{"id":"85cf948e-89bb-41c4-b963-757274dbe44b","arxiv_id":"2605.19653","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Two FRBs in the CHIME/FRB catalog look microlensed by black holes of roughly 550 and 2000 solar masses, presented as IMBH candidates.","lead":"The authors search CHIME/FRB catalog 2 for fast radio bursts with the double-peak shape expected when an intervening black hole lens delays part of the signal. They report two candidate events with inferred lens masses around 500–600 and 1500–2600 solar masses and use them to discuss primordial black holes as dark matter.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"No trials correction across 340 FRBs means the two 3σ ACF spikes could be the expected false positives; the IMBH evidence claim is not yet statistically anchored.","rationale":"The reader's weakest_assumption identifies exactly the same load-bearing concern: the 3σ threshold is applied independently to 340 multi-peak FRBs without trials correction, so the two surviving candidates could be the expected false positives. I agree with this assessment. I considered the abstract/body mass inconsistency and the single-band ACF for FRB 20211115A, but these affect individual candidate robustness rather than the sample-wide significance of the search. The trials-correction issue is upstream: if the two candidates are consistent with the null, the lens masses and PBH abundance estimates have no evidential basis regardless of other refinements. The paper is still useful as a candidate-identification and upper-limit study, so the reader's CONDITIONAL verdict remains appropriate; my read does not change it.","tokens_in":15386,"tokens_out":6410,"duration_ms":70219,"concrete_test":"Run the full §2.2 pipeline on 10^4 Monte Carlo realizations of 340 unlensed multi-peak FRBs with widths, SNRs, spectral shapes, and noise drawn from Catalog 2; record how many realizations produce at least two candidates passing all filters (ACF>3σ, peak-pair match, PSNR>10, global-max requirement, K-S drift rejection, hardness). If >5% of realizations yield ≥2 candidates, the two observed candidates are not statistically significant at 95% confidence, and the IMBH/PBH claims should be reframed as upper limits only.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The most load-bearing weakness is statistical control. Section 2.2 applies a 3σ ACF-spike threshold event-by-event, then filters by peak ordering, PSNR>10, K-S drift, and hardness. Across 340 multi-peak FRBs, the expected number of 3σ excursions under the null is already ~1 (and larger if each event's full lag grid is scanned), yet no trials correction or global false-alarm rate is given. The two surviving candidates are therefore consistent with the noise tail before the downstream filters are applied, and those filters are not independent of the spike search—they may preferentially select noise configurations that look lensed. Because the lens masses, the 'evidence for IMBHs' interpretation, and the ~4% PBH abundance in §3 are all conditional on these two candidates being true lensing events, the absence of a pipeline-level false-alarm estimate is load-bearing. The paper honestly notes the alternative non-lensing possibility, but the central claim requires the candidates to survive as detections, not just as upper-limit inputs.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents a search pipeline for gravitational microlensing signatures in the dynamic spectra of fast radio bursts and applies it to the 4539 bursts in CHIME/FRB Catalog 2. The pipeline combines an autocorrelation-function spike search, peak-flux ordering, a Kolmogorov-Smirnov frequency-drift test, and a hardness-ratio test. Two candidates survive: FRB 20190131D and FRB 20211115A, with inferred point-mass lens masses of roughly 1544–2571 Msun and 539–609 Msun. The authors interpret these as intermediate-mass black holes, argue that the lenses may be primordial if no intervening structures exist, and derive either a ~4% PBH dark-matter fraction in the relevant mass ranges or a ~13% upper limit at 95% confidence if the candidates are not genuine lensing events.","tokens_in":15653,"tokens_out":6573,"duration_ms":71413,"significance":"If the two candidates are genuine, the paper would add to the sparse observational evidence for isolated intermediate-mass black holes and would demonstrate a new use of FRB microlensing. The work has several genuine strengths: it uses a large public catalog, provides reproducible analysis code, presents a transparent list of the nine pre-hardness candidates, and improves on earlier FRB-based PBH constraints by nearly an order of magnitude. The authors also explicitly acknowledge plasma-lensing and intrinsic-emission alternatives. However, the significance of the central claim is conditional on statistical control of the selection pipeline; the candidate-level thresholds alone do not establish a detection significance, and the derived PBH abundance is calibrated to the same two events. The paper is therefore potentially important but needs substantive methodological revision.","major_comments":[{"comment":"The first filter is a 3-sigma ACF-spike threshold applied to each of the 340 multi-peak FRBs, with no trials correction or global false-alarm estimate. Under a Gaussian null, roughly 340 x P(>3sigma) ~ 