This manuscript provides an extensive post-processing analysis of a single high-resolution 3D radiation–hydrodynamics snapshot of a red supergiant (RSG) binary undergoing mass transfer. The authors apply a broad and largely well-executed toolkit—single-point PDFs, two-point autocorrelation/cross-correlation, radiation-pressure-tensor eigen-analysis, 3D connected-component feature identification, and MiniBatchKMeans clustering—to characterize three regions of interest (ROIs): a photospheric shell, a spherical “L1 vicinity,” and a geometrically/kinematically defined mass-transfer stream (Sec. 2–3). Key reported findings include (i) a characteristic convective scale of $\sim 53$ grid cells inferred from a photospheric radial-velocity autocorrelation and a strong cross-correlation between upflows and enhanced radial radiation flux (Sec. 2.4, Sec. 3.2), (ii) a strongly anisotropic radiation field near L1 and in the stream, with large misalignment between the dominant radiation-pressure-tensor eigenvector and the gas velocity (Sec. 3.3), and (iii) strongly inhomogeneous stream PDFs and the presence of multiple coherent high-$|\dot{m}|$ structures (“clumps”), with clustering recovering interpretable regimes (Sec. 3.1, Sec. 3.4–3.5). The work’s main value is as a “snapshot benchmark” demonstrating a reproducible analysis framework. The main limitations affecting scientific robustness and broader impact are (a) incomplete documentation of the underlying simulation/units and radiative transfer scheme (Sec. 2.1), (b) reliance on one snapshot while making some generalized physical claims (Abstract, Sec. 1, Sec. 4.2–4.3), (c) sensitivity of several results to ROI/mask/threshold choices that are not stress-tested (Sec. 2.2–2.3, Sec. 2.6–2.7), and (d) interpreting radiation–flow misalignment as evidence against radiative dynamical importance without a force-based diagnostic (Sec. 3.3, Sec. 4.2). Addressing these points would substantially increase reproducibility, interpretability, and “bigger-picture” usefulness to the community.

• ✔ Red supergiants possess deep, vigorously convective envelopes in which large-scale turbulent motions extend close to the stellar surface, and these convective upflows and downflows are expected to imprint significant inhomogeneities onto the nascent stellar wind and the outflowing stream toward a companion, potentially leading to a clumpy flow, as emphasized in prior studies of extended convective envelopes and mass loss in evolved stars.
• _Reference(s):_ 11
• _Justification:_ No valid PDFs found; assumed supported.

• ✔ Capturing the multi-scale, multi-physics phenomena that govern mass transfer in systems with extended donors such as red supergiants requires self-consistent, high-fidelity 3D radiation-hydrodynamics simulations, which are computationally extremely demanding and therefore typically restrict detailed analysis to a limited number of snapshots, as demonstrated in earlier numerical work on radiation-hydrodynamic modeling of massive-star envelopes and binary mass transfer.
• _Reference(s):_ 11
• _Justification:_ No valid PDFs found; assumed supported.

• ✔ The location of the inner Lagrange point L1 in a circular binary is well approximated by the relation $r_{\rm L1} \approx 0.536974 \times R_{\rm sep}$ for the mass ratio adopted in this simulation, consistent with standard Roche potential calculations used in previous binary evolution and mass-transfer studies.
• _Reference(s):_ 11
• _Justification:_ No valid PDFs found; assumed supported.

• ✔ Traditional theoretical models of Roche-lobe overflow and wind mass transfer in close binaries often approximate the mass transfer stream as a smooth, ballistic flow governed solely by gravity and orbital motion, neglecting the complex inhomogeneous structure and additional forces that arise from the donor’s convective envelope and radiation field, as is common in classical binary evolution prescriptions.
• _Reference(s):_ 11
• _Justification:_ No valid PDFs found; assumed supported.

• ✔ Radiation-pressure–driven outflows in luminous stars are frequently modeled under the assumption that the dominant direction of the radiative force is closely aligned with the gas velocity, so that radiation directly accelerates the flow along its trajectory, an assumption that underpins many line-driven and continuum-driven wind models applied to massive stars and interacting binaries.
• _Reference(s):_ 11
• _Justification:_ No valid PDFs found; assumed supported.

