Pith. sign in

REVIEW 3 major objections 5 minor 35 references

Molecular Machine Learning Using Euler Characteristic Transforms

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Computing the Euler Characteristic Transform on molecular graphs and appending it to AVALON fingerprints improves prediction of the inhibition constant Ki on most of nine binding-affinity benchmarks.

desk verdict Solid, reproducible application of ECT to Ki prediction, but the abstract's headline claim overstates what the table shows. read the letter →

arxiv 2507.03474 v1 pith:SQ27ZPRL submitted 2025-07-04 cs.LG math.ATq-bio.BM

Victor Toscano-Duran , Florian Rottach , Bastian Rieck This is my paper · ORCID
classification cs.LGmath.ATq-bio.BM
keywords EulerCharacteristicTransformTopologicalDataAnalysisMolecularMachineLearningRepresentationBindingAffinityPredictionInhibitionConstantKiFingerprintsGraphNeuralNetworks
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper proposes the Euler Characteristic Transform (ECT) as a molecular descriptor that captures multiscale shape information, which standard fingerprints and graph neural networks often miss. It evaluates the ECT on nine regression datasets for the inhibition constant Ki and finds the ECT alone is competitive, ranking among the best methods on several datasets. The central claim is that combining ECT features with the AVALON fingerprint enhances predictive performance, improving results on five of the nine datasets and on the combined dataset. A sympathetic reader would care because this suggests explicit shape information can complement established molecular representations in drug-discovery prediction tasks.

What carries the argument

The load-bearing object is the Euler Characteristic Transform (ECT), a topological summary of a filtered molecular graph. For each sampled direction, the graph's atoms are ordered by their projection onto that direction; as the filtration threshold rises, atoms and bonds enter, and the Euler characteristic, χ = |V| − |E|, tracks the changing topology. Stacking the per-direction curves into a matrix and flattening it yields a fixed-length feature vector recording multiscale, direction-dependent shape information. Concatenating this vector with AVALON fingerprints gives the hybrid representation, which is then fed to a gradient-boosted tree regressor.

What would settle it

Run a fully nested cross-validation in which the 158-direction, 16-threshold choice is made only on training folds, then compare RMSE of ECT+AVALON against AVALON alone; if the improvement disappears or is inconsistent across the nine datasets, the claimed enhancement is a tuning artifact rather than a property of ECT features.

Watch

Extended reading notes

Core claim

The paper claims that the Euler Characteristic Transform, computed directly on a molecular graph whose atoms carry a 9-dimensional handcrafted feature vector, yields a useful topological descriptor for molecular property prediction. Sampling 158 random directions in feature space and recording the Euler characteristic at 16 thresholds produces a 2528-dimensional vector; concatenating this with the 1024-bit AVALON fingerprint gives a 3552-dimensional hybrid representation. Across nine protein-ligand binding datasets focused on Ki, the authors report that the ECT alone achieves competitive performance, including the best result on the ADRA1A dataset, and that ECT+AVALON improves baseline predictive performance on five of nine datasets and on the combined dataset, with lower RMSE and higher R² than the graph neural network baselines. The paper interprets these results as evidence that multiscale topological shape information is complementary to traditional substructure fingerprints.

Load-bearing premise

The ECT hyperparameters, 158 directions and 16 thresholds, were fixed using a prior sensitivity analysis whose protocol is not detailed; if that analysis saw the test folds, the reported gains could come from tuning rather than from the representation itself.

Editorial extensions

If this is right

  • Adding ECT features to AVALON fingerprints should improve Ki prediction accuracy on new protein-ligand datasets of similar size, relative to using either representation alone.
  • The result suggests that expensive graph neural networks are not necessary for these benchmarks: gradient-boosted trees on ECT/fingerprint vectors matched or beat the GNN baselines at lower computational cost.
  • Because the ECT is computed from SMILES-derived graphs and generic atomic features, the same hybrid descriptor can be applied to any molecular property prediction task without requiring 3D conformer generation.
  • The ECT encodes shape information across scales and directions that substructure fingerprints do not capture, making hybrid topological-plus-traditional representations a generally promising design.
  • The observed robustness of the ECT+AVALON results across cross-validation folds indicates the improvement is stable rather than driven by a single favorable split.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Because the ECT implementation used here is differentiable, the 158 directions and 16 thresholds could be learned or adapted per dataset instead of fixed globally, a direction the paper leaves to future work.
  • The paper's own tables show the gain is not uniform: on ATR and JAK2, standard fingerprints remain at least as accurate as ECT+AVALON, so the complementarity is dataset-dependent rather than universal.
  • Extending the ECT to 3D atomic coordinates, rather than handcrafted feature vectors, might capture true conformational shape and could matter for targets where binding depends on 3D geometry.
  • The same pipeline could be tested on activity-cliff datasets, where small structural changes cause large Ki changes and multiscale shape information should be most informative.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper proposes the Euler Characteristic Transform (ECT) as a multiscale topological descriptor for molecular machine learning. The ECT is computed on molecular graphs with handcrafted atomic features, evaluated alone and concatenated with the AVALON fingerprint, across nine protein-ligand binding datasets for Ki regression, and compared against traditional fingerprints/descriptors and graph neural networks. The central claim is that ECT+AVALON significantly enhances predictive performance and outperforms other methods on most datasets. The authors provide code and data for reproducibility.

