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Core coordinate/regression/sign conventions are ambiguous or internally inconsistent, undermining the interpretation of slope sign (positive vs negative) and even the expected theoretical slope (Secs. 2.2.1–2.2.4, 3.2; multiple figure captions). The text alternates between describing “$\log_{10}(|\Delta a|)$–$\log_{10}(P)$” and fitting a model written as $y = m x + c$ with $y = \log_{10}(P)$ and $x = \log_{10}(|a-a_c|)$ (Sec. 2.2.2). Under a simple scaling $|\Delta a| \propto 1/\sqrt{P}$, one expects $\log|\Delta a| = -\frac{1}{2} \log P + {\rm const}$, which corresponds to $d(\log P)/d(\log|\Delta a|) = -2$ if fitting $\log P$ vs $\log|\Delta a|$—not small negative values near $0$ reported for many families. In addition, using $|a-a_c|$ removes the drift sign tied to obliquity, which complicates physical interpretation and any YORP-obliquity discussion.
Recommendation: Make the analyzed space unambiguous everywhere: explicitly define axes as $(x=..., y=...)$ and define the fitted model in the same orientation as the plotted axes (e.g., either $\log |\Delta a| = \alpha \log P + \beta$ or $\log P = m \log |\Delta a| + c$), stating clearly whether the regression is $y$-on-$x$ or $x$-on-$y$ and how uncertainties are handled. Reconcile the expected theoretical slope with the chosen regression direction (e.g., show the expected $\alpha$ or $m$ numerically). Audit and correct all figure captions and text where slope sign is interpreted (Secs. 3.2, 4.3; e.g., statements that contradict the implication of $f>0$ in $y = \log P$ vs $x = \log|\Delta a|$). Consider adding (or at least testing) an analysis using signed $\Delta a$ (not absolute value) in parallel, since the sign contains physical information about obliquity and drift direction.
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The Yarkovsky–YORP simulation model is not specified at an auditable/reproducible level, making it unclear whether simulation–data discrepancies (and any trends with age or V-shape class) reflect physics or modeling choices (Sec. 2.3.1, Secs. 3.5, 4.3–4.4). The manuscript references a “full, non-linear Yarkovsky formula” and a Gaussian-distributed YORP coefficient, but does not provide explicit equations for $da/dt$ and $d\omega/dt$, whether diurnal/seasonal components are included, the heliocentric-distance dependence, adopted thermophysical/material parameters (or distributions), any size scaling, nor numerical integration details (scheme, timestep, convergence). Handling of extreme/unphysical spin states ($\omega \rightarrow 0$, negative $\omega$, breakup barrier, resets) is also not described.
Recommendation: Expand Sec. 2.3.1 to include explicit functional forms (or exact canonical references plus a clear statement of which terms are used) for $\dot{a}_{\rm YK}(D, \omega, \epsilon, a, ...)$ and $\dot{\omega}_{\rm YORP}(D, ...)$, including units, sign conventions, and all parameter values/distributions (thermal inertia, conductivity, density, emissivity/albedo; diurnal vs seasonal; dependence on $a$). Specify the YORP-coefficient distribution (mean/$\sigma$, truncation, size dependence, calibration) and the numerical integrator (Euler/RK, $dt$, stability checks). State how unphysical spin states are prevented/treated (spin barrier, fission/reset, tumbling/$\omega$ sign). Provide at least one convergence/sensitivity test (e.g., halve $dt$; vary key parameters) showing that headline outputs (slope distributions and $D$-statistics in Sec. 3.5) are stable.
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Positive-slope “V-shapes” are a central claim, but robustness against methodological artifacts, selection effects, and element/center choices is not demonstrated (Secs. 2.2.1–2.2.4, 3.2–3.4, 4.3). The boundary estimator (bin-wise minima) is highly sensitive to outliers, sparse bins, bin edges, and heteroscedastic scatter; period/diameter measurement biases can correlate with size and thus with $|\Delta a|$; resonance truncation, interlopers, and family membership uncertainty can reshape envelopes. Additionally, it is not stated whether $a$ is proper or osculating—critical for family-structure work.
Recommendation: In Secs. 3.2–3.4, add robustness analyses for slope sign/magnitude: (i) bootstrap within each family to obtain confidence intervals on slopes; (ii) vary binning (number of bins, equal-width vs equal-count, bin edges) and report slope variability; (iii) test more robust envelope estimators (e.g., $1$–$5$\% quantile regression in $y|x$) alongside the min-per-bin method; (iv) explicitly state and justify whether semi-major axes are proper elements (preferred) or osculating, and, if currently osculating, repeat at least a subset using proper $a$ to verify that slope sign patterns persist; (v) for representative positive-slope families, run diagnostics excluding likely interlopers and/or testing alternate membership lists. Report which positive-slope cases remain statistically significant after these checks.
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The choice of family center $a_c$ (semi-major axis of the largest asteroid; Sec. 2.2.1) may systematically bias $|\Delta a|$ and thus both envelope slopes and “consistency” classifications, especially for asymmetric families and those affected by resonances. Because the full analysis depends on $|a-a_c|$, any offset in $a_c$ directly propagates into the inferred V-shape geometry (Secs. 2.2–3.3).
