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The vortex-filament model and numerical implementation are under-specified, limiting reproducibility and making it difficult to interpret heavy tails and scaling (Sec. 2.1). Key missing/ambiguous items include: domain geometry/size and boundary conditions; how “infinitely long” straight filaments are implemented together with periodicity (minimum-image, replicated images, Ewald-like sum, or something else); the explicit Biot–Savart expression used; filament circulation strength(s) $\Gamma$ and whether they vary across filaments; and, critically, the treatment of the Biot–Savart $1/r$ singularity (core radius / regularization / velocity cap). Trajectory integration details are also insufficient (integrator type, adaptive vs fixed step, tolerances, convergence tests). The definition and computation of the reported mean inter-filament spacing $\ell_{\rm inter}$ (Table 1) is not clearly described.
Recommendation: Expand Sec. 2.1 into a fully parameterized, reproducible specification: (i) state domain size/shape and boundary conditions; (ii) write the exact single-filament velocity field used (including $\Gamma$) and how multiple filaments are superposed; (iii) describe the singularity handling (core model, cutoff radius, any maximum velocity), since it controls whether moments (e.g., variance) exist and can strongly affect tail statistics; (iv) explain precisely how periodicity is treated with “infinite” lines; (v) report the ODE integrator and step-size control, and include a simple convergence check showing statistics (e.g., TAMSD slope, high-velocity tail) are stable to $\Delta t$/tolerances; and (vi) define $\ell_{\rm inter}$ explicitly (analytic from $N/V$ or nearest-neighbor statistic) and how Table 1 values are obtained.
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Statistical power is currently too limited for several central claims (Secs. 3.1–3.6): only $\sim 5$ tracer trajectories per configuration and a short total time horizon ($T \approx 25$ s) while reported correlation times are $O(10~{\rm s})$ (Sec. 3.4, Table 1). This makes exponent estimates ($\alpha(N)$), tail claims (velocity, residence-time, displacement PDFs), and statements about weak ergodicity breaking highly sensitive to finite-time and finite-sample effects. Reported errors such as $\alpha = 1.999 \pm 0.000$ (Table 1) are not credible as uncertainties on the underlying process; they likely reflect only regression fit residuals rather than inter-trajectory/inter-realization variability.
Recommendation: If feasible, increase (a) the number of tracers per $N$ and (b) the number of independent quenched filament realizations per $N$ (both matter for quenched disorder), and extend $T$ so that $T \gg \tau_c$ (ideally an order of magnitude). Recompute all reported exponents and tail statistics with uncertainty estimates that reflect variability across trajectories and disorder realizations (bootstrap or hierarchical resampling). If resource-limited, reframe the paper explicitly as a finite-time/finite-ensemble study: add clear error bars/bands, report how results change with $T$, and soften asymptotic/universality/ergodicity-breaking language in Sec. 4 accordingly.
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Holtsmark-related universality claims are mostly qualitative and partly conceptually inconsistent as currently presented (Secs. 3.2–3.3, 3.5–3.6, 4). The manuscript references Holtsmark tails (e.g., $P(v) \sim v^{-5/2}$) and an expected transport exponent near $3/2$, but (i) the highest-density case still yields $\alpha \approx 1.84$ (Table 1), far from $1.5$ without a finite-time scaling argument; (ii) tail “consistency” is asserted without systematic fitting ranges, uncertainties, or goodness-of-fit tests; and (iii) the text at points cites the Holtsmark tail for velocity *components* but compares it to the *speed* PDF, which need not have the same tail form/prefactor and should be compared like-for-like in 3D.
Recommendation: Make the theory-to-measurement comparison precise and quantitative: (i) state clearly whether the theoretical $v^{-5/2}$ prediction applies to a velocity component, the speed $|v|$, or both under your assumptions; then plot/analyze the matching quantity (e.g., component PDFs if that is the theory). (ii) For each purported power law (velocity tails, residence times), perform tail fits with reported fit windows and uncertainty (e.g., MLE-based power-law fitting with goodness-of-fit and comparison to alternatives such as truncated power law/stretched exponential). (iii) For the MSD/TAMSD exponent, show local slopes $d\log({\rm TAMSD})/d\log(\Delta t)$ vs $\Delta t$ (with uncertainty bands) and discuss finite-time drift; if claiming convergence toward $1.5$, provide supporting scaling with $N$ and/or $T$ or clearly label the conclusion as “Holtsmark-like/suggestive” rather than universal.