Significance. If the central claim were fully supported, the paper would provide a useful new representation that captures complementary multiscale shape information and could be combined with existing fingerprints. The ECT is a principled and relatively underused descriptor in molecular ML, and the experiments cover a reasonable set of benchmarks with a clear comparison to strong baselines. The paper also ships public code and data, which is a strength. However, the statistical evidence for the headline claim is currently weak, and the sensitivity-analysis protocol for choosing ECT hyperparameters is under-specified, so the significance of the contribution is not yet established beyond a promising empirical demonstration.

major comments (3)
  1. [Abstract; Section 4, Table 2] The abstract's claim that ECT+AVALON "significantly enhances predictive performance, outperforming other methods on most datasets" is not supported by Table 2. Counting strict best RMSE per dataset, ECT+FP is best on 4/9 datasets (ADRA1A, ALOX5P, MUSC1, MUSC2), tied best on DPP4, and is not best on ATR, JAK1, JAK2, or KOR. Moreover, every reported improvement over the best baseline is within one cross-validation standard deviation (e.g., ALOX5P: 1.52±0.17 vs 1.58±0.18; DPP4: 0.78±0.04 vs 0.78±0.05), and no paired significance tests are provided. Please add statistical tests across folds (e.g., paired t-test or Wilcoxon signed-rank test), or revise the abstract and Section 4 to describe the results as competitive or as improvements on several datasets.
  2. [Section 3.3] The "prior sensitivity analysis" that fixed 158 directions and 16 filtration thresholds is described only in broad qualitative terms. It is not stated which datasets were used, which metric was optimized, how directions and thresholds were varied, or whether the evaluation datasets were seen during this selection. If the same benchmark datasets were used to choose the ECT hyperparameters and then reported without nested validation, the gains of ECT+AVALON over AVALON may partly reflect selection on the test folds. Please provide the full protocol or, if the analysis was done on a separate dataset, state this explicitly.
  3. [Section 4, Figure 2] Section 3.3 states that both RMSE and R2 are used for evaluation, but Table 2 reports only RMSE while Figure 2 shows boxplots for both metrics. To substantiate the claim that the method "consistently achieves better values for RMSE and R2," the per-dataset R2 values should be reported in the table or in an appendix, and the variance/confidence intervals should be interpreted in relation to the overlapping standard deviations in Table 2.
minor comments (5)
  1. [Section 2] There are typos such as "acetid acid" and "information about the the number" in the paragraph introducing molecular graphs; these should be corrected.
  2. [Figure 1 caption] The caption says "rows to thresholds (set to 20)" while Section 3.3 fixes the number of filtration thresholds to 16. If the figure is an illustrative example with arbitrary values, clarify that the 20 thresholds are for illustration only and do not correspond to the experimental setup.
  3. [Abstract; Section 4] The paper says "improved baseline predictive performance in 5/9 datasets" in Section 4, while the abstract claims outperforming other methods on "most datasets." Please align these statements and define the comparison baseline explicitly (e.g., AVALON alone vs all other methods).
  4. [Section 2; References] Reference [27] appears closely related to the present work; the authors should clarify in the text how the ECT-based approach differs from or extends that prior study on topological molecular representations.
  5. [Throughout] The rendering "A V ALON" appears to be a spacing artifact of small caps; it should be consistently typeset as AVALON.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the ECT features are computed directly from molecular graphs and handcrafted atomic features without using the target values, and the reported performance comparisons are empirical rather than definitional.

