuming a cosmological model.","feed_headline":"Late-universe data put H0 at 73 without assuming a model","feed_subtitle":"Combining DESI BAO, lensed quasars, and supernovae gives H0 ≈ 73 and a short sound horizon, matching SH0ES not Planck.","key_machinery":"The central machinery is a model-independent cosmographic parameterization of the distance-redshift relation. The Taylor series expands H(z) to fourth order in terms of the present-day deceleration q0, jerk j0, and snap s0, and integrates to give the luminosity distance DL(z); the Padé (2,1) approximation instead represents DL(z) as a rational function with the same cosmographic coefficients, chosen because Padé has a larger convergence radius at high redshift. These relations generate the angular diameter distance DA = DL/(1+z)^2, the transverse comoving distance DM = DL/(1+z), the Hubble distance DH = c/H(z), and the dilation scale DV = [z $DM^{2}$ DH]^{1/3}, so the DESI BAO measurements of DV/rd and DM/rd, DH/rd can be combined with the lensing distances that fix the absolute scale, with rd left free.","core_discovery":"The authors claim that combining DESI-BAO with the six time-delay distances and four deflector angular diameter distances from H0LiCOW lenses together with the Pantheon SNe Ia gives H0 = 72.9 ± 1.8 km/s/Mpc for the Taylor series and H0 = 73.1 ± 1.8 km/s/Mpc for the Padé polynomials, with rd = 138.2 Mpc and 137.0 Mpc, respectively. These results are consistent with the SH0ES value of 73.04 ± 1.04 km/s/Mpc and in tension with Planck's 67.4 ± 0.5 km/s/Mpc under flat ΛCDM. The key point is that the absolute distances from strong lensing anchor the relative BAO distances, while supernovae track the expansion history and mainly sharpen the cosmographic parameters.","pith_inferences":["The paper never reports a fitted value for the curvature parameter Ω_k even though it appears explicitly in the Taylor luminosity distance; allowing Ω_k to float is a natural test that could shift the reported H0 and rd.","Given the known convergence problems of the Taylor series above z ≈ 1, the Padé (2,1) result is arguably the more reliable of the two, and a higher-order Padé check would show whether the central values are truly stable.","A confirmation of rd ≈ 137 Mpc by future DESI data would strengthen the motivation for early-universe models that reduce the sound horizon, tying this measurement directly to the wider Hubble-tension discussion."],"forward_implications":["If the result is right, the Hubble tension is not an artifact of assuming ΛCDM in the late-universe data: a model-independent late-time calibration still lands at about 73 km/s/Mpc.","The inferred rd ≈ 137–138 Mpc is smaller than the Planck-ΛCDM expectation, the direction needed to ease the tension if new pre-recombination physics shrinks the sound horizon.","The combination of absolute lensing distances with relative BAO distances acts as a model-independent ladder; future DESI data releases and larger lens samples should push the H0 uncertainty below 1 km/s/Mpc.","The close agreement between the Taylor and Padé results (≈ 0.2 km/s/Mpc) suggests the H0 value is robust to the choice of distance approximation, although the Taylor series is explicitly less reliable at high redshift.","Supernovae contribute mainly to constraining the cosmographic parameters q0, j0, and s0 rather than to H0 and rd, so further tightening of H0 and rd will come mostly from additional BAO and lensing data."],"supporting_citations":[{"why":"Supplies the DESI BAO measurements (DV/rd, DM/rd, DH/rd) across 0.1 < z < 4.2 that drive the distance-scale constraints.","marker":"Adame et al. 2024"},{"why":"Provides the six time-delay distances and four deflector angular diameter distances that anchor the absolute distance scale.","marker":"Wong et al. 2020"},{"why":"Provides the 1048 Pantheon SNe Ia whose luminosity distances map the expansion history.","marker":"Scolnic et al. 2018"},{"why":"Introduced the Padé approximation for cosmography; its larger convergence radius is the basis of the second, high-redshift-safe approach.","marker":"Gruber & Luongo 2014"},{"why":"The fourth-order Taylor expansion for H(z) and DL(z) (Eqs. 2–3) follows this work.","marker":"Macaulay et al. 2019"},{"why":"Provides the SH0ES value H0 = 73.04 ± 1.04 km/s/Mpc that the new results are found to agree with.","marker":"Riess et al. 2022"},{"why":"Justifies the choice of Padé order (2,1) as the most stable, which determines the exact form of Eq. 7.","marker":"Capozziello et al. 2020"},{"why":"Supplies the Planck flat-ΛCDM value H0 = 67.4 ± 0.5 km/s/Mpc against which the tension is measured.","marker":"Aghanim et al. 2020"}],"fun_headline_variants":["H0 = 73 without assuming a cosmology","Model-free H0 matches SH0ES, not Planck","BAO, quasars, supernovae align at H0 ≈ 73","DESI + H0LiCOW + Pantheon: H0 ≈ 73 model-independent"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole calibration rests on the assumption that the truncated fourth-order Taylor expansion (or the fixed Padé (2,1) form) is an accurate description of the distance-redshift relation across the full data range, including redshifts above z ≈ 2, and that spatial curvature can be held fixed rather than fitted.","fun_headline_variants_meta":{"raw":{"variants":["H0 = 73 without assuming a cosmology","Model-free H0 matches SH0ES, not Planck","BAO, quasars, supernovae align at H0 ≈ 73","DESI + H0LiCOW + Pantheon: H0 ≈ 73 model-independent"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000273,"raw_usage":{"total_tokens":1726,"prompt_tokens":1126,"completion_tokens":600,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":742,"completion_tokens_details":{"reasoning_tokens":522}},"tokens_in":742,"tokens_out":600,"duration_ms":5799,"temperature":1.0,"reasoning_tokens":522,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T04:14:25.443427+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Redo the joint fit with spatial curvature Ω_k included as a free parameter and with a higher-order approximation such as Padé (3,2) or a fifth-order Taylor series; if the inferred H0 shifts by more than about 2 km/s/Mpc or rd by more than about 4 Mpc relative to the quoted errors, the reported values are artifacts of the truncation and the fixed flatness assumption.","supporting_citations":[],"review_version":1}