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The definition of $\dot{a}_{\mathrm{YK,relative}}$ is not mathematically unambiguous and may be physically inconsistent as presented. In Eqs. (1)–(2) (Sec. 2.3), the thermal-function factor is typeset/parsed ambiguously (e.g., “$\Theta$ 2 + 2$\Theta$ + $\Theta^2$” without clear parentheses), preventing verification. More broadly, the quantity is labeled as a drift rate while constants/dependencies are dropped; it is unclear whether it is meant to be a dimensioned drift rate, a proportional surrogate, or a purely ad hoc “drift potential proxy”. This ambiguity propagates directly into the log–log diagram (Sec. 2.4), envelope fits (Sec. 3.3), and any interpretation of family morphology as dynamical rather than definitional.
Recommendation: In Sec. 2.3, rewrite Eqs. (1)–(2) with explicit fraction structure and parentheses (e.g., $\frac{\Theta}{2+2\Theta+\Theta^2}$ if that is intended), correct any typographical corruption, and cite the exact reference formula used (diurnal vs seasonal Yarkovsky; rapid-rotator approximation, etc.). Explicitly state whether $\dot{a}_{\mathrm{YK,relative}}$ is (i) a physically dimensioned estimate of $\dot{a}$ or (ii) a proxy score; use $\equiv$/$\propto$ consistently. If it is a proxy, list exactly which parameters are held fixed/omitted (density, albedo/Bond albedo, thermal inertia variation, roughness/beaming, etc.) and justify why comparing objects/families in this proxy is meaningful.
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The theoretical motivation for expecting informative “envelopes” in the proposed plane $\big(\log_{10}(a), \log_{10}(\dot{a}_{\mathrm{YK,relative}})\big)$ is currently underdeveloped. Traditional family V-shapes arise from integrated drift producing $|a-a_c|$ scaling with $1/D$ (and time), whereas the new diagram plots an (instantaneous/proxy) drift quantity against current $a$. Without a short derivation or conceptual model, it is unclear what the lower envelope represents physically, and thus what a “bucket/U” boundary means under pure Yarkovsky evolution versus resonance truncation (Secs. 1, 2.4, 3.3, 3.5).
Recommendation: Add a concise theoretical subsection (end of Sec. 1 or in Sec. 2) that derives/argues what boundary shape is expected in $(a, \dot{a}_{\mathrm{YK,relative}})$ under: (i) Yarkovsky-only drift without barriers, (ii) drift plus hard truncation at specific $a$ (resonances), and (iii) realistic mixtures of prograde/retrograde and size/spin distributions. Clearly state what the lower envelope is intended to approximate (e.g., a drift-feasibility limit, a selection-induced floor, or a resonance-imposed wall), and how this differs from or complements the traditional $(1/D, a)$ V-shape analysis (Sec. 3.2).
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The envelope-fitting algorithm (Sec. 2.4) is structured to select the steepest slope meeting a one-sided coverage constraint on a bounded slope grid. This design can mechanically drive fits to the grid limits ($\pm50$ in Sec. 3.3/Table 2), especially when the data cloud has any sharp cutoff in $a$, and thus can produce the observed near-vertical “bucket walls” and force YDFI saturation (Secs. 3.3–3.4). As implemented, it is therefore unclear how much of the “universal bucket” morphology is intrinsic vs an optimizer artifact.
Recommendation: Revise Sec. 2.4 and the fitting pipeline to estimate the envelope rather than maximize steepness. For example: (i) fit the desired lower quantile directly via quantile regression (with slope free) instead of selecting maximal $|m|$; (ii) use a hull/alpha-shape envelope extraction and measure local tangents; or (iii) explicitly compare parametric models (V-shape vs bucket-with-walls) using an objective criterion. In Sec. 3.3, add robustness tests varying (a) slope bounds (e.g., $\pm50$, $\pm100$, effectively unbounded), (b) slope step size, and (c) coverage quantile (e.g., 90/95/99%) for several benchmark families, and report whether steep walls persist.
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Core internal inconsistencies in the stated/implemented coverage criterion undermine confidence in the boundary fits. Sec. 2.4 states a 95% coverage target and uses a 5th-percentile intercept rule, but Table 2 reports coverage$_1 =$ coverage$_2 = 0.9$, and Table 1 reports coverages often below 0.95. This mismatch affects fitted lines and any downstream metric based on slope/coverage.
Recommendation: Make the target coverage parameter explicit and consistent throughout: define $q$ (e.g., $q = 0.95$) and set the intercept to the $(1-q)$ quantile (e.g., 5% for 0.95, 10% for 0.90). Regenerate Tables 1–2 under the declared $q$, or revise the text to match the implemented $q$, and add one sentence clarifying how “coverage” is computed in the tables.
