{"id":"4b0a790b-1ff3-4645-a681-d2656aa81c27","arxiv_id":"2502.08509","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":7,"one_line_summary":"Using 97 localized fast radio bursts, this paper estimates the Hubble constant at 65.13 +/- 2.52 km/s/Mpc via maximum likelihood, consistent with Planck but not with SH0ES.","lead":"This paper uses 97 localized fast radio bursts to estimate the Hubble constant, the universe's current expansion rate, through three statistical methods. A maximum-likelihood analysis gives H0 = 65.13 +/- 2.52 km/s/Mpc, compatible with Planck's early-universe value, and mock catalogs suggest precision will improve sharply as more bursts are localized.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Mock validation shows the MLE is biased by 2.7 km/s (about 3 sigma of its quoted error) at the claimed 1.4% precision, so the real-data H0 = 65.13 ± 2.52 and the SH0ES-level forecast rest on an uncalibrated host-DM model; Eq. 4 and Eqs. 16–17 also use inconsistent host conventions.","rationale":"The reader's verdict already flags the fixed host DM as the weak assumption. I agree that is central, but the strongest evidence is internal: the paper's own mock catalogs, which are supposed to validate the methods, do not recover the fiducial H0 in three of five estimators. The MLE, the method used for the headline real-data value, is biased low by 2.7 km/s, comparable to or larger than the reported statistical uncertainty. This means the 1.4% precision claim is not an accuracy claim, and the real-data error budget in Eq. 21 omits a systematic that is visible in the controlled test. I also found a concrete convention clash between Eq. 4 and Eqs. 16–17: the former defines DMhost = 100/(1+z), while the latter's derivative terms are only consistent with a constant 100 pc cm^-3 rest-frame host. If the MLE code follows the written Eq. 4, every number shifts; if it follows the derivative convention, the text is misstated. This should be settled by the test. I do not think the paper is worthless: the catalog and likelihood machinery are useful, and the real-data MLE may survive after marginalizing over host parameters. But as written, the central claim is not yet supported. The verdict remains conditional rather than accept; I would not reject outright because the concern is checkable and possibly fixable. The reader's weakest assumption is partial agreement: I extend it from 'host DM is a fixed constant' to 'the estimator is not validated even on the paper's own mocks, largely because of that host model.'","tokens_in":16011,"tokens_out":9684,"duration_ms":98397,"concrete_test":"Re-run the mock pipeline with the paper's own log-normal host distribution (Eq. 23) and fit the MLE under two host conventions: (a) host contribution 100/(1+z)^2 as written in Eqs. 3–4, and (b) host contribution 100/(1+z) as implied by the derivative terms in Eqs. 16–17. For each convention, record the mean recovered H0 over the 100 realizations against the fiducial 70. If neither recovers 70 within about 0.5 km/s, the estimator has an unidentified bias and Eq. 21 must be re-derived with a marginalized host term; if only (b) recovers 70, the real-data calculation uses the wrong convention and all quoted values change.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 4 generates 100 mock catalogs with fiducial H0 = 70 and then applies the same estimators. Table 1 reports MLE = 67.30 ± 0.91, median = 66.10 ± 1.89, linear H(z) = 54.34 ± 1.57, and power-law H(z) = 91.84 ± 1.82. The MLE is thus 2.7 km/s below the input value, about 3 sigma of its quoted 0.91 error, and the two H(z) methods miss by 16–22 km/s. These are the paper's own controlled simulations, so the 1.4% 'SH0ES-level' precision is statistical scatter, not accuracy; the real-data result H0 = 65.13 ± 2.52 (Eq. 21) inherits the same systematics. The likely culprit is the host-galaxy DM model: Section 2 fixes DMhost = 100/(1+z) pc cm^-3 (Eqs. 4–5) for every burst, whereas Section 4's own mock input draws DMhost from a log-normal with mean 40–80 pc cm^-3 (Eq. 23). There is also an internal inconsistency: Eqs. 16–17 contain a +100/(1+z)^2 derivative term that corresponds to a redshift-independent host term of 100 pc cm^-3, not the 100/(1+z) written in Eq. 4. Unless this is resolved and the MLE is shown unbiased on mocks, the H0 estimate and its quoted error are not trustworthy.