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REVIEW 2 major objections 5 minor 32 references

Thirteen binary black hole–AGN associations measure H0 at 4.4% precision without relying on GW170817, landing between Planck and SH0ES.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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T0 review · grok-4.5

2026-07-12 00:46 UTC pith:ZFYYB5DM

load-bearing objection Solid first multi-event AGN-BBH H0 result at 4.4%, but the whole precision rests on 13 associations from the companion paper that are not yet EM-confirmed. the 2 major comments →

arxiv 2607.03672 v2 pith:ZFYYB5DM submitted 2026-07-04 astro-ph.CO gr-qc

Hubble constant measurement with 13 bright standard sirens from binary black hole mergers inside active galactic nuclei

Dhruv Kumar , Alejandro Torres-Orjuela This is my paper
classification astro-ph.CO gr-qc
keywords Hubble constantstandard sirensbinary black holesactive galactic nucleigravitational wavescosmological tensionbright sirens
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper converts 13 gravitational-wave binary black hole mergers that have been associated with active galactic nucleus hosts into bright standard sirens and measures the present expansion rate of the Universe. Because each event is paired with a single spectroscopic host redshift rather than a probabilistic average over many galaxies, the luminosity distance extracted from the waveform translates almost directly into H0. The cosmology-agnostic combination yields H0 = 70.50^{+3.37}_{-2.89} (stat) ± 1.56 (cal) km s^{-1} Mpc^{-1}, a 4.4% statistical precision that is consistent with both the Planck CMB value and the SH0ES local ladder and is driven entirely by the AGN-associated sample. Adding the classic bright siren GW170817 and an external dark-plus-bright sample tightens the result further to 3.5%. The same associations, when the distance prior is deliberately centered on either cosmology, recover that cosmology at the percent level and formally reject the opposing value at ≳4σ, illustrating how tightly the method can constrain H0 once a background cosmology is assumed. A sympathetic reader cares because the approach bypasses both the distance-ladder calibration chain and the heavy host-galaxy averaging of dark-siren methods, offering an independent route that can scale to sub-percent precision as more BBH–AGN pairs are confirmed.

Core claim

Using only the 13 one-to-one BBH–AGN associations, a cosmology-agnostic standard-siren analysis returns H0 = 70.50^{+3.37}_{-2.89} (stat) ± 1.56 (cal) km s^{-1} Mpc^{-1} (4.4% statistical precision), consistent with Planck 2018 at 0.98σ and SH0ES 2024 at 0.76σ, with no significant preference between them; the constraint is driven by the AGN sample itself rather than by the BNS bright siren GW170817.

What carries the argument

The bright-siren inversion of the flat-ΛCDM distance–redshift relation for a fixed spectroscopic AGN redshift (Eq. 1), combined across events with a selection-function correction β_i(H0) that accounts for detector sensitivity (Eqs. 2–3).

Load-bearing premise

That each of the 13 Bayesian one-to-one BBH–AGN associations is the true physical host, so the spectroscopic redshift can be treated as a fixed source redshift rather than a probabilistic average over many galaxies.

What would settle it

Independent confirmation or refutation that the 13 claimed BBH–AGN associations are genuine physical counterparts (for example by deeper multi-wavelength follow-up that either solidifies or eliminates the optical flares and positional coincidences).

