{"id":"558d35c6-6bff-4a86-b297-be5033e76c9d","arxiv_id":"2501.13809","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"For FGK Kepler stars with both isochrone and gyrochronology ages, the planet occurrence rate is consistent with no trend from 1.5 to 8 Gyr, with only a tentative decrease in low-mass metal-rich stars.","lead":"This paper measures how many planets orbit Sun-like stars in the Kepler field and finds no noticeable change in that number as host stars age from 1.5 to 8 billion years. The result matters because it constrains theories that planetary systems lose planets over time through collisions, ejections, or engulfment.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The no-trend result is only as strong as the age bin labels; with 56% isochrone age errors and a 1.05 Gyr median cross-method disagreement, bin misassignment could hide a real occurrence-rate trend, so a sensitivity test is required.","rationale":"I read the paper as making a deliberately cautious null claim: after correcting for Kepler completeness, occurrence rate is consistent with no trend over 1.5 to 8 Gyr, with a tentative decline only in low-mass metal-rich stars. For that claim to be true, the bin labels must carry enough information about true age. The quoted age diagnostics make that premise doubtful. The paper is transparent about this, but transparency is not the same as a robustness check. Other issues are real but secondary: Table 2 slopes for Figure 5B do not match the text, the abstract's 1.5 to 2.5 sigma significance range is inconsistent with the quoted errors, and using 1/sigma rather than 1/sigma^2 in weighted least squares changes the regression weights. These affect the tentative positive hint and detailed numbers, but they do not determine whether the null itself is meaningful. The age-error sensitivity test does. I therefore keep the reader's conditional verdict: the analysis is publishable after adding a quantitative age-error or injection-recovery test and reconciling the numbers. The concern is not that the authors are careless; it is that the data, as analyzed, cannot yet distinguish 'no trend' from 'trend hidden by age noise.'","tokens_in":17696,"tokens_out":11797,"duration_ms":116413,"concrete_test":"Perform an injection-recovery test using the same 2,658 stars and completeness grid: assign synthetic systems a true age, draw planets with a known occurrence-rate slope, e.g., -0.05 Gyr^-1, smear the true ages with the reported B20/L24 age uncertainties, run the identical binning and regression, and repeat at least 1,000 times; report the fraction of trials that recover the injected slope at 2-sigma. If that fraction is low, the reported null is an upper limit on trend amplitude, not evidence for constancy.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim, no significant age trend in occurrence rate, depends on the assigned ages preserving enough true age ordering for five log-spaced bins to be meaningful. That condition is not demonstrated. Figure 1 shows the two age scales for the same 2,658 stars disagree with RMS 1.79 Gyr and median absolute deviation 1.05 Gyr, while the five bins are only roughly 0.6 to 2.3 Gyr wide. Table 1 gives mean isochrone age errors of 2.35 to 4.83 Gyr, and Section 4.2 reports age uncertainties averaging 56%, adding that bin assignment has a major effect on the rate of planets per star. The gyrochronology scale avoids the largest formal errors but is not immune: the paper notes stalled spin-down piling up stars near 2.5 Gyr in Figure 4, and Lu et al. (2024) report a 1.35 Gyr median absolute deviation against asteroseismic ages. If a real trend exists, this level of label noise compresses it toward zero. The paper discusses the caveat qualitatively but does not propagate age errors into the slopes, p-values, or any sensitivity analysis. The claimed null, slopes of -0.03 +/- 0.04 and -0.01 +/- 0.02 Gyr^-1, is therefore unverified: it may mean no trend, or it may mean the bin labels are too noisy to see one.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper measures Kepler exoplanet occurrence rates as a function of stellar age for FGK stars using two age indicators: isochrone ages from Berger et al. (2020) and gyrochronology ages from Lu et al. (2024). Restricting to 2,658 stars with both age estimates and 235 confirmed or candidate planets, the authors apply the inverse detection efficiency method with Kepler DR25 pipeline completeness to estimate occurrence rates in five log-spaced age bins between 1.5 and 8 Gyr. They report no significant trend in the full sample (slopes of -0.033 +/- 0.038 Gyr^-1 for isochrone ages and -0.009 +/- 0.023 Gyr^-1 for gyrochronology ages), and a tentative decreasing trend for low-mass, metal-rich stars. The paper discusses possible dynamical explanations, including planet engulfment, planet-planet scattering, and planet ejection, and urges caution due to age uncertainties and small sample size.","tokens_in":57,"tokens_out":6163,"duration_ms":114440,"significance":"If the central null result is robust, it would usefully constrain the long-term evolution of close-in planetary systems around FGK stars, suggesting that any net loss of planets over 1.5-8 Gyr is small. The analysis has several genuine strengths: it is an independent application of public Kepler completeness data, it uses two