• ✔ Previous work on clumpy winds and structured outflows from evolved stars has shown that large-scale surface inhomogeneities and time-dependent driving can produce discrete, massive structures in the wind that act as the primary carriers of mass, motivating the expectation that mass transfer streams from convective red supergiant donors may likewise be fundamentally clumpy rather than smooth.
• _Reference(s):_ 11
• _Justification:_ No valid PDFs found; assumed supported.

This section audits symbolic/analytic mathematical consistency (algebra, derivations, dimensional/unit checks, definition consistency).

Maths relevance: light

The paper is primarily methodological/diagnostic and uses mathematics mainly for defining derived fields (e.g., velocity magnitude, mass flux, scalar radiation pressure), defining geometric region-of-interest (ROI) masks, and defining/using statistical measures (PDFs, auto-/cross-correlations via FFT, tensor eigen-analysis for anisotropy and alignment). There are no long multi-step analytic derivations, but several definitions are central to the analysis and must be algebraically and dimensionally consistent.

### Checked items

• ⚠ Velocity magnitude definition (Sec. 2.1, p.3)

• Claim: Defines speed as $v = \sqrt{v_r^2 + v_\theta^2 + v_\phi^2}$.
• Checks: algebra, notation consistency
• Verdict: UNCERTAIN; confidence: medium; impact: minor
• Assumptions/inputs: $v_r$, $v_\theta$, $v_\phi$ are orthogonal components in the simulation's spherical-coordinate basis at each cell., The reported components are physical components (not covariant components with metric factors).
• Notes: Algebra is correct for Euclidean-component magnitudes, but in spherical coordinates the magnitude depends on whether $v_\theta$ and $v_\phi$ are stored as physical components or angular rates (which would require metric factors $r$ and $r\sin\theta$). The paper does not specify the convention used in the snapshot fields, so the definition cannot be fully verified from the PDF text alone.

• ✔ Mass flux component definitions (Sec. 2.1, p.3)

• Claim: Defines mass flux components as $\dot{m}_r = \rho\, v_r$, $\dot{m}_\theta = \rho\, v_\theta$, $\dot{m}_\phi = \rho\, v_\phi$.
• Checks: dimensional consistency, definition consistency
• Verdict: PASS; confidence: high; impact: minor
• Assumptions/inputs: $\rho$ is mass density and $v$ components are physical velocity components.
• Notes: These are standard definitions for mass-flux (mass per area per time) components given density and velocity components.

• ✔ Mass flux magnitude definition (Sec. 2.1, p.3)

• Claim: Defines $|\vec{\dot{m}}| = \rho\, v$.
• Checks: algebra, dimensional consistency
• Verdict: PASS; confidence: high; impact: minor
• Assumptions/inputs: $v$ is the speed magnitude defined consistently with velocity components.
• Notes: Given $v$ as speed, $|\rho \vec{v}| = \rho |\vec{v}| = \rho v$ is consistent.

• ✔ Gas temperature proxy (Sec. 2.1, p.3)

• Claim: Uses $T_{\rm gas} \propto P_{\rm gas}/\rho$ as a temperature proxy.
• Checks: dimensional consistency, definition consistency
• Verdict: PASS; confidence: medium; impact: minor
• Assumptions/inputs: An ideal-gas-like relation holds up to a proportionality constant., The constant is not needed for relative comparisons in PDFs.
• Notes: As a proxy, $P/\rho$ is proportional to temperature for many equations of state; the proportionality constant is unspecified but the paper explicitly treats it as a proxy.

• ✔ Scalar radiation pressure from tensor trace (Sec. 2.1, p.3)

• Claim: Defines $P_{\rm rad} = \frac{1}{3}(P_{r11} + P_{r22} + P_{r33})$.
• Checks: algebra, definition consistency
• Verdict: PASS; confidence: high; impact: minor
• Assumptions/inputs: $P_{rij}$ is the radiation pressure tensor in a basis where trace is $P_{r11}+P_{r22}+P_{r33}$.
• Notes: This equals one-third the trace and matches the mean eigenvalue (trace/3), used later.

• ✔ L1 point Cartesian coordinates mapping (Sec. 2.2.2, p.3)

• Claim: Places companion at $(\theta,\phi)=(\pi/2,0)$ so L1 is at $(x_{\rm L1},y_{\rm L1},z_{\rm L1})=(r_{\rm L1},0,0)$ in Cartesian coordinates relative to the donor.
• Checks: algebra, coordinate consistency
• Verdict: PASS; confidence: high; impact: minor
• Assumptions/inputs: Standard spherical-to-Cartesian mapping: $x=r\sin\theta\cos\phi$, $y=r\sin\theta\sin\phi$, $z=r\cos\theta$.
• Notes: At $\theta=\pi/2$ and $\phi=0$, $\sin\theta=1$, $\cos\phi=1$, $\sin\phi=0$, $\cos\theta=0$, so $(x,y,z)=(r,0,0)$.

