{"id":"e8bb1121-9ee7-446c-8a0c-50059ffb4cc1","arxiv_id":"2502.03155","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"qnmfits and KerrRingdown are two independently written, cross-verified software packages for performing multimode ringdown fits to numerical relativity waveforms.","lead":"This paper introduces two new software packages, qnmfits in Python and KerrRingdown in Mathematica, for extracting black hole quasinormal mode amplitudes from ringdown gravitational wave signals. The codes are independently written and cross-verified, giving researchers easy-to-use tools for multimode ringdown analysis.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 'identical up to machine precision' cross-validation rests on undocumented agreement of qnm and Ref. [40] QNM data conventions; absent verification data, the central claim is uncheckable from the paper.","rationale":"The reader's weakest_assumption correctly identifies the dataset-consistency issue as the crux. I read the paper in good faith: the packages are real, deposited on Zenodo, and the two-waveform demonstration is a reasonable smoke test. The cross-validation sentence in Section 3, however, is the only evidence for the headline 'verified against each other.' The two codes draw QNM data from different sources: qnm (Leaver solver and spectral angular solver, Stein 2019) for qnmfits, and the Cook 2024 Zenodo dataset for KerrRingdown. Since complex amplitudes are convention-dependent objects, phase conventions in the spheroidal harmonics and in the definition of mirror modes must match exactly for the fitted amplitudes to agree at machine precision. The paper does not show the comparison tables, nor state the phase convention for Ref. [40], nor include an externally runnable verification test. This is not an internal inconsistency—Section 2's equations are standard and correctly presented—but an evidentiary gap in the central claim. The honest limitation statement in Section 4 about absent fitting uncertainties is disclosed and does not by itself undermine the cross-validation claim, though it does limit practical applicability for subdominant modes. The proposed concrete test combines a reproducibility run and a direct comparison of ω and C coefficients at a representative spin; this settles whether the concern lands. If the test passes, the paper's conditional verdict should be upgraded; if it fails, the cross-validation claim is false as stated. Because the manuscript currently lacks this check, I do not move the verdict away from CONDITIONAL.","tokens_in":7383,"tokens_out":4431,"duration_ms":41154,"concrete_test":"Download the Zenodo packages (qnmfits 10.5281/zenodo.14806974, KerrRingdown 10.5281/zenodo.14804284) and run the same fit with both: SXS:BBH:0305, Set 1, t0-tpeak=30M, fitting (ℓ,2,0,±), ℓ=2..4 modes; require the complex amplitudes and mismatch to agree to <1e-12 in relative norm. Separately, at χ=0.7 compare the qnm values of ω_{220}, ω_{320}, C_{222}, C_{322}, C_{422} with the corresponding entries in Ref. [40]; if the phases or normalizations differ, verify the codes apply an explicit compensating convention. If either check fails or the test suite is absent, the machine-precision claim is not established.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claim is the Section 3 statement that qnmfits and KerrRingdown 'produce identical results, up to machine precision, for both the mismatch and complex QNM amplitudes for a variety of test cases.' This cross-validation is load-bearing because the abstract itself advertises the two codes as 'verified against each other,' yet the manuscript provides no verification numbers, plots, or test-suite output. The concrete technical risk is in the input data, not the least-squares solvers: qnmfits obtains QNM frequencies and spherical-spheroidal mixing coefficients C_{ℓ′ℓm} from the qnm package (Section 2.1), while KerrRingdown imports frequencies and mixing coefficients from the separate dataset of Ref. [40]. Complex QNM amplitudes are convention-dependent: a different phase choice for the spheroidal harmonics, a different sign convention for the mirror modes, or a different normalization of C_{ℓ′ℓm} would shift the fitted amplitudes by mode-dependent factors even if both fits are mathematically correct. The manuscript neither compares the two datasets nor states the phase convention used by Ref. [40], so the claimed agreement cannot currently be checked from the published record.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This note introduces two open-source packages, qnmfits (Python) and KerrRingdown (Mathematica), for performing multimode least-squares fits of quasinormal-mode amplitudes to numerical-relativity ringdown waveforms. The theoretical model (Eqs. 1–6) is the standard decomposition of spherical-harmonic waveform modes into spheroidal QNMs, including regular and mirror modes, with spherical–spheroidal mixing coefficients. The paper demonstrates the codes on two SXS waveforms, one aligned-spin and one precessing, showing the mismatch versus start time and normalized QNM amplitudes for three mode sets. The central claim is that the two independently written packages have been verified against each other and produce identical results up to machine precision for both the mismatch and complex QNM amplitudes (Section 3, final