different age indicators on the same stellar sample, and it explicitly isolates mass and metallicity as confounders. The inverse detection efficiency computation is transparent and closely follows established methodology. However, the significance of the result is currently limited by the fact that the dominant uncertainty in the problem, the stellar age, is not propagated into the binned occurrence rates, slopes, or p-values. The paper itself acknowledges this gap in Section 4.2. A null result based on age bins that may be heavily contaminated by misassigned stars is not yet a falsifiable statement about the age dependence of occurrence rates.","major_comments":[{"comment":"The central null claim is not established because age uncertainties are not propagated into the binned rates or the regression. Section 4.2 states that age uncertainties average 56% for the isochrone sample and that bin assignment 'has a major effect on the rate of planets per star.' Table 1 lists mean isochrone age errors of 2.35-4.83 Gyr against bin widths of roughly 0.6-2.3 Gyr, and Figure 1 shows an RMS disagreement of 1.79 Gyr between the two age scales. The reported slopes and p-values in Table 2 are therefore conditional on the age labels being correct; with this level of label noise, even a real trend would be attenuated toward zero. A sensitivity test is required, for example Monte Carlo resampling of stellar ages from their reported uncertainties and recomputing the binned occurrence rates and slopes, or a forward model of bin-assignment probabilities.","section":"§4.2, Table 1, Figure 3"},{"comment":"The low-mass metal-rich result is reported inconsistently. The text states that the gyrochronology sample in Figure 5B has a slope of -0.044 +/- 0.036 and describes the trend as 'significant in slope,' while Table 2 lists a slope of -0.055 +/- 0.018 with p = 0.205. These values cannot both be correct, and the description 'significant in slope' contradicts the reported p-value. Because this subpanel is the only tentative decreasing trend and motivates the dynamical-evolution discussion in Section 5, the numbers and language must be reconciled.","section":"§4.1, Table 2, Figure 5B"},{"comment":"The weighted least squares regression uses the inverse of sigma_Gamma as weights rather than the inverse variance 1/sigma_Gamma^2. This is not the standard WLS prescription and changes the relative contribution of the five bins to the fitted slope and p-value. The authors should either use inverse-variance weights or explicitly demonstrate that the slopes and p-values are unchanged under the alternative weighting.","section":"§3.3, §4.1, Eq. (12)"},{"comment":"The inverse detection efficiency step in Eq. (9) divides the observed planets-per-star rate by the mean efficiency Qbar_i, where Qbar_i is the mean over the Rp-P grid and then over stars. The paper notes in Section 3.2 that the per-star Q distribution is right-skewed, with mean, median, and mode differing substantially. The appropriate correction is not obviously the mean of Q over all stars rather than, for example, a per-planet inverse-efficiency sum. The authors state that the relative shape of the occurrence-rate distribution is unaffected by the choice of summary statistic, but they do not show this quantitatively; they should provide the slopes and p-values under mean, median, and mode Q, or use per-planet inverse efficiencies.","section":"§3.2, Eq. (9)"}],"minor_comments":[{"comment":"The text before Eq. (6) contains a typo: 'Guassian' should be 'Gaussian.'","section":"§3.1"},{"comment":"The citation 'Fernandes et al. (submitted)' appears in the introduction but is not included in the reference list; please add the reference or remove the citation.","section":"§1"},{"comment":"The statement that the lack of metal-poor older stars in Figure 4D could be caused by a detection bias 'in Lu et al. (2021)' appears to refer to the gyrochronology catalog of Lu et al. (2024); please verify and correct the citation.","section":"§4.1"},{"comment":"The sample selection section says the FGK definition follows Kunimoto & Matthews (2020), but the effective-temperature range is quoted without a citation to the original source; a brief reference would help the reader.","section":"§2"},{"comment":"The caption says 'error bars indicate Binomial errors' and 'propagated error'; using lower-case 'binomial' would improve consistency with standard nomenclature, and it would be helpful to state explicitly that the propagated errors do not include age uncertainty.","section":"Figure 3"}],"recommendation":"major_revision","confidential_remarks":"The manuscript relies heavily on two age catalogs produced within the author team (Berger et al. 2020 and Lu et al. 2024), with two authors of this paper also appearing on the latter. This is not improper, but the central null result would be considerably more persuasive if validated against an independent asteroseismic age sample or a public isochrone catalog outside the author group. The paper is within scope for an exoplanet demographics journal, and the topic is timely; however, the load-bearing statistical gaps described in the major comments need to be addressed before the null claim can be accepted."