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The description of dataset construction is internally inconsistent between Methods and Results, leading to confusion about the actual number of asteroids and families analyzed (Sec. 2.2 vs. Sec. 3.1, plus Abstract and Conclusion). Sec. 2.2 mentions 38,451 asteroids in 118 families, reduced to 42 families, whereas Sec. 3.1 states 15,749 asteroids in 62 families, reduced to 33 families. These discrepancies propagate into Table 1 and the $k$–age correlation analysis in Sec. 3.3 and undermine reproducibility and interpretation of sample size, selection effects, and statistical power.
Recommendation: Unify and document the full data curation pipeline. In Sec. 2.1–2.2 and Sec. 3.1, provide a single consistent sequence: (i) initial counts per source catalog (asteroids and families); (ii) counts after each filtering step (e.g., removal of missing $D$, $P$, $a$, or age; quality cuts; family merges); (iii) final number of asteroids and families used for V-shape fitting; and (iv) subset used for $k$–age correlations. Correct any erroneous numbers and ensure that Abstract, Table 1, Sec. 3.1, Sec. 3.3, and the Conclusion all quote the same finalized counts. Consider adding a flow diagram or summary table of these numbers.
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The boundary model $\Delta a_{\max} = k \cdot (1/Y)$ with a forced zero intercept, implemented via a binned-maxima, weighted linear regression, is central to defining $k_D$, $k_P$, and $k_{PD}$ but is insufficiently specified and not quantitatively validated (Sec. 2.3.1–2.3.3; Sec. 3.2.2). The diurnal Yarkovsky effect has non-linear dependence on spin period and strong obliquity dependence, so a strictly linear, zero-intercept relation is a simplification that may bias $k$. Moreover, key implementation details—bin number/edges, minimum bin population, exact weighting scheme, regression routine, and treatment of $\Delta a_{\max}$ uncertainties—are only described qualitatively, and no sensitivity tests to these choices or to the zero-intercept constraint are presented.
Recommendation: In Sec. 2.3.3, fully specify the boundary-fitting algorithm: (i) define how the number of bins is chosen (fixed $N$ or a function of sample size) and whether bins are equal-width in $1/Y$; (ii) give the formula for $\Delta a_{\max}$ per bin and the weights used in the regression (e.g., $w_j = N_j$); and (iii) state the regression method and software. Then, in Sec. 3.2.2 (or a new subsection), present robustness tests on several well-populated families: vary bin counts (e.g., 10, 15, 20, 30), minimum bin population, and whether an intercept is free or constrained to zero, and quantify how $k_Y$ changes and how goodness-of-fit metrics (e.g., $R^2$, residuals) behave. Discuss in Sec. 3.3 how potential systematic biases from these modeling choices could influence the inferred age correlations.
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Measurement uncertainties in diameters, spin periods, and especially family ages, as well as heterogeneity in age determinations, are acknowledged only qualitatively and are not propagated through to $k_Y$ estimates or to the $k_Y$–age regressions (Sec. 2.1–2.4; Sec. 3.3; Sec. 3.4). All correlations appear to be treated with simple linear regression and Pearson $r$ without accounting for errors-in-variables, confidence intervals on $k_Y$, or uncertainties on ages. This can lead to underestimated uncertainties and potentially overconfident assessment of correlation strengths, particularly where scatter is large (e.g., $k_P$).
Recommendation: Augment Sec. 2.4 and Sec. 3.3 with explicit uncertainty handling: (i) summarize typical or catalog-provided uncertainties for $D$, $P$, and family ages, citing sources; (ii) where feasible, propagate $D$ and $P$ errors into $\Delta a$ and the $1/Y$ proxies, or justify approximations; and (iii) perform bootstrap or Monte Carlo simulations in which $D$, $P$, and ages are perturbed within their uncertainties to obtain distributions for $k_D$, $k_P$, $k_{PD}$ and for the regression slopes and Pearson $r$-values. Report confidence intervals (e.g., 68% or 95%) on $k_Y$ and on the $k_Y$–age relations in Table 1 or supplementary material, and temper claims in Sec. 3.3 and the Conclusion where significance is sensitive to uncertainties.
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Selection effects and biases in the availability of spin periods, completeness of family membership, and adopted family ages are only briefly mentioned and not quantified (Sec. 2.2; Sec. 3.1; Sec. 3.4). The requirement of complete spin period data and a $\geq 50$-member threshold likely biases the sample toward larger, brighter, and better-studied objects and families, and may correlate with age, heliocentric distance, or dynamical environment. Without a quantitative bias assessment, it is unclear how representative the 33 analyzed families are and how selection might influence the observed $k_P$ and $k_{PD}$ trends and even the $k_D$–age correlation.
Recommendation: In Sec. 2.2 and Sec. 3.1, add a quantitative analysis of selection effects: (i) compare distributions of age, heliocentric distance, and typical size between included and excluded families; (ii) show histograms of diameter and spin period for the analyzed sample versus the full set of family members with known $D$ or $a$; and (iii) discuss how these differences might bias $k_P$ and $k_{PD}$ (e.g., preferential sampling of families with richer spin coverage or particular size ranges). If possible, recompute the $k_D$–age relation using a broader set of families that only require $D$ (not $P$) to test for selection-induced distortions. Emphasize in Sec. 3.4 and the Conclusion that current correlations apply to this biased subset and may not generalize to all families.