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Thirteen confirmed BBH–AGN pairs already match or exceed the precision of dark-siren analyses that use hundreds of events plus GW170817.
  • The same sample combined with existing dark and bright sirens reaches 3.5% precision, a factor-of-two improvement over the latest multi-event LVK combination.
  • Once a background cosmology is assumed, the method recovers that cosmology at ~1% precision and formally rejects the opposing anchor at ≳4σ.
  • Only 65, 258, or 1027 such pairs would be needed to reach 2%, 1%, or 0.5% accuracy, respectively.
  • Each new spectroscopically confirmed BBH–AGN association supplies as much redshift information as an entire galaxy catalogue does for a comparable dark siren.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the association purity remains high as the sample grows, BBH–AGN sirens could become the dominant independent arbiter of the Hubble tension within a few LVK observing runs.
  • The method’s sensitivity to the distance prior means that any residual bias in the AGN environmental redshift corrections would systematically shift the entire H0 posterior.
  • Future work that jointly samples association probability and cosmology could convert the current hard one-to-one assignments into a fully hierarchical analysis and quantify the impact of possible false positives.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The manuscript measures H0 from 13 BBH mergers identified as one-to-one associations with AGN hosts in a companion analysis. Using the inverted flat-ΛCDM distance-redshift relation (Eq. 1) with fixed spectroscopic AGN redshifts (including SMBH environmental corrections) and a hierarchical combination that includes a detection-probability selection function (Eqs. 2–3), the cosmology-agnostic Run 1 yields H0 = 70.50^{+3.37}_{-2.89} (stat) ± 1.56 (cal) km s^{-1} Mpc^{-1} (4.4% statistical precision). The result is consistent with both Planck 2018 (0.98σ) and SH0ES 2024 (0.76σ). Sequential addition of GW170817 and the Bom et al. dark+bright sample tightens the constraint to 3.5%. Runs 2 and 3, which tighten the luminosity-distance prior around Planck- or SH0ES-predicted distances, recover the respective anchors at ~1% precision and produce ≳4σ apparent rejections of the opposing value by construction.

Significance. If the 13 associations are genuine physical hosts, the work supplies a qualitatively new class of bright standard sirens that bypasses galaxy-catalogue redshift marginalisation. The claimed 4.4% precision from only 13 events would already match or exceed current dark-siren-only and combined LVK constraints while remaining independent of GW170817, and the scaling argument (65/258/1027 pairs for 2%/1%/0.5%) is a concrete, falsifiable forecast. The hierarchical combination, selection-function correction, and explicit separation of cosmology-agnostic versus anchored runs are standard and correctly applied; the Fisher-information ratios relative to GW170817 are a useful diagnostic. The result is therefore of high potential interest for the Hubble-tension literature provided the association purity is adequately quantified.

major comments (2)
  1. [Methodology / Eq. 1 / Table I] The central claim (Eq. 4 and Table I, “13 BBH-AGN” row) treats each of the 13 spectroscopic AGN redshifts as a fixed, unique source redshift that can be inserted directly into Eq. 1 without host-redshift marginalisation. That step is valid only if every association is a genuine physical host. The associations are taken wholesale from the companion paper (arXiv:2607.03674), which reports only log-Bayes factors >1 against a vacuum baseline and subsequent one-to-one adjudication; no electromagnetic flare confirmation is presented here. Because the joint posterior width scales roughly as 1/sqrt(N_true), even a modest false-positive fraction would inflate the statistical uncertainty well above the quoted 4.4% and erase the claimed improvement over existing dark-siren samples. The selection function β_i(H0) (Eq. 3) cannot compensate, because it assumes the redshift is already correctly assigne
  2. [Results & Discussion / Eq. 4] The calibration systematic is quoted as a flat ±1.56 km s^{-1} Mpc^{-1} (2.2%) but is never derived or referenced in the text. Given that the statistical error is already at the few-percent level, the origin, magnitude, and possible H0 dependence of this term must be stated explicitly (waveform systematics, distance-ladder-independent calibration of the LVK amplitude scale, AGN redshift corrections, etc.). Without that justification the total error budget is incomplete.
minor comments (5)
  1. [Abstract / Conclusion] The abstract and conclusion state that Runs 2/3 produce a ≳4σ rejection of the opposing anchor; the body correctly notes that this is an artifact of the anchored prior. The abstract wording should be softened to avoid implying independent cosmological discrimination.
  2. [Table I] Table I lists RF relative to GW170817, but the precise definition of the Fisher information (and whether it includes the selection-function term) is not given; a one-sentence clarification would help.
  3. [Figure 1] Figure 1 caption says events are added “in ascending z_AGN,i order”; the corresponding redshifts are not tabulated, so the ordering cannot be verified by the reader.
  4. [Results & Discussion] The Ωm posterior (0.307^{+0.263}_{-0.232}) is reported only in the text; adding it to Table I or a supplementary corner plot would improve completeness.
  5. [Throughout] Minor typographical inconsistencies appear (e.g., “Cosmology” capitalised inconsistently; “eta_i” vs. β_i notation in the selection function).