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper uses the dispersion measures (DMs) of 97 localized fast radio bursts (FRBs) to estimate the Hubble constant H0. It applies three estimators: an arithmetic mean of individual H0 values (H0 = 57.67 ± 11.99 km/s/Mpc), a maximum-likelihood estimate (H0 = 65.13 ± 2.52 km/s/Mpc), and a reconstruction of H(z) from fitted linear and power-law DM–z relations (H0 = 51.27 and 77.09 km/s/Mpc, respectively). The authors also generate 100 mock catalogs of 500 FRBs each and report Table 1: MLE 67.30 ± 0.91, arithmetic mean 66.21 ± 3.46, median 66.10 ± 1.89, linear H(z) 54.34 ± 1.57, and power-law H(z) 91.84 ± 1.82 km/s/Mpc. The abstract and conclusions emphasize that the mock MLE precision (1.4%) is comparable to SH0ES. The paper's central claim is that FRB DMs can provide a precision-competitive, independent constraint on H0.","tokens_in":16486,"tokens_out":5414,"duration_ms":50760,"significance":"If the analysis were sound, the paper would be a useful contribution: it assembles a current catalog of 97 localized FRBs, applies a standard likelihood machinery, and provides a concrete forecast that 500 localized FRBs could reach 1.4% statistical precision. The mock-testing framework is a genuine strength, as it exposes how each estimator behaves on controlled data. However, the paper's own mock results show that the estimators are biased at the claimed precision, and the host-galaxy DM treatment is internally inconsistent. The central numerical results therefore cannot be taken at face value; the significance of the paper depends on whether the systematics can be recalibrated.","major_comments":[{"comment":"The mock validation does not support the claimed precision. With fiducial H0 = 70, the MLE returns 67.30 ± 0.91 km/s/Mpc, a 2.7 km/s/Mpc bias that is about 3σ of the quoted error, while the linear and power-law H(z) methods return 54.34 ± 1.57 and 91.84 ± 1.82 km/s/Mpc, missing the input by 16–22 km/s/Mpc. The 1.4% figure is thus the statistical scatter of the estimator, not its accuracy. The real-data result in Eq. (21) inherits the same unmodeled systematics. In particular, the real-data analysis assumes DMhost = 100/(1+z) pc cm^-3 (Eq. 4), whereas the mock input (Eq. 23) draws DMhost from a log-normal with mean 40–80 pc cm^-3, so the estimator's host-galaxy model is mismatched to the simulation. The pipeline must be recalibrated on mocks whose host-galaxy model matches the one applied to real data, and the quoted errors must include host-galaxy systematics.","section":"Section 4, Table 1"},{"comment":"The derivative term 100/(1+z)^2 is inconsistent with the host-galaxy convention in Eqs. (3)–(4). In Eq. (13), the host term subtracted from DMobs is DMhost/(1+z); with Eq. (4), this is 100/(1+z)^2, whose derivative is 200/(1+z)^3. The denominator used in Eqs. (16)–(17) instead corresponds to a host contribution of 100/(1+z) in the observer frame, i.e., a redshift-independent rest-frame host DM of 100 pc cm^-3. Since the H0 values 51.27 and 77.09 are computed directly from this derivative, they must be re-derived under one consistent convention before they can be reported.","section":"Eqs. (16)–(17)"},{"comment":"The quoted H0 = 65.13 ± 2.52 km/s/Mpc is obtained from likelihood curvature at fixed