1 spike is expected by chance, and scanning the full lag grid increases the effective number of trials. Because the downstream filters (peak ordering, PSNR>10, K-S drift, hardness) are applied after selecting spikes and are not independent of the spike search, the two surviving candidates cannot be assigned a detection significance from the reported thresholds. This is load-bearing: the lens masses in Sec. 2.3 and the PBH statements in Sec. 3 are all conditional on these two events being real lensing signatures. Please provide null simulations of the complete pipeline, or an analytic trials factor, and report a false-alarm probability for the two candidates.","section":"Section 2.2, ACF spike selection"},{"comment":"The hardness criterion ('consistent within the 1-sigma region') is weak and applied inconsistently. For FRB 20190131D, HR_HM = 0.35 +/- 0.09 versus 0.55 +/- 0.12 differ by about 1.3 sigma, yet the event is retained. For FRB 20211115A, only the M-band ACF exceeds 3 sigma at the candidate delay; the L and H bands do not. The number of noise realizations that would pass a 1-sigma-overlap test should be quantified. In addition, the K-S test in Sec. 2.2 rebins 32 frequency channels into 512, which cannot create independent samples, and the quoted D_crit ~ 0.1 is not what the stated formula gives for n_f = 512 (approximately 0.085). Please justify or replace this step.","section":"Table 1 and Sec. 2.2, hardness and K-S tests"},{"comment":"The ~4% PBH abundance is not derived in the text. It appears to be obtained by normalizing the expected number N_lensed in Eq. (15) to the two candidate events and solving for f_PBH. This is a calibration to the same data used for the discovery, not an independent measurement, and it ignores Poisson uncertainties, selection efficiency, and the fact that the two candidates have different masses (they should imply two different f_PBH constraints unless a specific mass function is assumed). The 95% upper limit of 13% is also presented as applying 'if these candidates are not genuine lensing signals,' but the calculation uses zero true detections; the two observed spikes should either be modeled as background events or the limit should be derived from a full likelihood that includes them. Please present the actual likelihood, the derivation of f_PBH, and the uncertainties.","section":"Section 3, Eq. (15) and Fig. 5"},{"comment":"The inference that the lenses are 'isolated and of primordial origins' rests on the absence of reported galaxies or galaxy clusters along the lines of sight. CHIME/FRB Catalog 2 burst positions have substantial uncertainties, and no deep multi-wavelength follow-up is presented in this paper. The absence of known galaxies in current catalogs therefore does not exclude a lens inside a foreground galaxy or cluster. This does not affect the inferred lens masses, but it directly affects the PBH interpretation and the f_PBH constraints. Please add a quantitative check using the best available localizations and foreground catalogs, or soften the primordial-origin claim.","section":"Section 4 and Sec. 2.3, intervening-structure claim"},{"comment":"Eq. (4) defines sigma_dt using a sum over 'delta t in Delta t' after first defining Delta t as the time grid in Eq. (2). The notation is confusing: Eq. (2) uses delta t as the lag, while Eq. (4) writes 'delta t in Delta t' and also uses Delta t as both a lag and a set. Please clarify the indexing and whether the sigma estimate is computed from the full ACF or only from the window around candidate lags; this matters for the meaning of the 3-sigma threshold.","section":"Section 2.2, Eq. (4) and ACF definition"}],"minor_comments":[{"comment":"There are several typographical issues: 'abundace' in Sec. 1, 'T wo' in the abstract, inconsistent capitalization such as 'Dayal & maiolino', and duplicated words ('and and' in Sec. 2.3). Please copyedit.","section":"Throughout"},{"comment":"The mass-inversion formula is stated without derivation. Please define all symbols and show how Eq. (10) follows from the point-mass time-delay expression in Eq. (11), including the treatment of the flux ratio Rf and the redshifted mass ML,z.","section":"Eq. (10)"},{"comment":"The right panels mark ACF spikes with colored dots for total, L, M, and H bands. Please add a legend or caption explanation of the colors and of what 'a colored dot on a spike' signifies, since the text says only that a dot indicates the threshold is exceeded.","section":"Fig. 4"},{"comment":"Some references are arXiv preprints with the same year as the manuscript and may not be peer-reviewed; please mark them clearly as preprint citations and ensure the CHIME/FRB Catalog 2 reference (Abbott et al. 2026) matches the published or accepted version.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The central claim is not yet statistically anchored: the absence of a trials correction for 340 events is a genuine load-bearing gap, and the 4% abundance is a self-calibration to the two candidates. These issues can likely be fixed with null simulations and a fuller likelihood treatment, so I do not recommend rejection. Given the borderline hardness values and the questionable K-S rebinning, a methodologically careful revision is essential before the candidate claim can be considered established."