Circularity Check

2 steps flagged

Main 4.4% H0 result rests on self-cited companion associations treated as unique fixed hosts; Runs 2/3 recover the input cosmology by construction of the distance prior.

specific steps
  1. self citation load bearing [Introduction, paragraph on BBH-AGN associations; Methodology opening]
    "In Ref. [25], we performed a Bayesian coincidence-classification analysis of 18 gravitational-wave events from the LVK O3–O4b catalogue against 28 candidate AGN counterparts... 13 unique one-to-one BBH–AGN associations were then identified... In this letter, we exploit these 13 favoured associations to perform GW-based H0 measurements. ... Because each event is associated with a single, spectroscopically identified AGN host, zAGN,i enters as a fixed quantity rather than the marginalised host-redshift distribution p(z)"

    The entire precision claim (4.4% from 13 events, no host-redshift marginalisation) rests on treating the 13 associations as true unique hosts. Those associations are supplied solely by the authors’ companion paper; without that self-citation the fixed-z premise of Eq. 1 collapses and the hierarchical product (Eq. 2) reverts to a dark-siren analysis. The companion’s log-Bayes factors >1 are not independently verified or machine-checked here, making the self-citation load-bearing for the central result.

  2. self definitional [Results & Discussion, Runs 2 and 3 paragraphs; Abstract final sentence]
    "Run 2 (Planck-anchored) yields H0=67.62+0.72−0.72 km s−1 Mpc−1 (1.1%), and Run 3 (SH0ES-anchored) yields H0=72.91+0.72−0.72 km s−1 Mpc−1 (1.0%), each recovering its respective anchor as expected by construction... We show that under such an assumption, a rejection of ≳4σ to the opposing anchor is obtained... a signature of the anchored construction rather than an independent cosmological discriminant."

    The luminosity-distance prior is deliberately centred on the DL value predicted by a fixed cosmology at the known zAGN,i. Inverting that prior through the same distance-redshift relation (Eq. 1) necessarily recovers the input H0 (and rejects the alternative) by algebraic construction; the reported ≳4σ tensions are therefore tautological rather than empirical.

full rationale

The core Run-1 measurement applies the standard bright-siren inversion (Eq. 1) and hierarchical combination (Eq. 2) with a deliberately wide, cosmology-bracketing DL prior; once the 13 redshifts are accepted as fixed, the H0 posterior is an independent statistical product and is not forced to any particular value. The load-bearing premise that each of those 13 AGN redshifts can be inserted as a unique spectroscopic host (removing catalogue marginalisation) is taken wholesale from the authors’ own companion Bayesian coincidence analysis (Ref. [25]/ that self-citation is therefore essential to the claimed precision gain over dark-siren samples, but it does not make the subsequent H0 arithmetic circular. Runs 2 and 3 are explicitly constructed by centering the DL prior on the luminosity distance implied by a fixed cosmology; they recover that cosmology (and reject the opposing anchor at ≳4σ) by design, a fact the paper itself states. No fitted parameter is re-labelled a prediction, no uniqueness theorem is imported, and no known empirical pattern is merely renamed. The circularity is therefore limited to one load-bearing self-citation plus two transparent, by-construction demonstrations; the central agnostic result retains independent content.