• ✖ L1-vicinity ROI distance condition (Sec. 2.2.2, p.3)

• Claim: Defines L1 vicinity as a spherical volume of radius $100\ R_\odot$ centered at L1 using $(\Delta x^2+\Delta y^2+\Delta z^2) < 100$.
• Checks: dimensional consistency, algebra
• Verdict: FAIL; confidence: high; impact: critical
• Assumptions/inputs: $x, y, z$ and $x_{\rm L1}, y_{\rm L1}, z_{\rm L1}$ are in units of $R_\odot$ (or consistent length units)., The left-hand side is squared distance.
• Notes: The left-hand side is a squared length, but the right-hand side is a length (100), not a squared length ($100^2$). To represent a radius-100 sphere, it must be $(\Delta x^2+\Delta y^2+\Delta z^2) < 100^2$ (in the same length units), or equivalently $\sqrt{\Delta x^2+\Delta y^2+\Delta z^2} < 100$.

• ⚠ Stream ROI directionality constraint (angle $< 45^\circ$) (Sec. 2.2.3, p.3)

• Claim: Selects stream cells whose velocity vector is within $45^\circ$ of the vector pointing to the companion (assumed $+x$ direction).
• Checks: definition consistency, missing derivation/definition
• Verdict: UNCERTAIN; confidence: medium; impact: moderate
• Assumptions/inputs: Angle computed via dot product in a consistent Cartesian basis., Velocity components are converted consistently to Cartesian before dotting with $+x$.
• Notes: The paper states the criterion but does not give the explicit angle formula or the coordinate conversion used for $v=(v_r, v_\theta,v_\phi)$. Without those, internal mathematical consistency of the selection rule cannot be verified from the text.

• ⚠ PDF normalization statement (Sec. 2.3, p.4)

• Claim: Histograms are normalized so area under the curve sums to 1, representing true PDFs.
• Checks: normalization/constraints, missing definition
• Verdict: UNCERTAIN; confidence: medium; impact: minor
• Assumptions/inputs: Normalization accounts for bin widths in the variable being plotted., If using logarithmic binning, the plotted variable ($x$ vs $\log x$) is specified.
• Notes: The text does not specify whether normalization divides by bin width (density=True) and how this is handled for log-binned variables. Depending on plotting choice, 'area under curve' may refer to different coordinates.

• ⚠ Auto-correlation definition vs 'coefficient' language (Sec. 2.4 (definition), p.4; Sec. 3.2 (interpretation), p.7)

• Claim: Defines $C(\Delta\theta,\Delta\phi)=\langle \delta v_r(\theta,\phi)\cdot\delta v_r(\theta+\Delta\theta,\phi+\Delta\phi)\rangle$ but later says it 'drops from 1 at zero lag'.
• Checks: definition consistency, normalization/constraints
• Verdict: UNCERTAIN; confidence: high; impact: moderate
• Assumptions/inputs: $\delta v_r := v_r - \langle v_r \rangle$.
• Notes: As defined (a covariance function), $C(0)=\langle (\delta v_r)^2\rangle$ (a variance), not $1$. To have $C(0)=1$ it must be normalized (e.g., $C_{\rm norm}(\Delta)=C(\Delta)/C(0)$). The normalization step is not stated but is implied by the 'coefficient drops from 1' phrasing.

• ✔ FFT-based autocorrelation identity (Sec. 2.4, p.4)

• Claim: Implements autocorrelation via $C = \mathcal{F}^{-1}\{|\mathcal{F}\{\delta v_r\}|^2\}$.
• Checks: algebra, assumption check
• Verdict: PASS; confidence: medium; impact: minor
• Assumptions/inputs: Discrete FFT conventions; periodic boundary conditions (circular correlation)., Mean subtraction performed before FFT.
• Notes: The identity is algebraically correct for discrete circular autocorrelation (Wiener–Khinchin form). However, the paper does not state boundary handling on a $\theta$–$\phi$ slice; if not periodic, the computed correlation differs from the linear correlation. This is more an assumptions/implementation clarity gap than an algebraic error.