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: the paper finds two plausible microlensed FRBs in CHIME/FRB Catalog 2 and derives an improved PBH upper limit, but the evidence-for-IMBHs headline is not yet statistically anchored. The pipeline is a genuine step forward and the candidate list is worth following up; just don't cite the 4% PBH abundance as a measurement.\n\nWhat's actually new: a refined ACF-based search applied to the full Catalog 2, with a K-S frequency-drift test and a hardness filter. It turns up two events not previously flagged as lensed candidates—FRB 20190131D (which Zhou et al. 2022a had looked at and excluded) and FRB 20211115A. The authors also ship code and data on GitHub, which is good practice. The upper limit on f_PBH in the >300 M_sun range (~13% at 95% CL) is a legitimate and useful update, an order-of-magnitude improvement over catalog 1.\n\nThe main problem is statistical control. The first filter is a 3-sigma ACF spike applied event-by-event to 340 multi-peak FRBs. Under the null you expect roughly one 3-sigma excursion in 340 independent trials, and more if you scan each event's full lag grid. No trials correction or global false-alarm rate is computed. The two surviving candidates are therefore consistent with the noise tail before the downstream filters are applied, and those filters (PSNR, K-S, hardness) are not independent of the spike search—they can preferentially keep noise configurations that look lensed. The lens masses, the IMBH interpretation, and the 4% PBH estimate all rest on those two events being real. The paper is honest about the non-lensing alternative, but the title and abstract make a stronger claim than the statistics support.\n\nOther soft spots: the hardness test for FRB 20190131D is marginal—the two H/M ratios differ by ~1.3 sigma, which barely satisfies their own 1-sigma criterion. For FRB 20211115A, only the M-band ACF shows the spike; the L and H bands don't, which weakens the frequency-independence check. And there's an internal inconsistency in the lens masses: the abstract gives [280-467] and [539-609] M_sun, while the body gives [1544-2571] and [539-609] M_sun. That has to be fixed.\n\nThe 4% PBH abundance is essentially a fit to the two candidates, not a measurement, and the authors themselves note tension with other constraints. Fine to present as an illustration, not as evidence.\n\nWho this is for: anyone working on FRB lensing, PBH constraints, or IMBH candidates. It deserves a serious referee—the pipeline is reproducible and the upper limit is valuable—but the authors need to add a trials correction or at least tone down the evidence claim before I'd call it a detection. Send to review, with the expectation of a major revision.","headline":"A useful FRB lensing search with two candidates and an improved PBH upper limit, but the 'evidence for IMBHs' claim outruns the statistics.","tokens_in":16209,"tokens_out":3023,"would_cite":true,"duration_ms":28445,"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":"Two fast radio bursts carry candidate gravitational-microlensing echoes from lenses of about 540–610 and 1540–2570 solar masses, interpreted as intermediate-mass black holes.","keywords":["fast radio bursts","microlensing","intermediate-mass black holes","primordial black holes","dark matter abundance","gravitational lensing","time delays","autocorrelation analysis"],"falsifier":"Reanalyze all 340 multi-peak bursts with a global false-alarm estimate: scramble or simulate unlensed dynamic spectra under the same noise model and count how often the pipeline produces a 3-sigma autocorrelation spike that survives the peak-ordering, drift, and hardness tests. If two or more false positives emerge per trial, the candidates are consistent with noise. Separately, high-time-resolution follow-up of the two bursts should confirm the predicted 8.82 ms and 6.86 ms echoes and frequency-independent flux ratios.","tokens_in":15246,"feed_emoji":"🕳️","tokens_out":5475,"duration_ms":51026,"temperature":0.7,"pith_summary":"This paper searches for gravitational microlensing in the dynamic spectra of thousands of fast radio bursts and argues that two bursts carry true lensing echoes. In the point-mass lens picture, the measured time delays and flux ratios translate into lens masses of roughly 540–610 and 1540–2570 solar masses, squarely in the poorly observed intermediate-mass black hole range. If the signals are real and no galaxies or clusters lie on the lines of sight, the lenses would be isolated primordial black holes contributing about 4% of dark matter in these mass ranges. Even if the two candidates are false, the same search yields a 95% upper limit of about 13% on primordial black holes above 300 solar masses, about an order of magnitude stronger than previous fast-radio-burst–based constraints. The paper's central claim is that fast-radio-burst microlensing is a working probe of the missing black-hole mass gap.","feed_headline":"Two fast radio bursts hint at mid-size black holes","feed_subtitle":"Microlensing time delays in two bursts imply masses near 600 and 2,000 suns, with primordial origins possible.","key_machinery":"The pipeline's core is the normalized autocorrelation function of each burst's light curve, compared against a smoothed baseline; a spike above the 3-sigma level identifies a candidate