Recommendation: Justify $a_c = $ largest-member-$a$ physically and empirically. Add a sensitivity study (Sec. 2.2.1 or Sec. 3.1) comparing slopes and $C$ under alternative $a_c$ definitions (median/mean/mode of the family’s proper-$a$ distribution; a fitted vertex; catalog-reported family center). Quantify how often the slope sign or the “Well-defined/Obscure/Absent” class changes when $a_c$ is perturbed within plausible ranges, and flag families that are $a_c$-sensitive in Table 2 or text.
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The 2D two-sample comparison (2D-KS) is under-documented, not reported per family, and not obviously calibrated for stochastic simulations, weakening conclusions drawn from $D$-statistics and claimed age/V-shape clarity trends (Sec. 2.3.2, Sec. 3.5, Sec. 4.3). The specific 2D-KS variant is not stated; $p$-values and their computation are not described; limitations of 2D-KS in multidimensions are not addressed. Because simulations include randomness (initial spins, YORP coefficients), a single realization per family can produce seed-dependent $D$.
Recommendation: In Sec. 2.3.2, specify the exact 2D-KS algorithm (e.g., Peacock; Fasano–Franceschini), implementation/library, and how $p$-values are obtained (analytic approximation vs permutation). In Sec. 3.5, report per-family $D$ and $p$ in a table (analogous to Table 2), and add summary plots ($D$ vs age; $D$ vs $C$). Run ensembles of Monte Carlo realizations per family (multiple seeds) and report the distribution of $D$ (median and CI) rather than a single value. Consider complementing/replacing 2D-KS with better-behaved two-sample tests in 2D (e.g., energy distance or MMD) and show that qualitative conclusions (which families fit well; whether $D$ increases with age) are robust.
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YORP obliquity evolution is invoked as an explanation for blurred V-shapes and age-dependent discrepancies, but the simulations explicitly keep obliquity fixed (Sec. 2.3.1) and the empirical analysis uses $|\Delta a|$ which removes drift direction—together making obliquity-driven interpretations hard to support with the present framework (Secs. 3.4–3.5, 4.3–4.4).
Recommendation: Align claims with what is modeled. Clearly state in Sec. 2.3.1 and again in Secs. 3.5/4.3 that obliquity is held fixed and therefore YORP-driven obliquity evolution is not simulated. Either (i) implement a simplified obliquity evolution prescription (e.g., drift toward YORP equilibria or a stochastic/random-walk model) for a subset of families and show how it changes $(a,P)$ distributions and $D$; or (ii) substantially temper causal statements, framing obliquity evolution as a plausible hypothesis rather than a conclusion. If feasible, also analyze signed $\Delta a$ to retain the key obliquity-linked signature.
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Family ages are central inputs to the simulations and to the paper’s age–misfit narrative, but age provenance, uncertainty, and propagation into results are not documented (Secs. 2.1.1–2.1.2, 3.5, 4.2–4.3). In addition, Table 1 vs Table 2 show conflicting ages for example families (e.g., Eunomia, Koronis, Flora) beyond stated uncertainties, suggesting either inconsistent sources or a bookkeeping issue.
Recommendation: Document, for each family in Table 2, the age source(s), method class (e.g., V-shape dating vs dynamical spreading), and typical uncertainties (Sec. 2.1). Reconcile Table 1 vs Table 2 age discrepancies explicitly (different sources/definitions vs error). In Sec. 3.5, propagate age uncertainties via sensitivity runs (e.g., age $\pm 1\sigma$ for selected families) and report how much $D$ and inferred slopes/envelopes change. Qualify any claimed correlation between age and $D$ accordingly.
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Sample definition and internal consistency issues (Tables 1–2) reduce clarity and confidence in the dataset being analyzed (Sec. 2.1.2, Sec. 3.1). Table 1 references “$28$ families with $N > 30$,” while the analysis repeatedly refers to $41$ families. Member counts $N$ in Table 1 do not match Table 2 for several named families (e.g., Vesta, Eunomia, Koronis, Eos), indicating either different selection cuts or inconsistent reporting.
Recommendation: Make the sample definition explicit in Sec. 2.1.2: inclusion thresholds, which families are included, and which quantities define $N$ (full family membership vs those with measured $P$ and $D$). Update Table 1 caption to clarify that it is illustrative (if so) and ensure all $N$s/ages are consistently defined across tables, with footnotes explaining any deliberate differences (e.g., “$N$ with measured periods” vs “catalog family size”).
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Positioning relative to prior work is currently too light for readers to assess novelty and appropriateness of methodological choices (Sec. 1, Sec. 4.1–4.4). In particular, the paper should better situate the use of spin-period–based V-shapes (vs classical $a$–$1/D$ V-shapes used for family dating), and justify why the chosen summary metrics and tests are appropriate compared to established envelope-fitting and forward-modeling approaches.
Recommendation: Add a concise related-work subsection in Sec. 1 (or new Sec. 1.1) summarizing: (i) classical family V-shape methods in $a$–$1/D$ (or $a$–$H$) and age-dating approaches; (ii) prior YORP spin-evolution modeling relevant to families; (iii) prior distribution-level comparisons (if any). Explicitly state what is new here (e.g., systematic period-based envelopes across $41$ families; the particular boundary/consistency metrics; family-by-family generative comparisons) and clarify how conclusions complement (not replace) classical V-shape dating.