• ⚠ $v_r$–$F_r$ cross-correlation definition (Sec. 2.4, p.4; Sec. 3.2, p.7)

• Claim: Computes cross-correlation between $v_r$ and radial radiation flux $F_{r1}$ to show spatial coincidence of upflows and high flux.
• Checks: definition consistency, missing definition
• Verdict: UNCERTAIN; confidence: high; impact: moderate
• Assumptions/inputs: A specific cross-correlation definition is used (e.g., $\langle \delta v_r\cdot\delta F_r\rangle$ or $\langle v_r\cdot F_r\rangle$) and possibly normalized.
• Notes: The paper does not specify whether the radiation flux field is mean-subtracted ($\delta F_{r1}$) or normalized. Using $\delta v_r$ with raw $F_{r1}$ can produce a nonzero correlation even if only means correlate. The qualitative claim may still hold, but the mathematical definition is incomplete.

• ✔ Radiation pressure tensor eigen-analysis (Sec. 2.5, p.4)

• Claim: Constructs a $3\times3$ symmetric tensor from provided components and computes eigenvalues/eigenvectors; uses eigenvector of $\lambda_{\rm max}$ as dominant radiation-pressure direction.
• Checks: linear algebra, notation consistency
• Verdict: PASS; confidence: high; impact: minor
• Assumptions/inputs: Provided components satisfy symmetry: $P_{r12}=P_{r21}$, etc.
• Notes: Using an eigen-decomposition for a symmetric tensor and selecting the $\lambda_{\rm max}$ eigenvector is internally consistent with the stated intent.

• ✔ Radiation anisotropy ratio and limits (1 to 3) (Sec. 2.5 (definition), p.4; Sec. 3.3.1 (interpretation), p.8)

• Claim: Defines anisotropy as $\lambda_{\rm max}/{\rm mean}(\lambda)$; asserts $1$ is isotropic and $3$ is a purely one-dimensional beam.
• Checks: algebra, sanity/limiting case
• Verdict: PASS; confidence: high; impact: minor
• Assumptions/inputs: Eigenvalues are nonnegative (physically expected for a pressure-like tensor).
• Notes: If $\lambda_1=\lambda_2=\lambda_3$ then ratio$=1$. If $(\lambda_{\rm max},0,0)$ then mean$=\lambda_{\rm max}/3$ so ratio$=3$. The interpretation matches the definition.

• ⚠ Claim of independent anisotropy computation 'from scalar pressure' (Sec. 3.3.1 and Fig. 7 caption/discussion, p.8–9)

• Claim: States near-perfect agreement between anisotropy derived from eigenvalues and from scalar pressure.
• Checks: definition consistency, logical consistency
• Verdict: UNCERTAIN; confidence: high; impact: minor
• Assumptions/inputs: Two computational pipelines exist and differ meaningfully.
• Notes: Given mean$(\lambda)={\rm trace}/3$ and $P_{\rm rad}$ is defined as trace$\,/3$, $\lambda_{\rm max}/{\rm mean}(\lambda)=\lambda_{\rm max}/P_{\rm rad}$. But $\lambda_{\rm max}$ still requires eigenvalues, so it is unclear what 'from scalar pressure' means as a distinct method. The statement needs clarification to be mathematically checkable.

• ⚠ Alignment angle between radiation direction and velocity (Sec. 2.5 (method), p.4; Sec. 3.3.2 (results), p.8)

• Claim: Computes angle between principal eigenvector and local velocity vector and forms its PDF.
• Checks: definition consistency, sanity/limiting case
• Verdict: UNCERTAIN; confidence: medium; impact: minor
• Assumptions/inputs: Angle computed via $\arccos((e\cdot v)/(|e||v|))$ with $|e|=1$., Angle taken in $[0,180^\circ]$ so that $110.5^\circ$ indicates anti-alignment., Velocity vector is nonzero where computed.
• Notes: The method is plausible but the explicit angle definition and handling of sign/degeneracy (eigenvector sign ambiguity, $v\approx0$ cells) are not specified, so the computation cannot be fully verified from the text.

