{"id":"b11beca9-3eed-473a-8c26-18bf689fefed","arxiv_id":"2607.26561","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"GW250114's fundamental ringdown mode bounds theory-agnostic deviations from the Teukolsky equation to be consistent with zero at characteristic scales of 60-100 km.","lead":"GW250114, the loudest gravitational-wave event yet, is used to place the first observational bounds on theory-agnostic changes to the Teukolsky equation, the master equation for black-hole ringdowns in general relativity. All tested deviations agree with general relativity, with sensitivity reaching characteristic length scales of tens of kilometers.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"λ=1 ζ bounds double-count ringdown data via the IMR-informed (M,χ) prior; the quoted 60–100 km scales are prior-dominated and uncalibrated.","rationale":"The reader's weakest_assumption identifies the same load-bearing issue: the ζ_k constraints exist only because (M,χ) are pinned by the GR-assuming IMR analysis, and the λ=1 bounds double-count ringdown information because the IMR posterior already contains ringdown data. I find this to be the most load-bearing concern because the paper's novelty and headline numbers (60–100 km scales) depend directly on the width of these priors, whereas the secondary linearity concern (|ζ_k|~O(1) outside the validity of Eq. 7) affects only the tails of the posteriors and is partially mitigated by the cited 1% accuracy from Ref. [82]. The paper is transparent about the optimistic character of λ=1 and includes a widened prior, but it does not calibrate λ or quantify the double-counting effect. The GR-consistency conclusion ('ζ_k in agreement with GR') is robust — even the wider priors show consistency — so the concern does not warrant rejection; it strengthens the existing CONDITIONAL verdict. I thus recommend UNCHANGED, as my read does not alter the reader's verdict. The concrete test of replacing the IMR prior with a ringdown-excluded estimate would settle whether the quoted optimistic bounds are inflated and would provide the missing calibration.","tokens_in":13336,"tokens_out":5839,"duration_ms":59141,"concrete_test":"Re-run the analysis with the (M,χ) prior taken from a GW250114 parameter estimation that excludes ringdown data (e.g., an inspiral-merger-only NRSur7dq4 fit truncated before the merger, or the LVK 'no-ringdown' posterior if available), keeping Eq. (10) identical. Compare the λ=1 credible intervals for each ζ_k with Fig. 2. If any interval broadens by more than a factor of 1.5, the optimistic bounds in Fig. 2 are confirmed to be inflated by double-counting of the ringdown information.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central quantitative claim — characteristic Teukolsky-deviation scales of ~60–100 km from GW250114 — rests entirely on the Gaussian prior for (M,χ) taken from the NRSur7dq4 full-IMR posterior (Eq. 8, Fig. 1). That posterior already contains ringdown information from the same data that later enters the ringdown likelihood (Eq. 10): the likelihood compares the predicted (2,2,0) frequency to the LVK damped-sinusoid posterior, while the prior on M and χ was derived from a fit that includes that same ringdown. For λ=1 the two datasets are therefore not independent; the ζ posteriors in Fig. 2 are a re-projection of a single ringdown measurement through a GR-based mapping, and their width is set by the prior covariance, not by new information. The paper acknowledges this qualitatively ('underestimate the statistical errors since they use the full IMR information') but does not quantify the effect on the headline 60–100 km length scale. The λ=25 'pessimistic' bound is an ad hoc widening with no calibration: there is no injected-signal study showing that the prior covers plausible beyond-GR shifts in (M,χ). Without such a calibration, the 'first bounds' framing is statistically underdetermined.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a lightweight method to constrain theory-agnostic deviations from the Teukolsky equation using the fundamental (l=m=2, n=0) ringdown mode of the high-SNR event GW250114. The authors combine a Gaussian approximation of the LVK full-IMR posterior for the remnant mass and spin (Prior 1, Eq. 8; Prior 2, Eq. 12) with a Gaussian approximation of the LVK agnostic damped-sinusoid posterior for ω_220, and sample the likelihood (Eq. 10) with MCMC. They vary one complex beyond-Teukolsky parameter ζ_k at a time and report that all ζ_k are consistent with GR (ζ_k=0). They translate the marginalized uncertainties into characteristic length scales √σ_ζ M ≈ 60–100 km and claim the first bounds on the beyond-Teukolsky framework.","tokens_in":13539,"tokens_out":6212,"duration_ms":59234,"significance":"If the bounds are robust, this would be the first observational constraint on the beyond-Teukolsky formalism of Ref. [82], complementing the independent ParSpec analysis of the same event. The methodological idea of using a simplified Gaussian likelihood for high-SNR ringdowns is pragmatic and could