DMhost, DMMW, and f_IGM assumptions. DMhost is not measured independently for most of the 97 bursts, so the scatter in Eq. (19) is a model assumption rather than a measured uncertainty. The analysis does not marginalize over DMhost, DMMW, or f_IGM, and the error bar therefore understates the total uncertainty. The compatibility with Planck is not a robust statement until a systematic-error budget is included.","section":"Section 3.3, Eq. (21)"},{"comment":"The H(z) method fits DMobs(z) to the same 97 data points and then differentiates the fitted relation, so H0 at z=0 is a direct re-expression of the fitted slope and intercept. The quoted values 51.27 and 77.09 are not independent cosmological constraints but restatements of the assumed functional form; the large spread between them reflects the two arbitrary fitting functions rather than a measurement of H0. This should be stated explicitly, and the method should not be presented as a separate probe.","section":"Section 3.2, Eqs. (12)–(17)"}],"minor_comments":[{"comment":"The Data Availability section reproduces MNRAS policy text but does not actually provide a data availability statement or a link to the catalog. The authors should supply the catalog as supplementary material or state a repository.","section":"Data Availability"},{"comment":"The Reference column contains incomplete entries such as '2016' and '2020; 2023b', and several of these abbreviations cannot be unambiguously matched to the reference list. Please provide full citations or a dedicated reference key.","section":"Table A1"},{"comment":"The Conclusions paragraph misstates Table 1: it reports 66.10 ± 3.46 km/s/Mpc for the median and 67.30 ± 1.89 km/s/Mpc for the MLE, whereas Table 1 gives 66.10 ± 1.89 and 67.30 ± 0.91 km/s/Mpc. The error bars in the conclusions should be corrected.","section":"Conclusions"},{"comment":"The factor 10^4 Ω_b h^2 appears without derivation; Eq. (7) uses Ω_b directly. Please clarify the notation and the relation between the two expressions.","section":"Eq. (8)"},{"comment":"There are several typographical issues, including 'FBRs' in Section 1 and the use of 'pccm−3' without spaces. Please standardize units and fix typos throughout.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"For the editor: the mock-table bias and the host-convention inconsistency are load-bearing, so the paper should not be accepted in its present form. The catalog and the likelihood machinery are potentially useful, and the paper would be salvageable if the authors recalibrate the pipeline on consistent mocks, re-derive Eqs. (16)–(17), and report a systematic error budget. I would also encourage the authors to tone down the SH0ES-level comparison in the abstract until the bias is addressed."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: the MLE result H0 = 65.13 ± 2.52 km/s/Mpc is the kind of number people will quote, but the paper's own mock tests show it's biased by ~2.7 km/s (about 3 sigma of the quoted error) relative to the fiducial input, and the two H(z) reconstruction methods miss by 16–22 km/s. That doesn't make the MLE worthless, but it means the headline precision is not accuracy.\n\nWhat's genuinely useful here: the compilation of 97 localized FRBs with a clear table of DMs, redshifts, and references. That's a working catalog for anyone testing host-DM priors. The MLE section is well-written and the likelihood is standard. The mock forecasting exercise is the right instinct, even if the execution undermines the paper's conclusions.