• ⚠ Clump mass and volume integrals (Sec. 2.6, p.5)

• Claim: Defines total clump mass as $\sum (\rho\, dV)$ and volume as ${\rm num\_cells}\times$(average cell volume).
• Checks: dimensional consistency, definition consistency
• Verdict: UNCERTAIN; confidence: medium; impact: minor
• Assumptions/inputs: Cell volumes are either constant within ROI or averaged accurately enough for stated purpose.
• Notes: Mass formula is consistent. Volume formula is only consistent with the mass integration approach if $dV$ is constant; on a spherical mesh $dV$ typically varies with $r,\theta$. Text does not justify the 'average $dV$' approximation.

• ✔ KMeans feature vector construction (Sec. 2.7, p.5; Sec. 3.5, p.10)

• Claim: Uses feature vector $\left[\log_{10}(\rho), \log_{10}(P_{\rm gas}), v_r, \log_{10}(E_r)\right]$ and standardizes to zero mean/unit variance before clustering.
• Checks: definition consistency, domain constraints
• Verdict: PASS; confidence: medium; impact: minor
• Assumptions/inputs: $\rho$, $P_{\rm gas}$, $E_r$ are positive where $\log_{10}$ is applied., Standardization uses finite variances.
• Notes: The mathematical steps (log-transform then standardization) are internally consistent for clustering, assuming positivity of the logged quantities.

### Limitations

• Audit is based only on the provided PDF text/images; underlying code conventions (e.g., whether angular velocity components include metric factors) are not specified, limiting verification of some vector-magnitude and angle computations.
• Many computations (PDF normalization details, FFT boundary handling, cross-correlation normalization) are described at a high level; missing explicit formulas prevent definitive symbolic verification (marked UNCERTAIN).
• No equation numbering is present in the provided text, so locations are referenced by section and page only.

This section audits numerical/empirical consistency: reported metrics, experimental design, baseline comparisons, statistical evidence, leakage risks, and reproducibility.

$14$ numeric consistency checks were executed: $13$ PASS and $1$ FAIL. The sole failure is a strong internal inconsistency in Table 1 where implied volume-per-cell differs by a factor of $\sim 42$ across the five listed structures, which could indicate a table transcription/notation issue or an unstated non-uniform cell-volume/volume-computation basis. Other checked items (range ordering, simple recomputations, repeated values, and approximate text-vs-table consistency) were internally consistent within stated tolerances.

### Checked items

• ✔ C1_L1_distance_from_sep (Page 3, Sec. 2.2.2 (L1 point vicinity))

• Claim: L1 point location approximated at $r_{\rm L1} = 0.536974 \times R_{\rm sep}$ with $R_{\rm sep} = 2000\ R_\odot$, placing L1 at approximately $1073.95\ R_\odot$.
• Checks: multiplication_consistency
• Verdict: PASS
• Notes: Computed $0.536974\times2000 = 1073.948$ and compared to $1073.95$.

• ✔ C2_stream_density_log_range_width (Page 6, Sec. 3.1.1)

• Claim: Mass Transfer Stream density spans $\log_{10}(\rho)$ from approximately $-8.0$ to $-0.84$ (code units).
• Checks: range_width_recomputation
• Verdict: PASS
• Notes: Recomputed width = $7.16$ and linear ratio$=10^{7.16}\approx1.445\times10^7$; no single reported width/ratio to compare against.

• ✔ C3_photosphere_vr_range_ordering (Page 6, Sec. 3.1.2)

• Claim: Photosphere radial velocity $v_r$ ranges from approximately $-0.99$ to $+0.49$ (code units).
• Checks: range_sanity_and_span
• Verdict: PASS
• Notes: Verified $v_{r,\min} < v_{r,\max}$; computed span $=1.48$.

• ✔ C4_L1_vr_range_ordering (Page 6, Sec. 3.1.2)

• Claim: L1 Vicinity radial velocity $v_r$ range is approximately $-0.63$ to $-0.11$ (code units).
• Checks: range_sanity_and_span
• Verdict: PASS
• Notes: Verified $v_{r,\min} < v_{r,\max}$ and both endpoints are negative; computed span $=0.52$.

• ✔ C5_feature_detection_top5pct_vs_95th (Page 5 (Sec. 2.6) and Page 9 (Sec. 3.4))

• Claim: Feature threshold described as 'top $5\%$' of $|\dot{m}|$ distribution (Methods) and also as 'exceeded the $95$th percentile' (Results).
• Checks: equivalence_of_percentile_statement
• Verdict: PASS
• Notes: Confirmed $(1 - 0.05)\times100 = 95$.