be applied to future loud events. The paper is unusually transparent about the limited constraining power of a single mode and about the prior-dependence of the results, presenting both 'optimistic' (λ=1) and 'pessimistic' (λ=25 or λ=5) choices. It also correctly notes that the linearized framework has limited accuracy for large ζ_k. These strengths make the work potentially useful to the ringdown community.","major_comments":[{"comment":"The Gaussian prior on (M,χ) is taken from the NRSur7dq4 full-IMR posterior, which already contains the ringdown information used later in the likelihood Eq. (10). For λ=1, the prior and likelihood are not independent, so the ζ_k posteriors are largely a re-projection of the GR-based IMR mapping rather than new information. The paper acknowledges this qualitatively ('underestimate the statistical errors') but does not quantify the impact on the quoted 60–100 km length scale. An injection study or an inspiral-only prior is needed to establish what these bounds actually measure.","section":"Sec. II.C, Eq. (8) and Fig. 2"},{"comment":"The '60–100 km' characteristic scales are quoted only from the λ=1 'optimistic' bounds, which are the most affected by the double-counting problem above. The λ=25 'pessimistic' bounds are not translated to length scales, so the headline quantitative claim does not reflect the full range of prior choices. The paper should either report the length-scale range for both prior choices or explicitly state that the 60–100 km figure is conditional on the optimistic prior.","section":"Sec. III, length-scale paragraph"},{"comment":"The scaling parameter λ is set ad hoc (λ=1/25 for the Gaussian prior, λ=1/5 for the box prior) with no calibration to known beyond-GR theories or to plausible shifts in final mass/spin. The relationship between a covariance multiplier and a percentage box is not justified. Consequently, even the 'pessimistic' bounds remain uncalibrated; they are not a systematic treatment of theoretical uncertainty. A prescription for λ based on theory-specific estimates or on injection tests is required to support the claim of providing 'bounds'.","section":"Sec. II.C, Eq. (12) and λ choices"},{"comment":"The beyond-Teukolsky framework assumes |ζ_k| ≪ 1 for the linear expansion Eq. (7) to be valid, but the marginalized posteriors in Figs. 2 and 3 extend to |ζ| ≳ 1. The text states that linear corrections are about 1% accurate for the considered ranges, but this is not demonstrated for the actual posterior support. If the posterior overlaps the non-perturbative regime, the reported bounds cannot be interpreted as bounds on the linear deviation parameters. The paper should identify the region of validity and restrict its reporting to that region.","section":"Sec. II.A, Eqs. (6)–(7) and Figs. 2–3"}],"minor_comments":[{"comment":"The phrase 'The high signal-to-noise (SNR) ratio' is redundant; 'SNR' already includes 'ratio'.","section":"Sec. II.B"},{"comment":"The truncation value K is not stated in the text; the figures show k = -2,...,4, so K=2. Please state this explicitly and justify the truncation.","section":"Sec. II.A, Eq. (6)"},{"comment":"The symbol λ is used both as a covariance multiplier (Eq. 8) and as a percentage width (Eq. 12). Clarify this in the notation, or use a different symbol for the box prior.","section":"Sec. II.C"},{"comment":"The phrase 'the here presented analysis' is awkward; suggest 'the present analysis'.","section":"General"},{"comment":"The conclusion mentions future applications but does not quantify the expected improvement for next-generation detectors; a short estimate would strengthen the outlook.","section":"Sec. IV"}],"recommendation":"major_revision","confidential_remarks":"The paper is self-cited heavily for the theoretical framework, but this is not inappropriate given that the framework was developed by the authors. The main concern is statistical: the constraining power of the analysis is almost entirely inherited from the GR-based IMR prior, and the λ scalings are uncalibrated. The paper's own caveats are honest, but the framing as 'first bounds' and the 60–100 km length scale are not supported unless the prior-dependence is quantified and calibrated. A major revision with an injection study or a substantially weakened interpretation is warranted."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First thing you should know: this is the first application of the authors' beyond-Teukolsky parametrization to a real event, and the main result—all ζ_k consistent with zero—is solid. If you care about ringdown tests of GR, this is a genuine data point, not a toy. The paper is also unusually transparent: public LVK posteriors, explicit likelihood (Eq. 10), MCMC settings, and a public repository for the QNM shift coefficients.\n\nThe central claim survives scrutiny. The framework in Ref. [82] is a parameter-free perturbative derivation, and the data inputs are independent of the authors' own analysis. Agreement with the ParSpec bound [95] at ~80 km is a good cross-check even if the two parametrizations are not identical. The authors also flag the main limitations themselves: the optimistic/pessimistic prior distinction, the one-at-a-time variation, and the fact that they only use the fundamental mode.