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First thing to know: this is a careful, honest null result, not a breakthrough. The paper measures Kepler occurrence rate versus age on 2658 FGK stars that have both B20 isochrone and L24 gyro ages, with 235 planets, periods 0.2–100 days, radii 0.2–20 Earth radii, and ages 1.5–8 Gyr. The joint use of both age estimators on the same stars is genuinely new, as is the mass/metallicity stratification. The inverse detection efficiency method is standard and is applied cleanly to public Kepler completeness data. The full-sample slopes are small relative to their errors (-0.03 ± 0.04 and -0.01 ± 0.02 Gyr^-1), and the authors are appropriately cautious in their conclusion.\n\nThe soft spots are real and mostly concentrated in one place: age label accuracy. Average isochrone age errors are 56%; Table 1 lists mean age errors of 2.35–4.83 Gyr while the five log-spaced bins are only roughly 0.6–2.3 Gyr wide. The two age scales for the same stars agree with a median absolute deviation of 1.05 Gyr and RMS of 1.79 Gyr. The paper states that age uncertainty “has a major effect on the rate of planets per star,” but it does not propagate age errors into the rates, slopes, or p-values, and offers no sensitivity analysis. That matters more than usual because the central claim is a null result. Label noise compresses real trends toward zero; without a test that reassigns stars within their age errors, “no trend” is not yet established. This is fixable and should be the main revision request.\n\nThere are also smaller inconsistencies. The abstract’s “1.5–2.5 sigma” decreasing trend for low-mass, metal-rich stars matches neither Table 2 (gyro slope -0.055 ± 0.018, which is about 3 sigma, p = 0.205) nor the text’s -0.044 ± 0.036 (about 1.2 sigma). The weighted least squares description says it uses the inverse of sigma rather than the inverse of variance; probably a typo, but it should be corrected. The sample selection also concentrates on exactly the low-mass, metal-rich population where the only hint appears, and that selection bias deserves a more explicit caveat.\n\nBottom line: the paper deserves a serious referee and, after a sensitivity analysis on age errors plus a corrected Table 2 and abstract consistency check, would be a solid contribution. The literature comparison is fair, including Yang et al. (2023); the self-citations to B20 and L24 are not a problem because the occurrence calculation rests on public Kepler completeness data. I would send it to review and ask for the age-noise test before acceptance.","headline":"A careful null result that is not yet verified because age-label noise is not propagated into the rates.","tokens_in":18581,"tokens_out":2332,"would_cite":true,"duration_ms":20956,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper claims that the occurrence rate of Kepler exoplanets around FGK stars shows no statistically significant trend with stellar age between 1.5 and 8 Gyr, after correcting for Kepler's detection efficiency.","keywords":["exoplanet occurrence rate","stellar age","isochrone fitting","gyrochronology","Kepler survey","inverse detection efficiency","FGK stars","planet evolution"],"falsifier":"Re-analyze the same 235 planets and 2658 stars with asteroseismic ages accurate to about 10 percent and recompute the binned occurrence-rate slope; if the slope is significantly negative (p < 0.05), the paper's conclusion of no trend with age would be refuted.","tokens_in":17458,"feed_emoji":"🪐","tokens_out":8620,"duration_ms":70334,"temperature":0.7,"pith_summary":"This paper asks whether the number of planets per star changes as Sun-like stars age from 1.5 to 8 billion years. Using two independent age indicators — isochrone fitting and gyrochronology (rotation slowdown) — and correcting for how easily Kepler would have detected each planet, the authors find no statistically significant trend in occurrence rate with age. A mild decreasing trend, within about 1.5–2.5σ, appears only for low-mass, metal-rich stars, which dominate the sample. The authors read this as a hint that planetary systems may lose planets over time through scattering or ejection, but state that accurate ages and larger samples are needed to settle the question.","feed_headline":"Planet frequency holds steady as FGK stars age from 1.5 to 8 Gyr","feed_subtitle":"Corrected for Kepler's detection limits, planet occurrence shows no significant drop over 6.5 billion years.","key_machinery":"The carrying mechanism is the inverse detection efficiency method, in which the observed number of planets per star in each age bin is divided by the average Kepler detection completeness $\\bar{Q}$ of the stars in that bin, giving $\\Gamma_i = n_{i,\\mathrm{planets}}/(N_{i,\\mathrm{stars}}\\bar{Q}_i)$. The completeness itself is the product of three probabilities, $Q = P_{\\mathrm{geom}} P_{\\mathrm{det}} P_{\\mathrm{win}}$: the chance of a geometric transit, the chance the transit-search pipeline detects the signal, and the chance that enough transits fall in the observing window. The age binning is provided by two published stellar age catalogs, isochrone ages from stellar evolution models and gyrochronology ages from rotation slowdown, and the trend is quantified with weighted least-squares regression using inverse errors as weights.","core_discovery":"The paper's central discovery is a null result with a hint. After correcting 235 confirmed or candidate Kepler planets for