paragraph).","tokens_in":7610,"tokens_out":8628,"duration_ms":76917,"significance":"If the cross-validation claim can be substantiated, this is a genuinely useful software contribution: it provides two independent, DOI-issued, open-source implementations of a standard and widely used method, along with a helpful clarification of the regular/mirror versus prograde/retrograde convention. The demonstration on an aligned-spin and a precessing CCE waveform is a sensible first illustration, and the authors are explicit about the least-squares method's limitation of not providing fit uncertainties. However, the paper's main advertised result—the machine-precision agreement of the two codes—is currently only asserted, not demonstrated, and the convention consistency between the two QNM data sources is not established. The contribution therefore reads more as a software announcement than as a fully checkable cross-validation study.","major_comments":[{"comment":"The statement that qnmfits and KerrRingdown 'produce identical results, up to machine precision, for both the mismatch and complex QNM amplitudes for a variety of test cases' is the central claim advertised in the abstract and introduction, yet no supporting evidence appears in the manuscript. There is no comparison table, verification plot, list of the test cases, or test-suite output. Because the two codes use different linear-algebra strategies (numpy.linalg.lstsq versus a normal-equations implementation), numerical agreement is not automatic. Please add a reproducibility section or appendix reporting the measured differences (for example, maximum absolute and relative deviations in M and in A±_{ℓmn} across the test cases) together with the definition of the machine-precision threshold used.","section":"Section 3, final paragraph"},{"comment":"qnmfits obtains QNM frequencies and spherical–spheroidal mixing coefficients from the qnm package (with Ref. [38] for the (2,2,8) mode), while KerrRingdown imports them from the dataset of Ref. [40]. Complex QNM amplitudes are convention-dependent: a different phase convention for the spheroidal harmonics, a different sign convention for mirror modes, or a different normalization of C_{ℓℓ′m}(aω) would shift fitted amplitudes by mode-dependent factors. The manuscript does not state the conventions of Ref. [40] nor demonstrate that they are mutually consistent with those of the qnm package. Please include a direct comparison of the input data for representative modes (frequencies and mixing coefficients), or state and verify the convention mapping between the two sources.","section":"Sections 2.1 and 2.2"},{"comment":"The cross-validation claim refers to 'a variety of test cases', but the demonstration section presents only two NR waveforms and does not specify what the full test suite was. The details of waveform preprocessing (resampling, alignment, mapping to the superrest frame) are also not given, which makes the demonstration hard to reproduce independently. Please specify the test cases and preprocessing steps used for the verification, or point to a persistent test-suite artifact in the code repositories.","section":"Section 3"}],"minor_comments":[{"comment":"The numerator of the mismatch expression appears to have a typographical error: what is printed as '|p' should presumably be a squared absolute value (|Σℓm⟨aℓm|bℓm⟩|²). Please correct the formula.","section":"Eq. (5)"},{"comment":"The caption's phrase 'right panels' is ambiguous because the right side contains two stacked panels; please refer to 'top right' and 'bottom right' panels for clarity.","section":"Fig. 2 caption"},{"comment":"For m = 0 modes, the notation '(ℓ, 0, n, ±)' may be confusing because the regular and mirror modes coincide; a brief remark explaining how the ± label is interpreted for m = 0 would help the reader.","section":"Section 3, mode lists"},{"comment":"For reproducibility, please include the specific version or DOI for the qnm package, the access date for Ref. [38], and the version of Ref. [40] used in the fits.","section":"References [35,37,38,40]"}],"recommendation":"major_revision","confidential_remarks":"The paper is well suited to a software-note format, but the main advertised result is unsupported in the manuscript. The fixes required are local and can be made within the scope of the paper: add the verification data (agreement metrics and test-case descriptions) and the convention consistency check between the two QNM datasets. I would not recommend rejection, as the theoretical framework is standard and the code appears useful, but the current manuscript does not allow an independent reader to check its central claim."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: useful, honest software note, but the abstract's headline claim—the two codes agree to machine precision—is asserted, not shown. The reader's conditional verdict and the stress-test concern both land.\n\nWhat is actually new: qnmfits (Python) and KerrRingdown (Mathematica) are independent, open-source implementations of multimode least-squares ringdown fits, with an optional greedy-mode selector, mass/spin fitting, and mode mixing built in. The method is standard and the paper does not pretend otherwise; the contribution is two clean, cross-checkable tools for a subfield that keeps reimplementing this. The demonstration on SXS:BBH:0305 and ExtCCE:0013 is tidy, and the final limitation paragraph—no fit uncertainties in the core functions—is candid.