\n\nNow the soft spots, in order of importance. First, the λ=1 bounds double-count ringdown information. The prior on (M, χ) comes from the NRSur7dq4 full-IMR posterior, which already includes the ringdown data that later enters the ringdown likelihood in Eq. (10). So the 'optimistic' bounds are not just optimistic; they're effectively a re-projection of a single ringdown measurement through a GR mapping. The paper acknowledges this qualitatively but does not quantify how much the quoted 60–100 km length scales would widen if the ringdown were excluded from the prior. A simple check would be to use an inspiral-only posterior for (M, χ) or to introduce a prior that explicitly excludes ringdown information. Without that, the headline numbers should be read as a floor.\n\nSecond, the λ scaling is ad hoc. Setting λ=25 because the theoretical error is five times the statistical error has no calibration. No injection study shows that the widened prior actually covers plausible beyond-GR shifts in final mass and spin. This matters because with two ringdown measurements and four parameters, the ζ_k constraints exist only through these priors. A bias in the IMR-derived (M, χ) would bias ζ_k, and the current analysis doesn't bound that systematic.\n\nThird, the linear mapping in Eq. (7) is used over posterior tails where |ζ_k| can approach unity. The paper cites Fig. 2 of Ref. [82] to claim ~1% accuracy for the considered ranges, but it doesn't show that the actual posteriors stay in that range, nor does it propagate the linearization error. This is minor relative to the other two, but it should be addressed.\n\nBottom line: the GR-consistency conclusion is believable and the paper is a useful step. The quoted length scales, however, are prior-dominated and uncalibrated. I'd send it to peer review, but I'd ask the authors to quantify the double-counting and run a simple injection test for the priors. It deserves a serious referee, and the core result will likely survive—but the numbers in the abstract should not be taken at face value until that is done.","headline":"First real-data beyond-Teukolsky bounds, but the quoted 60–100 km scales are prior-dominated and the λ=1 bounds double-count ringdown information.","tokens_in":14176,"tokens_out":3528,"would_cite":true,"duration_ms":32914,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["04.30.-w","04.70.-s"],"model":"deepseek-v4-flash","headline":"The paper derives the first observational bounds on theory-agnostic deviations from the Teukolsky equation from the GW250114 ringdown, finding all deviation parameters consistent with general relativity.","keywords":["black hole ringdown","Teukolsky equation","quasinormal modes","tests of general relativity","GW250114","beyond-Teukolsky formalism","gravitational wave astronomy","black hole spectroscopy"],"falsifier":"Take the public GW250114 posteriors, inject a simulated ringdown signal with a known nonzero ζ_k and a remnant mass and spin shifted by ~1% away from the GR IMR maximum-likelihood values, then run the paper's pipeline; if the recovered ζ_k posterior fails to exclude zero or recover the injected value, the IMR-anchored priors are demonstrably insufficient to constrain beyond-Teukolsky deviations.","tokens_in":13069,"feed_emoji":"🕳️","tokens_out":9287,"duration_ms":67932,"temperature":0.7,"pith_summary":"This paper sets out to answer a sharp question: if the Teukolsky equation that governs black-hole ringdown in general relativity were slightly wrong, how wrong could its effective potential be, given the exceptionally loud gravitational-wave event GW250114? Using the beyond-Teukolsky formalism, which parametrizes small complex corrections ζ_k to the Teukolsky potential and computes their linear effect on the quasinormal-mode spectrum, the authors combine an inspiral-merger-ringdown estimate of the remnant mass and spin with the ringdown-only measurement of the fundamental (2,2,0) mode. They introduce two theory-agnostic priors that rescale the IMR posterior covariance or box the maximum-likelihood values, controlled by a hand-set factor λ. Their central result is that every ζ_k is consistent with zero, with one-standard-deviation uncertainties corresponding to length scales of roughly 60–100 km — the first such constraints on the perturbation equation itself. These bounds are an order-of-magnitude statement about how much the Kerr perturbation equations can deviate at the scale of tens of kilometers and still match the loudest ringdown observed to date.","feed_headline":"GW250114 ringdown: all Teukolsky deviations consistent with zero","feed_subtitle":"First theory-agnostic bounds on the black hole perturbation equation, with deviations capped at tens of kilometers.","key_machinery":"The machinery is the beyond-Teukolsky framework combined with a simplified Gaussian