\n\nThe soft spots are severe. First, the mock validation: Table 1 shows MLE returns 67.30 ± 0.91 for a fiducial H0 = 70. That's a 3-sigma offset under their own controlled simulation. The authors interpret this as 'our predictions for H0 with mock data increase' but never ask why the estimator fails to recover the input. The answer is almost certainly the host-DM model mismatch: Section 2 fixes DMhost = 100/(1+z) pc cm^-3 with scatter 50/(1+z), while Section 4's mock generator draws DMhost from a log-normal with mean 40–80 pc cm^-3. You can't calibrate an estimator with one host model and then apply it to data under a different one.\n\nSecond, there's a real internal inconsistency in the H(z) section. Eq. (4) says DMhost = 100/(1+z), but the derivative terms in Eqs. (16)–(17), with +100/(1+z)^2, correspond to a redshift-independent host term of 100 pc cm^-3. That's a factor of (1+z) difference, and it affects the H0 estimates.\n\nThird, the H(z) method is essentially a re-parameterization of the fitted DM-z relation; at z=0 it just gives back the slope and intercept. The mock test shows it's unusable at current precision. The paper would be stronger if that section were removed or heavily reworked.\n\nFourth, the quoted MLE error of 2.52 km/s is only the likelihood curvature. Host, Milky Way, and IGM uncertainties are not marginalized over, so the real error is larger. The Conclusions section also transposes errors (66.10 ± 3.46 vs. 1.89; 67.30 ± 1.89 vs. 0.91), which doesn't inspire confidence.\n\nWho is this for? Anyone working on FRB cosmology will want the catalog, but the H0 numbers should not be used without first fixing the host-DM calibration. It's a solid working paper, not a breakthrough. I'd send it to peer review, but with the strong expectation of major revision: fix the host-DM calculation, run a mock test that uses the same host model as the analysis, and downplay the H(z) results.","headline":"A useful catalog and a clear MLE exercise, but the paper's own mocks show the estimators are biased and the quoted errors are too small.","tokens_in":17054,"tokens_out":3857,"would_cite":false,"duration_ms":37522,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The dispersion measures of 97 localized fast radio bursts, after subtracting Milky Way and host-galaxy contributions, give a maximum-likelihood Hubble constant of 65.13 ± 2.52 km/s/Mpc, matching Planck and heading toward SH0ES-level…","keywords":["fast radio bursts","dispersion measure","Hubble constant","Hubble tension","cosmological probes","maximum likelihood estimation","mock catalogs","H(z) reconstruction"],"falsifier":"Rerun the maximum-likelihood analysis on the same 97 FRBs with the host-galaxy prior replaced by the log-normal distribution used in the mock catalog (geometric mean 40–80 pc cm$^{-3}$, scatter 0.4–1.0); if $H_0$ moves outside 65.13 ± 2.52 km/s/Mpc, the fixed host-DM assumption is falsified. Observationally, measuring host-galaxy DMs for a subset of localized FRBs via H$\\alpha$ emission and comparing the mean with $100/(1+z)$ would settle the same question directly.","tokens_in":15816,"feed_emoji":"📡","tokens_out":10848,"duration_ms":96137,"temperature":0.7,"pith_summary":"This paper argues that the dispersion measures (DMs) of fast radio bursts can act as cosmological distance probes: the intergalactic-medium contribution to DM is proportional to $H_0$ times a redshift integral, so $H_0$ can be read off once the Milky Way and host-galaxy terms are subtracted. Using 97 localized FRBs, the maximum-likelihood estimate yields $H_0 = 65.13 \\pm 2.52$ km/s/Mpc, a 3.9% measurement compatible with Planck 2018 and lower than the SH0ES value. Reconstructing $H(z)$ from assumed linear or power-law DM–redshift relations gives divergent values, 51.27 and 77.09 km/s/Mpc, exposing the method's current model dependence. Simulated catalogs of 500 FRBs push the MLE precision to 1.4%, the same order as SH0ES, which the paper takes as evidence that a fivefold increase in localized FRBs would make this an independent, competitively precise probe of the Hubble constant. The key caveat is that host-galaxy DM is assumed, not