full rationale

The paper's derivation chain is self-contained and target-independent. The ECT is constructed from molecular graphs using a fixed 9-dimensional handcrafted atomic feature vector and random filtration directions; neither the feature computation nor the concatenation with the AVALON fingerprint incorporates the Ki values being predicted. The abstract's claim that ECT+AVALON 'significantly enhances predictive performance' is an empirical statement supported by cross-validated RMSE values in Table 2, and whether those results are statistically significant or constitute 'most datasets' is a correctness/overclaiming issue, not a circularity issue. The only hand-chosen quantities are the 158 directions and 16 thresholds, selected by a 'prior sensitivity analysis' described in Section 3.3; even if that analysis used the same benchmark datasets, this would be a hyperparameter-selection or leakage concern, not a case where a prediction reduces by construction to a fitted input, and the paper's own Future work section concedes that optimal parameter selection remains open. The citation of the DECT package [26], whose author overlaps with the present paper, is an implementation credit rather than a load-bearing theoretical premise: the ECT definition is standard mathematics and is stated directly in Section 2. No equation equates the reported predictive gains with the feature construction, no parameter is fitted to the target and then renamed as a prediction, and no uniqueness theorem is invoked to force the representation choice. Therefore the appropriate finding is no significant circularity, score 0.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central claim is empirical, so the ledger mainly contains the ECT hyperparameters (n_directions, n_thresholds) and the experimental assumptions about data and evaluation. There are no invented physical or mathematical entities.

free parameters (2)
  • n_directions = 158
    Number of random directions used to compute the ECT, fixed in Section 3.3 based on a sensitivity analysis whose protocol is not described.
  • n_thresholds = 16
    Number of filtration thresholds in each ECC, fixed in Section 3.3; the paper says this value has minimal effect on performance.
assumptions (5)
  • standard math ECT is a valid topological summary statistic for weighted graphs
    The paper uses the Euler characteristic and its transform as background theory in Section 2; this is established mathematics.
  • domain assumption Nine-dimensional atomic feature vectors from PyTorch Geometric adequately represent the chemistry relevant to Ki
    The ECT is computed over these features in Section 3.3; if they are uninformative, the representation is weak.
  • domain assumption The sensitivity analysis used to set ECT hyperparameters did not use the evaluation folds
    Section 3.3 states the directions and thresholds were fixed based on a prior sensitivity analysis but does not describe the validation protocol, leaving open the possibility of test leakage.
  • domain assumption 10-fold cross-validation with a fixed seed gives unbiased and comparable performance estimates
    The evaluation protocol in Section 3.3 assumes that a single random split with fixed seed is sufficient for fair comparison.
  • domain assumption The combined dataset, mixing molecules from different protein targets, is a meaningful regression benchmark
    Random splitting of the combined dataset can place molecules from the same target in both train and test, which may inflate performance; the paper does not address this.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Molecular Machine Learning Using Euler Characteristic Transforms." pith.science (2026). https://pith.science/paper/SQ27ZPRL

@misc{pith2026250703474,
  author       = {Pith},
  title        = {Pith review of: Molecular Machine Learning Using Euler Characteristic Transforms},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SQ27ZPRL}},
  note         = {Machine review of arXiv:2507.03474}
}
abstract

The shape of a molecule determines its physicochemical and biological properties. However, it is often underrepresented in standard molecular representation learning approaches. Here, we propose using the Euler Characteristic Transform (ECT) as a geometrical-topological descriptor. Computed directly on a molecular graph derived from handcrafted atomic features, the ECT enables the extraction of multiscale structural features, offering a novel way to represent and encode molecular shape in the feature space. We assess the predictive performance of this representation across nine benchmark regression datasets, all centered around predicting the inhibition constant $K_i$. In addition, we compare our proposed ECT-based representation against traditional molecular representations and methods, such as molecular fingerprints/descriptors and graph neural networks (GNNs). Our results show that our ECT-based representation achieves competitive performance, ranking among the best-performing methods on several datasets. More importantly, its combination with traditional representations, particularly with the AVALON fingerprint, significantly \emph{enhances predictive performance}, outperforming other methods on most datasets. These findings highlight the complementary value of multiscale topological information and its potential for being combined with established techniques. Our study suggests that hybrid approaches incorporating explicit shape information can lead to more informative and robust molecular representations, enhancing and opening new avenues in molecular machine learning tasks. To support reproducibility and foster open biomedical research, we provide open access to all experiments and code used in this work.

Figures

Figures reproduced from arXiv: 2507.03474 by the authors.