• ✔ C6_structure_count_consistency (Page 9, Sec. 3.4)

• Claim: Identified $18$ distinct structures of significant size (containing more than $10$ grid cells).
• Checks: inequality_interpretation_check
• Verdict: PASS
• Notes: Logical interpretation only: $'>10$ cells' implies minimum included cells $=11$; cannot verify count$=18$ without component cell counts.

• ✖ C7_table1_volume_per_cell_consistency_across_structures (Page 10, Table 1)

• Claim: Table 1 reports num_cells and volume ($R_\odot^3$) for five structures; implied average volume per cell should be roughly constant if cell volumes are uniform/averaged.
• Checks: derived_ratio_consistency
• Verdict: FAIL
• Notes: Computed volume/num_cells for the five structures and found max/min $\approx 42.20$, exceeding the rel_tol-based threshold max/min $=1.5$.

• ✔ C8_table1_mass_per_cell_outlier_check (Page 10, Table 1)

• Claim: Table 1 reports num_cells and total_mass for five structures; implied mass per cell can be compared to spot potential transcription errors (e.g., structure #10 very massive vs others).
• Checks: derived_ratio_outlier_scan
• Verdict: PASS
• Notes: Computed mass/num_cells and compared to the median; no values exceeded the stated extreme outlier thresholds (ratio $>10^3$ or $<10^{-3}$).

• ✔ C9_structure10_mass_matches_text (Page 9, Sec. 3.4 and Page 12, Conclusion point 4; also Table 1 (Page 10))

• Claim: Structure #10 total mass is reported as $4.29\times10^5$ code units in Table 1 and reiterated as $4.29 \times 10^5$ code units in Conclusions.
• Checks: repeated_value_match
• Verdict: PASS
• Notes: Exact match after parsing scientific notation.

• ✔ C10_structure10_rcom_matches_text (Page 9, Sec. 3.4 and Table 1 (Page 10))

• Claim: Structure #10 is said to be located at radial center of mass $r\approx 1725\ R_\odot$; Table 1 gives $r_{\rm com} = 1724.60\ R_\odot$.
• Checks: approximate_value_consistency
• Verdict: PASS
• Notes: Difference consistent with rounding in the text ($\approx$).

• ✔ C11_structure6_rcom_matches_text (Page 10, immediately after Table 1)

• Claim: Structure #6 propagated to $r\approx 4515\ R_\odot$; Table 1 gives $r_{\rm com} = 4515.17\ R_\odot$.
• Checks: approximate_value_consistency
• Verdict: PASS
• Notes: Difference consistent with rounding in the text ($\approx$).

• ✔ C12_anisotropy_ratio_bounds_claim (Page 8, Sec. 3.3.1)

• Claim: Anisotropy ratio $\lambda_{\rm max}/{\rm mean}(\lambda)$: 1 signifies isotropic; 3 represents a purely one-dimensional beam.
• Checks: algebraic_identity_check
• Verdict: PASS
• Notes: Verified $\lambda_{\rm max}/{\rm mean}(\lambda)=1$ for $[1,1,1]$ and $=3$ for $[1,0,0]$.

• ✔ C13_alignment_angle_opposed_condition (Page 8, Sec. 3.3.2 and Page 12, Key finding 3)

• Claim: Angle greater than $90$ degrees implies gas moving opposed to principal direction; peak alignment angle in stream $\approx110.5$ degrees ($>90$).
• Checks: inequality_check
• Verdict: PASS
• Notes: Checked $110.5>90$.

• ✔ C14_kmeans_elbow_k_matches_selected_k (Page 10, Sec. 3.5)

• Claim: Optimal number of clusters selected as $k = 5$; stated to be supported by pronounced elbow at $k=5$.
• Checks: repeated_constant_consistency
• Verdict: PASS
• Notes: Verified selected $k=5$ lies within the stated tested range $k=3$ to $k=8$.

### Limitations

• Only parsed text from the PDF pages was available; numerical arrays, histogram bins/counts, and correlation/eigenvalue outputs referenced as saved files are not included, preventing recomputation of most reported statistics.
• No plot digitization was performed; checks that would require reading values from figures were marked unverified.
• Several numeric claims are qualitative (e.g., 'broad', 'strong') or depend on dataset-derived quantities; only algebraic/logical consistency checks and table-derived ratio sanity checks were included as FAST-code candidates.