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YDFI (Sec. 2.5) is not currently a stable or physically interpretable index: it saturates for most families because it is driven by extreme fitted slopes (Sec. 3.4, Table 3), and its “sharpness” component is inherently dependent on arbitrary choices (log scaling, slope-grid bounds, and units/normalization of the logged quantities). As a result, the paper’s original central hypothesis (age $\rightarrow$ spin evolution $\rightarrow$ degraded fidelity) is not meaningfully testable with the current YDFI design.
Recommendation: Either (a) redesign YDFI to be bounded and less sensitive to arbitrary slope caps (e.g., using curvature, wall verticality measured via derivative distribution, residual dispersion from an envelope model, or a likelihood ratio comparing “Yarkovsky-only” vs “Yarkovsky+barrier” models), and re-run Sec. 3.4; or (b) reframe the paper so YDFI is explicitly presented as an exploratory metric that failed (due to saturation), moving the main contribution to the diagnostic diagram and the boundary morphology. Update the Abstract, Sec. 1, Sec. 2.6, Sec. 3.4, and Sec. 4.1–4.2 accordingly.
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The age–YDFI correlation analysis (Secs. 2.6, 3.4; Fig. 17) is explicitly acknowledged to be invalid due to a severe merge error (duplicated rows; misassigned ages). Reporting a numerical Spearman $\rho$ and p-value in the Results despite invalid data risks confusing readers and undermines statistical credibility.
Recommendation: Fix the merge procedure (document join keys and row counts before/after), rebuild the correct 62-family analysis table, and re-run the correlation (even if null). If a corrected analysis cannot be completed, remove Fig. 17 and the numerical correlation from the main Results, and confine the failed attempt to an Appendix with a clear “invalid” label. Ensure the Abstract/Conclusions do not imply a completed age test.
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The manuscript attributes the steep-walled boundaries to “hard dynamical barriers” such as mean-motion or secular resonances (Secs. 3.5, 4.2–4.3), but this is not quantitatively demonstrated. Additionally, it is unclear whether $a$ is osculating or proper semimajor axis; resonance/family analyses typically require proper elements, and mixing osculating elements can blur resonance alignment. Without systematic resonance mapping, the central dynamical interpretation remains largely qualitative.
Recommendation: Clarify in Sec. 2.1/2.4 whether semimajor axis is osculating or proper, and strongly consider repeating the analysis in proper $a_p$. For representative families (e.g., Vesta, Flora, Eunomia, Themis), overplot the locations of major resonances on the $a$-axis in Figs. 13–16 and/or provide a table listing: (i) inferred wall locations (in $a$), (ii) nearby strong resonances, and (iii) a qualitative match score. Clearly separate “supported by overlays/table” from “hypothesis” in Secs. 3.5 and 4.2–4.3.
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The simplified thermophysical/spin assumptions used to compute $\dot{a}_{\mathrm{YK,relative}}$ (single $\Gamma$, fixed emissivity/albedo handling, rapid-rotator assumption, and a single effective obliquity factor $\cos(30^\circ)$; Sec. 2.3) are strong enough to potentially reshape the distribution in the diagnostic plane. In particular, using a fixed positive $\cos(\epsilon)$ removes sign information and ignores known bimodal obliquity distributions in families, which is central to interpreting drift-driven morphology and asymmetry.
Recommendation: Expand Sec. 2.3 with justification and citations for the chosen parameter values and approximations, and add sensitivity tests (Sec. 3.3 or Appendix) varying $\Gamma$, obliquity distributions (e.g., isotropic, bimodal at $\pm1$), and rotation-regime assumptions for a few benchmark families. Explicitly discuss how losing drift-direction (prograde vs retrograde) affects the meaning of “lower envelope” in the new diagram, and whether separating objects by inferred drift sign is possible or required for interpretation.
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Key validation steps are missing to distinguish physical discovery from pipeline-induced structure. Given the novelty of the diagnostic plane and the envelope-fitting rule, the current analysis would benefit greatly from synthetic tests demonstrating that the pipeline (i) recovers known shapes when they are present and (ii) does not create buckets from smooth V-shaped data clouds.
Recommendation: Add a validation subsection (end of Sec. 2 or in Sec. 3) using synthetic/mocked families: generate ensembles with known Yarkovsky-only evolution (producing traditional V-shapes) and with imposed resonance truncations, then run the full pipeline (drift proxy $\rightarrow$ diagram $\rightarrow$ envelope fit $\rightarrow$ YDFI). Report whether and when the method yields bucket walls and slope saturation. This single test would substantially strengthen the credibility of Sec. 3.3–3.4 outcomes.