measured, for each burst.","feed_headline":"97 fast radio bursts put H₀ at 65.13 ± 2.52","feed_subtitle":"FRB dispersion measures match Planck and reach SH0ES-level precision once the sample grows fivefold.","key_machinery":"The central object is the observed dispersion-measure decomposition $\\mathrm{DM}_{\\rm obs} = \\mathrm{DM}_{\\rm IGM} + \\mathrm{DM}_{\\rm MW} + \\mathrm{DM}_{\\rm host}/(1+z)$, with the intergalactic term written as $\\mathrm{DM}_{\\rm IGM}(z) = \\frac{3c\\Omega_b H_0}{8\\pi G m_p}\\chi_e f_{\\rm IGM}\\int_0^z \\frac{1+z'}{E(z')}\\,dz'$. Because the prefactor in front of the integral is proportional to $H_0$, each burst's DM becomes a noisy measurement of $H_0$ once $\\mathrm{DM}_{\\rm MW}=100$ pc cm$^{-3}$ and $\\mathrm{DM}_{\\rm host}=100/(1+z)$ pc cm$^{-3}$ are subtracted. The paper also differentiates fitted linear and power-law $\\mathrm{DM}_{\\rm obs}(z)$ relations to build $H(z)$ and evaluate it at $z=0$, and it maximizes a Gaussian likelihood with $\\sigma^2 = \\sigma_{\\rm MW}^2 + \\sigma_{\\rm host}^2 + \\sigma_{\\rm LSS}^2$ to extract the best $H_0$.","core_discovery":"The central claim is that the dispersion measure of a localized FRB, after subtracting the Milky Way's fixed 100 pc cm$^{-3}$ and a host-galaxy term of $100/(1+z)$ pc cm$^{-3}$ with $50/(1+z)$ scatter, leaves an intergalactic-medium component whose normalization is tied to $H_0$. Maximizing the Gaussian likelihood over 97 bursts gives $H_0 = 65.13 \\pm 2.52$ km/s/Mpc, a 3.9% measurement consistent with Planck 2018 and well below the SH0ES value. Fitting a linear DM–$z$ relation and then evaluating $H(z)$ at $z=0$ gives $H_0 = 51.27^{+3.80}_{-3.31}$ km/s/Mpc, while a power-law fit gives $H_0 = 77.09^{+8.89}_{-7.64}$ km/s/Mpc, bracketing the Planck and SH0ES values and illustrating the systematic spread of the reconstruction approach. In 100 mock catalogs of 500 FRBs each, the MLE recovers $H_0 = 67.30 \\pm 0.91$ km/s/Mpc (1.4% precision), matching the SH0ES precision, with the median ($66.10 \\pm 1.89$) more robust than the arithmetic mean ($66.21 \\pm 3.46$). The paper concludes that FRB DMs are a viable independent cosmological probe whose precision will improve steeply as the localized sample grows.","pith_inferences":["Since the mock catalogs use a log-normal host DM with geometric mean 40–80 pc cm$^{-3}$ while the real-data analysis assumes a fixed $100/(1+z)$ pc cm$^{-3}$, the quoted 1.4% mock precision likely omits a systematic that could shift the observed-data $H_0$; rerunning the MLE on the 97 bursts with the log-normal host prior would quantify this.","Independent host-galaxy DM measurements, for example from H$\\alpha$ emission or resolved host imaging, could break the host-DM degeneracy and turn the FRB method into a genuinely assumption-light cosmological probe.","The paper's mock pipeline could be extended to joint fits with supernova and baryon acoustic oscillation data, where 500 FRBs would help constrain dark energy alongside $H_0$."],"forward_implications":["A fivefold increase in localized FRBs would bring the maximum-likelihood precision to roughly 1.4%, comparable to the SH0ES measurement, giving an independent check on the Hubble tension.","The arithmetic mean of per-FRB $H_0$ values is the least reliable estimator (5.2% precision on mock data); the median and the maximum-likelihood estimator are preferred.","The current 97-burst sample may underestimate $H_0$: every method applied to mock catalogs returns a larger value than the same method applied to the observed catalog.","The linear and power-law DM–$z$ reconstructions give $H_0$ values on opposite sides of the Planck–SH0ES gap, so the functional form of the DM–$z$ relation must be pinned down before the method's accuracy can match its precision."],"supporting_citations":[{"why":"It supplies the host-galaxy