likelihood. The framework modifies the Teukolsky equation by adding a small potential δV(r) = (1/Δ) Σ_{k=-K}^{4} α_k (r/r_+)^k, with dimensionless complex parameters ζ_k = α_k/M^2. At linear order, the quasinormal-mode frequency shifts as ω = ω_GR + (1/M) Σ ζ_k d^k_ω, where the coefficients d^k_ω are precomputed for each (ℓ,m,n). The analysis then approximates the LVK posteriors for (M, χ) and for the fundamental mode frequency and damping time as multivariate Gaussians, and samples the likelihood of the measured ω_{220} against the model prediction, varying one ζ_k at a time. The remnant mass and spin are an","core_discovery":"The central claim is that the ringdown of GW250114, analyzed through the beyond-Teukolsky framework, provides the first observational bounds on deviations from the Teukolsky equation. The authors demonstrate that all complex deviation parameters ζ_k, which encode small modifications δV(r) to the Teukolsky potential in powers of (r/r_+)^k, are consistent with zero within both optimistic and pessimistic priors on the remnant mass and spin. The one-standard-deviation uncertainties on Re(ζ_k) and Im(ζ_k), converted to length scales via sqrt(σ_ζ)·M, fall in the range of roughly 60–100 km, in agreement with the independent ParSpec bound of about 80 km. The method itself — a simplified Gaussian lik","pith_inferences":["The hand-set λ parameter is the real dial of the analysis: λ=1 double-counts ringdown information already present in the IMR posterior, while large λ weakens the priors to the point where the ζ_k bounds may be dominated by prior ignorance. A fully Bayesian joint fit of M, χ, and ζ_k would determine where between these extremes the true constraint lies.","If a beyond-GR theory predicts a final mass or spin that differs from the GR IMR value by more than the λ-scaled width, the ζ_k posteriors will be systematically shifted. A direct test would be to inject a simulated signal with a known nonzero ζ_k and a shifted remnant and check whether the pipeline recovers the injection.","The one-at-a-time variation of ζ_k means the bounds are conditional; simultaneous marginalization would likely be far less informative, but mapping the joint posterior to local properties of the effective potential near its maximum, as done in the non-rotating case with WKB, could restore interpretability."],"forward_implications":["If the central claim holds, deviations in the effective potential of Kerr black-hole perturbation theory are bounded at the tens-of-kilometers scale for this event — the sharpest such bound to date.","The simplified likelihood pipeline can be rerun quickly on future high-SNR events without a full Bayesian analysis, making it a practical screening test for beyond-GR theories.","The consistency with the independent ParSpec bound (~80 km) suggests that different agnostic parametrizations are converging on the same length-scale ceiling for deviations.","The reported ζ_k constraints can be translated into bounds on specific theories, such as higher-derivative gravity, once their predicted potential deviations are mapped to ζ_k."],"fun_headline_variants":["First bounds on Teukolsky deviations: all zero","GW250114 ringdown: no deviation from Teukolsky","Ringdown data caps Teukolsky deviations at ~100 km","GW250114 agrees with GR: deviations null","Teukolsky confirmed: ringdown bounds tighten"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The entire constraint rests on the assumption that the remnant black hole's mass and spin, as predicted by the GR-based inspiral-merger-ringdown analysis, are close enough to the true values that the IMR-informed priors (with the hand-set width λ) cover the actual (M, χ); if a beyond-GR theory shifted the remnant parameters by more than that width, the reported ζ_k bounds would be biased toward zero and would not reflect the true deviations.","fun_headline_variants_meta":{"raw":{"variants":["First bounds on Teukolsky deviations: all zero","GW250114 ringdown: no deviation from Teukolsky","Ringdown data caps Teukolsky deviations at ~100 km","GW250114 agrees with GR: deviations null","Teukolsky confirmed: ringdown bounds tighten"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00021,"raw_usage":{"total_tokens":1269,"prompt_tokens":788,"completion_tokens":481,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":532,"completion_tokens_details":{"reasoning_tokens":399}},"tokens_in":532,"tokens_out":481,"duration_ms":4707,"temperature":1.0,"reasoning_tokens":399,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T13:19:55.198010+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take the public GW250114 posteriors, inject a simulated ringdown signal with a known nonzero ζ_k and a remnant mass and spin shifted by ~1% away from the GR IMR maximum-likelihood values, then run the paper's pipeline; if the recovered ζ_k posterior fails to exclude zero or recover the injected value, the IMR-anchored priors are demonstrably insufficient to constrain beyond-Teukolsky deviations.","supporting_citations":[],"review_version":1}