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The physical interpretation of $k_P$ and $k_{PD}$, and their relation to underlying Yarkovsky and YORP physics, remains somewhat underdeveloped and partially inconsistent with the complexities acknowledged later (Sec. 1; Sec. 3.2.2; Sec. 3.3.2–3.3.3; Sec. 3.4; Conclusion). The linear dependence on $1/P$ is treated as a first-order approximation, but potential non-linearities (e.g., saturation or regime changes for very fast/slow rotators), obliquity distributions, and YORP-driven spin evolution are not examined empirically. As a result, statements that $k_P$ and $k_{PD}$ provide “physically grounded chronometers” risk over-interpretation, given that these coefficients may be better viewed as empirical descriptors integrating multiple processes.
Recommendation: Refine the interpretation in Sec. 3.2.2, Sec. 3.3.2–3.3.3, Sec. 3.4, and the Conclusion by: (i) clearly distinguishing $k_D$, which more directly reflects size-dependent Yarkovsky drift, from $k_P$ and $k_{PD}$, which are empirical effective parameters combining Yarkovsky, YORP, obliquity distributions, and thermophysical diversity; (ii) exploring non-linearity for a few well-sampled families (e.g., by inspecting $\Delta a_{\max}$ vs. $1/P$ in log–log space or allowing simple curvature/broken-line fits) and commenting on any deviations from linearity; and (iii) softening or qualifying claims that $k_P$ and $k_{PD}$ are new “physically grounded chronometers,” presenting them instead as promising empirical proxies whose physical calibration requires further modeling and, where possible, spin-axis information. Include at least one order-of-magnitude comparison between $k_D$-derived drift rates and canonical Yarkovsky $da/dt$ values to anchor the discussion.
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There is no explicit external benchmarking of the derived $k_D$ values or implied drift rates against existing V-shape age estimates or theoretical Yarkovsky calibrations, limiting the ability to assess external validity (Sec. 1; Sec. 3.2.2–3.3.1; Conclusion). While internal $k_D$–age correlations are presented as a validation of the method, the paper does not show whether $k_D$ for well-studied families (e.g., Vesta-like, Eos, Karin, Veritas) are of the expected magnitude, nor whether inverting $k_D$ reproduces literature ages within uncertainties.
Recommendation: In Sec. 3.2.2 and/or Sec. 3.3.1, include an external consistency check: (i) for several benchmark families with published V-shape or dynamical ages, compare the $k_D$-derived characteristic drift (e.g., via $da/dt \approx k_D/T_{\rm family}$) to standard Yarkovsky model predictions; (ii) where feasible, invert $k_D$ to estimate ages and compare to literature values; and (iii) briefly discuss how $k_P$ and $k_{PD}$ might be calibrated using theoretical spin-dependent Yarkovsky/YORP models. Use these comparisons to demonstrate that the empirical coefficients are physically reasonable and to clarify any systematic offsets. This will better situate the work within the broader literature and strengthen confidence in the method.
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Across Figures 1–21, there are frequent omissions of explicit axis units, normalization details, and key parameter annotations (such as drift coefficients $k$, their uncertainties, and family center $a_c/a_0$), as well as a lack of confidence intervals or uncertainty bands on fitted boundaries. These omissions hinder quantitative interpretation, reproducibility, and cross-figure comparison. Additionally, sample sizes, selection criteria, and interloper handling are often not indicated, which can bias the envelope fits and limit the credibility of the results.
Recommendation: For all figures, explicitly label axes with symbols and units (e.g., $a$ [AU], $1/D$ [1/km], $1/P$ [1/hr], $1/(D\cdot P)$ [1/(km$\cdot$hr)]), annotate fitted drift coefficients ($k$) with uncertainties directly on the panels or in the caption, and mark the family center ($a_c/a_0$) with a labeled line and value. Add confidence bands (e.g., bootstrap or Monte Carlo) around fitted boundaries, and report sample sizes, selection criteria, and interloper/outlier handling in captions or legends. Ensure all figures use consistent terminology, notation, and visual styling.
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Many figures (especially multi-panel layouts) suffer from small physical size, low font and line weights, and overplotting of dense gray points, which together reduce readability, obscure density structure, and make key annotations difficult to discern at print or screen scale. Legends, panel labels, and in-figure explanations are often minimal or absent, requiring readers to rely on captions for symbol/line meanings.
Recommendation: Increase figure and panel sizes, font and line weights, and use partial transparency or density/hexbin overlays to reduce overplotting. Add clear panel labels (a, b, c), concise legends or in-panel annotations for symbol/line meanings, and harmonize axis ranges and tick formatting across panels for comparability. Export figures as vector graphics (PDF/SVG) or high-resolution raster to ensure clarity in publication.
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Internal inconsistency in dataset and selection counts between Methods and Results: Sec. 2.2 (p.3) states 38,451 asteroids across 118 families with 42 families selected ($\geq 50$ members), whereas Sec. 3.1 (p.5) and the Abstract state 15,749 asteroids across 62 families with 33 families selected ($\geq 50$ members). These figures are not reconciled, making it unclear which dataset underlies the mathematical fitting and the reported coefficients/correlations.
Recommendation: Add a clear, step-by-step accounting table (or paragraph) showing how the dataset changes across preprocessing steps (e.g., after requiring ages, after requiring spin periods, after family-age join, after filtering), and ensure the counts in Sec. 2.2, Sec. 3.1, and the Abstract refer to the same stage or are explicitly labeled as different stages.
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Unresolved internal inconsistency in reported dataset sizes and selected-family counts: some sections report 15,749 asteroids from 62 families with selection to 33 families, while Methods (Sec 2.2) reports 38,451 asteroids among 118 families and selection to 42 families.
Recommendation: Reconcile all dataset totals and selection outcomes across Abstract/Methods/Results/Conclusions; explicitly define which dataset each number refers to (source, filters, and final regression/analysis sample) and ensure consistent reporting.