DM prior ($100/(1+z) \\pm 50/(1+z)$ pc cm$^{-3}$), the IGM baryon fraction $f_{\\rm IGM}=0.84$, and the IGM scatter model used in the likelihood.","marker":"Hagstotz et al. (2022)"},{"why":"It establishes the linear DM–redshift (Macquart) relation used as one of the two fits in the $H(z)$ reconstruction.","marker":"Macquart et al. (2020)"},{"why":"It provides the linear and power-law DM–$z$ models and the original localized-FRB catalog that this paper extends to 98 bursts.","marker":"Piratova-Moreno & García (2024)"},{"why":"It supplies the method of deriving $H(z)$ by differentiating $\\mathrm{DM}_{\\rm IGM}(z)$ and evaluating at $z=0$.","marker":"Fortunato et al. (2024)"},{"why":"It sets the flat $\\Lambda$CDM fiducial parameters and provides the early-universe $H_0 = 67.4 \\pm 0.5$ km/s/Mpc value that the FRB results are compared against.","marker":"Planck Collaboration et al. (2020a)"},{"why":"It provides the SH0ES local measurement $H_0 = 73.0 \\pm 1.0$ km/s/Mpc that defines the tension and serves as the precision benchmark for the mock forecasts.","marker":"Riess et al. (2022)"},{"why":"It supplies the mock-catalog recipe, including the redshift distribution $z^2 e^{-\\alpha z}$ and the procedure for scattering $\\mathrm{DM}_{\\rm IGM}$.","marker":"Yu, H. & Wang, F. Y. (2017)"},{"why":"It provides the mock-generation approach and the use of the $\\mathrm{DM}_{\\rm IGM}$ derivative to estimate $H_0$.","marker":"Liu et al. (2023)"},{"why":"It gives the Milky Way dispersion-measure range of 50–100 pc cm$^{-3}$ that motivates the assumed $\\mathrm{DM}_{\\rm MW}=100$ pc cm$^{-3}$.","marker":"Prochaska & Zheng (2019)"}],"fun_headline_variants":["97 FRBs pin Hubble constant to 65.13±2.52","FRB dispersion measures match Planck: H₀=65.13±2.52","Fast radio bursts measure cosmic expansion rate with 4% precision","H₀ from fast radio bursts: 65.13±2.52, matching Planck","Radio bursts as Hubble probes: 97 bursts yield 65.13±2.52"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The calculation assumes every FRB's host galaxy contributes a dispersion measure of $100/(1+z)$ pc cm$^{-3}$ with $50/(1+z)$ scatter and the Milky Way contributes 100 pc cm$^{-3}$, even though these are not measured for most bursts; if the true host-galaxy DM distribution differs, every derived $H_0$ shifts.","fun_headline_variants_meta":{"raw":{"variants":["97 FRBs pin Hubble constant to 65.13±2.52","FRB dispersion measures match Planck: H₀=65.13±2.52","Fast radio bursts measure cosmic expansion rate with 4% precision","H₀ from fast radio bursts: 65.13±2.52, matching Planck","Radio bursts as Hubble probes: 97 bursts yield 65.13±2.52"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000852,"raw_usage":{"total_tokens":3926,"prompt_tokens":1387,"completion_tokens":2539,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":1003,"completion_tokens_details":{"reasoning_tokens":2431}},"tokens_in":1003,"tokens_out":2539,"duration_ms":19702,"temperature":1.0,"reasoning_tokens":2431,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-08T04:49:08.712322+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Rerun the maximum-likelihood analysis on the same 97 FRBs with the host-galaxy prior replaced by the log-normal distribution used in the mock catalog (geometric mean 40–80 pc cm$^{-3}$, scatter 0.4–1.0); if $H_0$ moves outside 65.13 ± 2.52 km/s/Mpc, the fixed host-DM assumption is falsified. Observationally, measuring host-galaxy DMs for a subset of localized FRBs via H$\\alpha$ emission and comparing the mean with $100/(1+z)$ would settle the same question directly.","supporting_citations":[{"cited_title":"F., Garc \\' a L","cited_arxiv_id":null,"evidence_quote":"It provides the linear and power-law DM–$z$ models and the original localized-FRB catalog that this paper extends to 98 bursts."}],"review_version":1}