\n\nSoft spots. The main one is the cross-validation claim. Section 3's last sentence says both mismatch and complex amplitudes agree up to machine precision 'for a variety of test cases,' but no verification numbers, plots, or test-suite output appear anywhere in the manuscript. The real risk is exactly what the stress-test note flags: qnmfits gets frequencies and mixing coefficients from qnm, KerrRingdown from Ref. [40], and those two datasets could differ in phase conventions, mirror-mode sign, or C_{l'l m} normalization. The paper does not compare them or state Ref. [40]'s conventions. Both fits could be correct and still disagree by mode-dependent phases. The fix is cheap: include one comparison table of fitted amplitudes and mismatches from both codes, or link to a reproducible test script. Without that, the advertised verification is uncheckable. Second, the no-uncertainty limitation is real and acknowledged; for rapidly damped or subdominant modes, users need to know the best-fit amplitudes can be biased by waveform error or unmodeled features. The authors say this plainly. Third, this is a tools note, not a new physics result; anyone expecting a new effect or a resolved controversy should look elsewhere.\n\nI don't see a circularity problem: amplitudes are fitted to NR data, and the cross-code agreement claim is separate from their earlier greedy-fit work. Citations look appropriate, including the prior greedy/superrest paper and the standard QNM packages.\n\nWho this is for: anyone doing NR ringdown fits who wants a turnkey, two-language reference implementation with an honest statement of limitations. It deserves a serious referee; I would send it out and ask for the verification artifacts and a short conventions appendix. With those, it is a solid contribution.","headline":"A useful and honest pair of ringdown-fitting codes, but the advertised machine-precision cross-validation is asserted without evidence; easy fix, worth refereeing.","tokens_in":8130,"tokens_out":3294,"would_cite":false,"duration_ms":33398,"reading_group":"maybe","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":"Two independently written codes for extracting black-hole ringdown mode amplitudes agree to machine precision.","keywords":["gravitational waves","ringdown","quasinormal modes","numerical relativity","least-squares fitting","mode mixing","code cross-validation","Kerr black holes"],"falsifier":"Run both packages on a synthetic ringdown generated from the model itself with known amplitudes, including at least one mode where the two codes depend on different data sources; if the recovered complex amplitudes or mismatches differ by more than round-off (roughly a relative difference above $10^{-13}$), the machine-precision claim fails.","tokens_in":7188,"feed_emoji":"🕳️","tokens_out":10815,"duration_ms":93901,"temperature":0.7,"pith_summary":"The paper aims to establish that quasinormal-mode amplitudes of a black-hole ringdown can be extracted reliably by two independent, open-source fitting tools: qnmfits in Python and KerrRingdown in Mathematica. The authors model the ringdown as a sum of damped sinusoids with Kerr quasinormal-mode frequencies, account for spherical-spheroidal mode mixing, and fit the complex amplitudes by least squares. They report that for multiple test cases, including aligned-spin and precessing numerical-relativity waveforms, both codes give identical mismatches and identical complex mode amplitudes. A sympathetic reader would care because a cross-checked, easy-to-use toolset lets the ringdown community compare extractions of mode content from numerical simulations without worrying about implementation artifacts.","feed_headline":"Two ringdown-fitting codes agree to machine precision","feed_subtitle":"Independently written Python and Mathematica tools return identical ringdown mode fits on the same black-hole waveforms.","key_machinery":"The load-bearing object is the mode-mixed QNM expansion $h_{\\ell m}(t) = \\sum_{\\ell' n \\pm} A^\\pm_{\\ell' mn} e^{-i\\omega^\\pm_{\\ell' mn}(t-t_0)} C_{\\ell\\ell' m}(a\\omega^\\pm_{\\ell' mn})$, together with the mismatch $\\mathcal{M}$ of Eq. (5) that the least-squares fit minimizes. The spherical-spheroidal mixing coefficients $C_{\\ell\\ell' m}$ are what let a single spheroidal QNM contribute to several spherical-harmonic data channels, and the fact that the two codes reach the same minimum through different linear-algebra routes is what makes their agreement nontrivial. Both codes label modes by the sign of the real frequency, distinguishing regular from mirror modes, and obtain their frequency and mixing data from tabulated sources.","core_discovery":"On the paper's own terms, the central claim is that multimode least-squares ringdown fitting can be performed reliably in two independent software implementations: given a numerical-relativity waveform decomposed into spherical harmonics and a user-chosen set of Kerr quasinormal modes, qnmfits and KerrRingdown return the same complex amplitudes $A^\\pm_{\\ell mn}$ and the same mismatch $\\mathcal{M}$ up to machine precision, across a variety of fit configurations. The two codes were written independently and use different numerical routes, one calling a standard linear-algebra solver and the other solving the normal equations, so the