Axiom & Free-Parameter Ledger

4 free parameters · 4 axioms · 0 invented entities

The central H0 number is obtained by treating 13 spectroscopically identified AGN redshifts as fixed hosts of LVK BBH events, inverting the flat-ΛCDM luminosity-distance relation, and combining with a detector selection function. Everything therefore rests on the validity of those associations, the flat-ΛCDM assumption, the SMBH environmental redshift corrections, and the injection-calibrated detection probability; no new free parameters are fitted to the H0 data themselves beyond the usual cosmological priors.

free parameters (4)
  • H0 prior range = [20,140]
    Uniform prior H0 ∈ [20,140] km s^{-1} Mpc^{-1} chosen by hand to bracket both Planck and SH0ES; affects the reported credible intervals.
  • Ωm prior range = [0.05,0.6]
    Uniform prior Ωm ∈ [0.05,0.6]; jointly sampled with H0.
  • calibration systematic = ±1.56
    Additive ±1.56 km s^{-1} Mpc^{-1} (2.2%) floor quoted without derivation in the present text; treated as an external uncertainty.
  • detection-probability curve P_det(DL)
    Injection-calibrated selection function constructed from O1–O4b LVK injections; enters βi(H0) and therefore the hierarchical likelihood.
axioms (4)
  • domain assumption Flat ΛCDM distance-redshift relation (Eq. 1) with E(z) = [Ωm(1+z)^3 + (1-Ωm)]^{1/2}
    Standard cosmological model assumed throughout; no curvature or dark-energy equation-of-state freedom is explored.
  • ad hoc to paper The 13 BBH–AGN pairs identified in the companion paper are true one-to-one physical associations
    Load-bearing input taken from arXiv:2607.03674; each z_AGN is treated as a fixed spectroscopic redshift rather than a marginalised host distribution.
  • domain assumption SMBH-induced Doppler and gravitational redshift corrections derived in Refs. [24,27] correctly convert observed AGN redshifts to source-frame redshifts
    Applied to every event before inversion; magnitude of the correction is not re-derived here.
  • domain assumption GW luminosity distances from LVK parameter estimation (with the stated distance prior of each Run) are unbiased
    Standard assumption of the standard-siren method; waveform systematics are absorbed into the quoted calibration floor.

pith-pipeline@v1.1.0-grok45 · 13975 in / 3289 out tokens · 31307 ms · 2026-07-12T00:46:56.137472+00:00 · methodology

0 comments
read the original abstract

We measure the Hubble constant $H_0$ using 13 gravitational-wave binary black hole mergers associated with active galactic nucleus hosts. We find $H_0=70.50^{+3.37}_{-2.89}\,({\rm stat})\pm1.56\,({\rm cal})$\,km\,s$^{-1}$\,Mpc$^{-1}$ ($4.4\%$ precision), consistent with both Planck\,2018 ($0.98\sigma$) and SH0ES\,2024 ($0.76\sigma$), with no significant preference between the two. Combining with the bright siren GW170817 sharpens the constraint to $H_0=70.31^{+3.00}_{-2.85}\,({\rm stat})\pm1.55\,({\rm cal})$\,km\,s$^{-1}$\,Mpc$^{-1}$ ($4.2\%$ precision), and further combining with an independent dark-and-bright-siren sample tightens it to $H_0=69.71^{+2.55}_{-2.40}\,({\rm stat})\pm1.54\,({\rm cal})$\,km\,s$^{-1}$\,Mpc$^{-1}$ ($3.5\%$ precision). Assuming a luminosity-distance prior centered around the value related to a fixed cosmology in turn, recovers $H_0=67.62\pm0.72$ (Planck-anchored) and $H_0=72.91\pm0.72$\,km\,s$^{-1}$\,Mpc$^{-1}$ (SH0ES-anchored). We show that under such an assumption, a rejection of $\gtrsim4\sigma$ to the opposing anchor is obtained.

Figures

Figures reproduced from arXiv: 2607.03672 by Alejandro Torres-Orjuela, Dhruv Kumar.

Figure 1
Figure 1. Figure 1: Cumulative build-up of the joint H0 posterior for Run 1 as the 13 BBH-AGN events are added in ascending zAGN,i order (dark-to-light gradient); the final 13-event posterior is highlighted (13 BBH-AGN ). Vertical dotted lines mark the Planck 2018 and SH0ES 2024 values. in tension with either Planck or SH0ES beyond 0.9σ. For comparison, the Fisher information of individual 13 BBH-AGN events ranges from 0.88–1… view at source ↗
Figure 2
Figure 2. Figure 2: The 13 BBH-AGN posterior of Fig. 1, [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

discussion (0)

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