time delay. Candidate peak pairs must satisfy point-mass ordering (main peak before echo), a peak signal-to-noise threshold, and a distribution-comparison test showing no severe frequency drift between the paired peaks. A final hardness test requires the flux ratio between the two peaks to be frequency-independent in three rebinned radio bands, as gravitational lensing demands. The point-mass time-delay identity then maps the selected delay and flux ratio to a lens mass, and the lensing optical depth formula c","core_discovery":"The paper's central claim is that two fast radio bursts, FRB 20190131D and FRB 20211115A, each contain a pair of peaks with the hallmarks of gravitational microlensing by a point mass: an autocorrelation spike at the expected time delay, correct arrival ordering, no significant frequency drift between the two peaks, and frequency-independent flux ratios across three radio bands. Applying the point-mass lens time-delay formula converts the observed delays and flux ratios into lens masses of about 540–610 and 1540–2570 solar masses, placing both in the intermediate-mass black hole range. The paper further claims that, absent intervening galaxies or clusters, these isolated lenses would be prim","pith_inferences":["The 3-sigma autocorrelation threshold was applied independently to 340 multi-peak bursts with no correction for multiple trials, so roughly one chance spike is expected; the global false-alarm probability of the two surviving candidates should be computed before accepting them as real.","High-time-resolution follow-up of the two bursts, or a search for the same time delay in repeated bursts from the same sources, would directly test whether the echoes are gravitational rather than intrinsic or plasma-induced.","The same autocorrelation-plus-hardness pipeline could be applied to other coherent transients or to repeating fast radio bursts, where multiple bursts provide independent trials and plasma lensing alternatives can be separated by frequency-dependent behavior.","If confirmed, the tension between the implied 4% abundance and existing dynamical and accretion limits may indicate that these lenses are not primordial but formed through dynamical assembly, or that the primordial mass function is narrowly peaked; more events would distinguish these cases."],"forward_implications":["If the two candidates are genuine, fast-radio-burst microlensing becomes a demonstrated way to find isolated intermediate-mass black holes in an otherwise hard-to-probe mass range.","Their inferred masses, hundreds to a few thousand solar masses, would fill part of the gap between stellar-mass and supermassive black holes.","If primordial, the implied roughly 4% dark-matter fraction in these narrow mass windows is a quantitative target for primordial black hole formation models and sits in tension with other constraints from accretion and dynamics.","If the candidates are false, the pipeline still delivers an improved upper limit, roughly 13% at 95% confidence for masses above 300 solar masses, on intermediate-mass primordial black holes.","Scaling the method to future larger and higher-time-resolution fast-radio-burst samples should sharpen both the candidate detections and the exclusion limits."],"fun_headline_variants":["FRB microlensing finds two mid-size black holes","Two fast radio bursts reveal black hole missing link","Microlensed FRBs point to intermediate-mass black holes","Hidden black holes seen in fast radio burst echoes","Fast radio bursts unmask pair of mid-mass black holes"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The load-bearing premise is that a 3-sigma autocorrelation spike in any one of 340 multi-peak bursts counts as meaningful evidence, but because the threshold is applied independently with no correction for the number of trials, about one such spike is expected by chance; if the two surviving candidates are those chance fluctuations, the lensing interpretation collapses.","fun_headline_variants_meta":{"raw":{"variants":["FRB microlensing finds two mid-size black holes","Two fast radio bursts reveal black hole missing link","Microlensed FRBs point to intermediate-mass black holes","Hidden black holes seen in fast radio burst echoes","Fast radio bursts unmask pair of mid-mass black holes"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000175,"raw_usage":{"total_tokens":1196,"prompt_tokens":893,"completion_tokens":303,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":637,"completion_tokens_details":{"reasoning_tokens":226}},"tokens_in":637,"tokens_out":303,"duration_ms":3120,"temperature":1.0,"reasoning_tokens":226,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-02T13:36:49.410730+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Reanalyze all 340 multi-peak bursts with a global false-alarm estimate: scramble or simulate unlensed dynamic spectra under the same noise model and count how often the pipeline produces a 3-sigma autocorrelation spike that survives the peak-ordering, drift, and hardness tests. If two or more false positives emerge per trial, the candidates are consistent with noise. Separately, high-time-resolution follow-up of the two bursts should confirm the predicted 8.82 ms and 6.86 ms echoes and frequency-independent flux ratios.","supporting_citations":[],"review_version":2}