pipeline incompleteness using the inverse detection efficiency method, the occurrence rate of planets with radii 0.2–20 Earth radii and periods 0.2–100 days around 2658 FGK stars is consistent with being constant between 1.5 and 8 Gyr. The weighted least-squares slopes are −0.03 ± 0.04 per gigayear for isochrone ages and −0.01 ± 0.02 per gigayear for gyrochronology ages, with p-values of 0.45 and 0.73. Only when the sample is split into mass and metallicity bins does a decreasing slope emerge, for low-mass (0.8–1.0 solar masses), metal-rich ([Fe/H] 0.0–0.5 dex) stars, and even there the p-value is 0.2–0.4, so the decline is not statistically significant. The intended contribution is to show that any age-driven decline in planet occurrence over multi-gigayear timescales is weak at most and possibly confined to one stellar subpopulation.","pith_inferences":["The paper treats age as a discrete binning variable and does not propagate age errors into the occurrence-rate uncertainty budget; a hierarchical model that propagates age uncertainties could convert the null into a quantitative upper limit on planet-loss rates.","The 1.05 Gyr median absolute deviation between the two age indicators suggests that requiring cross-agreement between isochrone and gyrochronology ages might yield a cleaner, though smaller, sample for detecting trends.","The dependence of the absolute occurrence rate on the choice of mean, median, or mode detection efficiency implies that absolute rates are less reliable than the relative trend, which the paper argues is stable.","A direct extension would be to split the sample by planet radius or orbital period to see whether the age trend differs for hot Jupiters, sub-Neptunes, and super-Earths, which the current sample size does not allow."],"forward_implications":["If the null result is correct, the number of detectable planets around Sun-like stars does not change measurably between 1.5 and 8 billion years, so destructive processes like engulfment, scattering, and ejection must be too rare to leave a population-level signature.","The slope uncertainties (−0.03 ± 0.04 and −0.01 ± 0.02 per gigayear) set an upper limit on any real decline in occurrence rate over this age range.","The mild decline seen for low-mass, metal-rich stars, if real, would point to dynamical instability preferentially removing planets from that subgroup.","Because age errors are large enough to shuffle stars between bins, the null result also means that a genuine age trend cannot be ruled out until more precise ages are available."],"supporting_citations":[{"why":"Supplies the isochrone stellar ages, masses, metallicities, and radii used to construct the primary age sample.","marker":"Berger et al. (2020)"},{"why":"Supplies the gyrochronology ages from rotation periods, calibrated with gyro-kinematic ages and clusters.","marker":"Lu et al. (2024)"},{"why":"Provides the analytic Kepler pipeline completeness model (Pgeom, Pdet, Pwin) that defines the detection efficiency Q.","marker":"Burke et al. (2015)"},{"why":"Validates the Kepler pipeline completeness model used for the inverse detection efficiency correction.","marker":"Christiansen et al. (2020)"},{"why":"Gives the geometric transit probability relation and the ~10% eccentricity correction that the circular-orbit assumption relies on.","marker":"Kipping (2014)"},{"why":"Reports the earlier decreasing occurrence-rate trend with gyrochronology age that this paper's null result is compared against.","marker":"Yang et al. (2023)"}],"fun_headline_variants":["Planet rates steady for FGK stars over 6.5 Gyr in Kepler","No age-linked change in exoplanet frequency for FGK stars","Kepler finds planet occurrence constant across stellar ages","Exoplanet occurrence age-invariant in Kepler FGK sample","Planet occurrence shows no significant trend with star age"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The result depends on one load-bearing assumption: the assigned stellar ages are accurate enough that stars binned into 1.5–8 Gyr groups preserve the true age ordering, since the paper's own comparison shows isochrone and gyrochronology ages disagree by a median absolute deviation of 1.05 Gyr and average isochrone age errors are 56%.","fun_headline_variants_meta":{"raw":{"variants":["Planet rates steady for FGK stars over 6.5 Gyr in Kepler","No age-linked change in exoplanet frequency for FGK stars","Kepler finds planet occurrence constant across stellar ages","Exoplanet occurrence age-invariant in Kepler FGK sample","Planet occurrence shows no significant trend with star age"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000561,"raw_usage":{"total_tokens":2702,"prompt_tokens":1018,"completion_tokens":1684,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":634,"completion_tokens_details":{"reasoning_tokens":1597}},"tokens_in":634,"tokens_out":1684,"duration_ms":12708,"temperature":1.0,"reasoning_tokens":1597,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T15:35:07.502303+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-analyze the same 235 planets and 2658 stars with asteroseismic ages accurate to about 10 percent and recompute the binned occurrence-rate slope; if the slope is significantly negative (p < 0.05), the paper's conclusion of no trend with age would be refuted.","supporting_citations":[],"review_version":1}