agreement is presented as cross-validation of the implementations and of the underlying QNM-frequency and mixing-coefficient data. The demonstration covers mode-mixing fits, overtone fits, and a greedy-selected twenty-mode all-sky fit, on both an aligned-spin and a precessing waveform.","pith_inferences":["Because the two codes draw QNM frequencies and mixing coefficients from different datasets, their machine-precision agreement also implies that those datasets are mutually consistent in phase and normalization; the paper does not show that table-level comparison, so publishing it would strengthen reproducibility.","A natural next step is to run the same cross-check on synthetic waveforms with exactly known injected amplitudes, which would quantify the accuracy of the method itself rather than only the consistency of the two implementations.","The paper itself notes that least-squares fits carry no uncertainty estimate and can be biased for rapidly decaying or subdominant QNMs, so the machine-precision agreement establishes consistency between the codes, not automatic physical accuracy of every recovered amplitude.","The fast least-squares fits could serve as a cheap frequentist companion to Bayesian ringdown analyses, giving an immediate first estimate of mode amplitudes and of whether a mode merits a full posterior investigation."],"forward_implications":["Users can fit the same numerical-relativity ringdown with either package and use the agreement between them as a built-in sanity check.","The packages make QNM amplitude extraction fast enough to scan start times and mode choices, since the least-squares fits are essentially instantaneous.","The greedy-fit algorithm gives a practical way to rank which quasinormal modes matter for a given binary system, informing which overtones, mirror modes, or higher multipoles should be included in a model.","Fitting the remnant mass and spin is built into both codes, so the user can jointly obtain remnant parameters and mode amplitudes rather than using fixed values.","The demonstration on a precessing waveform mapped to the superrest frame indicates the codes work for CCE-type waveforms, not only simple aligned-spin data."],"supporting_citations":[{"why":"The Python package qnmfits, one of the two codes whose outputs are claimed to agree to machine precision.","marker":"[26]"},{"why":"The Mathematica package KerrRingdown, the other code in the cross-check.","marker":"[27]"},{"why":"Establishes that the least-squares fit is equivalent to minimizing the mismatch, and supplies the normal-equations method used by KerrRingdown.","marker":"[42]"},{"why":"Supplies the QNM frequencies and spherical-spheroidal mixing coefficients used by qnmfits.","marker":"[37]"},{"why":"Supplies the QNM frequencies and mixing coefficients loaded by KerrRingdown, needed for the two-code comparison.","marker":"[40]"},{"why":"Provides the spherical-spheroidal mixing formalism and coefficient data that the mode-mixing expansion relies on.","marker":"[36]"},{"why":"Defines the superrest-frame mapping and the greedy mode-selection procedure used in the demonstration fits.","marker":"[34]"},{"why":"The numerical-relativity waveform catalog from which the two demonstration simulations are taken.","marker":"[28]"}],"fun_headline_variants":["Independent ringdown codes match to machine precision","Two ringdown codes, one machine-precision fit","Python and Mathematica ringdown fits tie","Ringdown fits from independent codes agree exactly","Independent ringdown codes, identical results"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the QNM frequency and mixing-coefficient tables on which the two codes rely agree in sign and scaling conventions, even though they come from different sources and the paper does not display that table-level comparison.","fun_headline_variants_meta":{"raw":{"variants":["Independent ringdown codes match to machine precision","Two ringdown codes, one machine-precision fit","Python and Mathematica ringdown fits tie","Ringdown fits from independent codes agree exactly","Independent ringdown codes, identical results"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00179,"raw_usage":{"total_tokens":6974,"prompt_tokens":783,"completion_tokens":6191,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":399,"completion_tokens_details":{"reasoning_tokens":6124}},"tokens_in":399,"tokens_out":6191,"duration_ms":40784,"temperature":1.0,"reasoning_tokens":6124,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-09T05:41:25.387996+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run both packages on a synthetic ringdown generated from the model itself with known amplitudes, including at least one mode where the two codes depend on different data sources; if the recovered complex amplitudes or mismatches differ by more than round-off (roughly a relative difference above $10^{-13}$), the machine-precision claim fails.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The Python package qnmfits, one of the two codes whose outputs are claimed to agree to machine precision."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The Mathematica package KerrRingdown, the other code in the cross-check."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the QNM frequencies and mixing coefficients loaded by KerrRingdown, needed for the two-code comparison."}],"review_version":1}