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The manuscript uses second-moment-based normalizations (e.g., $v_c$ as a speed standard deviation; VACF normalization with $\langle |v|^2 \rangle$; persistence length $L_p = v_c \int C_v$) while simultaneously invoking Holtsmark-like tails that would render second moments divergent in the idealized limit (Secs. 2.2, 3.3–3.4). Even if the simulation has an implicit cutoff (core radius, finite resolution), this must be stated because it controls these normalizations and any “collapse” claims.
Recommendation: Explicitly identify the effective high-velocity regularization/cutoff (core model, maximum speed, grid resolution) and discuss its implications for moment existence. Consider adopting robust velocity scales (median, interquartile range, MAD) for normalization in Sec. 3.3 and for defining $v_c$ in Sec. 2.2, or explicitly state that moments are computed for the *regularized* field and are cutoff-dependent. Ensure VACF normalization and persistence-length definitions are consistent with the intended asymptotic regime (or with the regularized model actually simulated).
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The Lévy-walk “ground truth” comparator is under-specified and appears internally inconsistent with standard theory (Secs. 2.1–2.2, 3.2, 3.4; Table 2). Large discrepancies between $\alpha_{\rm theory}$ and $\alpha_{\rm measured}$ are not explained, and Table 2 contains at least one formula inconsistency ($\beta = 2.5$ row). As written, this weakens the intended contrast between quenched deterministic dynamics and renewal superdiffusion and may confuse readers about numerical correctness.
Recommendation: Provide a complete Lévy-walk model specification (flight-time distribution with lower/upper cutoffs, constant speed value or speed distribution, 3D isotropic direction sampling, number of trajectories, total time, discretization) in Sec. 2.1–2.2. Validate the implementation by demonstrating recovery of known scaling over increasing $T$ and ensemble size, or (if finite-time bias is the point) quantify the bias systematically versus $T$ and cutoffs. Correct Table 2’s theoretical-exponent row(s) and state clearly which theoretical regime/formula applies for each $\beta$.
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The Okubo–Weiss (OW)-like topology analysis in 3D needs clearer definition and justification (Secs. 2.3, 3.5). OW is standard in 2D; in 3D the choice of criterion is not unique (often Q-criterion/invariants of $\nabla v$ are used). The manuscript defines ${\rm OW} = s^2 - \omega^2$ (Eq. (3)) but does not provide explicit definitions of $s^2$ and $\omega^2$ (tensor contractions, prefactors), nor does it explain how $\nabla v$ is computed robustly for a singular/regularized Biot–Savart field. Additionally, the detailed OW/trapping analysis is largely shown for $N = 40$, limiting generality.
Recommendation: In Sec. 2.3, write explicit formulas for $s^2$ and $\omega^2$ in terms of the symmetric/antisymmetric parts of $\nabla v$, including prefactors, so sign conventions are unambiguous. Justify why this OW-like diagnostic is appropriate in your 3D setting or switch to (or cross-check with) a standard 3D diagnostic (e.g., Q-criterion). Describe how $\nabla v$ is computed (analytic differentiation vs finite differences), including grid spacing/smoothing/interpolation along trajectories. In Sec. 3.5, extend at least key OW–speed/trapping correlations to additional $N$ (e.g., $N = 10,~ 20$) or clearly scope the mechanistic claim to the single case analyzed.
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Figure/table reporting is often missing essential metadata (sample sizes, averaging operators, normalization choices, fit ranges) and in places captions/labels appear inconsistent with plotted content (multiple figures noted in the structured report, e.g., Figs. 1–4, 6–7). This prevents readers from verifying claims and reproducing plots.
Recommendation: Audit all figures and captions: (i) ensure numbering matches text references; (ii) label axes with units and define all normalizations (e.g., what exactly is $v_c$); (iii) state $N_{\rm tracers}$, number of filament realizations, trajectory duration $T$, binning/KDE choices, and how averages are performed (time vs ensemble); (iv) overlay and annotate reference slopes/lines used for scaling claims; and (v) add uncertainty visualization where fits are discussed (bootstrap bands/error bars), especially in tail regions.