Figure 1
Figure 1. Extracting topological shape information from molecular graphs. (a): Exemplary 2D graph representation of the acetic acid molecule, derived from its SMILES string CC(O)=O. The graph contains 8 vertices (2 carbon, 2 oxygen, and 4 hydrogen atoms) and 7 edges, resulting in an Euler characteristic of 1 (χ = 1). (b): Filtration values of the nodes along the x-axis direction. (c) Filtration sequence along the x-axis direc… view at source ↗
Figure 2
Figure 2. Boxplots showing the distribution of test errors for each representation method across all datasets. From left [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

35 extracted references · 33 canonical work pages

  1. [1]

    Measuring hidden phenotype: quantifying the shape of barley seeds using the euler characteristic transform

    Erik J Amézquita, Michelle Y Quigley, Tim Ophelders, Jacob B Landis, Daniel Koenig, Elizabeth Munch, and Daniel H Chitwood. Measuring hidden phenotype: quantifying the shape of barley seeds using the euler characteristic transform. in silico Plants, 4(1):diab033, 12 2021

    work page 2021

  2. [2]

    Geometric deep learning on molecular representations

    Kenneth Atz, Francesca Grisoni, and Gisbert Schneider. Geometric deep learning on molecular representations. Nature Machine Intelligence, 3(12):1023–1032, 2021

    work page 2021

  3. [3]

    Evaluating molecular representations in machine learning models for drug response prediction and interpretability

    Delora Baptista, João Correia, Bruno Pereira, and Miguel Rocha. Evaluating molecular representations in machine learning models for drug response prediction and interpretability. Journal of Integrative Bioinformatics, 19(3):20220006, 2022

    work page 2022

  4. [4]

    A review on machine learning approaches and trends in drug discovery

    Paula Carracedo-Reboredo, Jose Liñares-Blanco, Nereida Rodríguez-Fernández, Francisco Cedrón, Francisco J Novoa, Adrian Carballal, Victor Maojo, Alejandro Pazos, and Carlos Fernandez-Lozano. A review on machine learning approaches and trends in drug discovery. Computational and structural biotechnology journal, 19:4538– 4558, 2021

    work page 2021

  5. [5]

    XGBoost: A scalable tree boosting system

    Tianqi Chen and Carlos Guestrin. XGBoost: A scalable tree boosting system. In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, page 785–794, New York, NY , USA, 2016. Association for Computing Machinery

    work page 2016

  6. [6]

    Molecules and medicine

    Elias James Corey, Barbara Czakó, and László Kürti. Molecules and medicine. John Wiley & Sons, 2007. 9 V . Toscano et al

    work page 2007

  7. [7]

    Predicting Clinical Outcomes in Glioblastoma: An Application of Topological and Functional Data Analysis

    Lorin Crawford, Anthea Monod, Andrew X Chen, Sayan Mukherjee, and Raúl Rabadán. Functional data analysis using a topological summary statistic: the smooth Euler characteristic transform. arXiv preprint arXiv:1611.06818, 2016

    work page Pith review arXiv 2016

  8. [8]

    Molecular representations in AI-driven drug discovery: a review and practical guide

    Laurianne David, Amol Thakkar, Rocío Mercado, and Ola Engkvist. Molecular representations in AI-driven drug discovery: a review and practical guide. Journal of Cheminformatics, 12(1):56, 2020

    work page 2020

Show all 35 references
  1. [9]

    Artificial intelligence in drug discovery: applications and techniques

    Jianyuan Deng, Zhibo Yang, Iwao Ojima, Dimitris Samaras, and Fusheng Wang. Artificial intelligence in drug discovery: applications and techniques. Briefings in Bioinformatics, 23(1):bbab430, 2022

    2022

  2. [10]

    A systematic study of key elements underlying molecular property prediction

    Jianyuan Deng, Zhibo Yang, Hehe Wang, Iwao Ojima, Dimitris Samaras, and Fusheng Wang. A systematic study of key elements underlying molecular property prediction. Nature Communications, 14(1):6395, 2023

    2023

  3. [11]

    Drug discovery: A historical perspective

    Jurgen Drews. Drug discovery: A historical perspective. Science, 287(5460):1960–1964, 2000

    1960

  4. [12]

    Computational topology: an introduction

    Herbert Edelsbrunner and John L Harer. Computational topology: an introduction . American Mathematical Society, 2022

    2022

  5. [13]

    Hamilton

    William L. Hamilton. Graph representation learning. Synthesis Lectures on Artificial Intelligence and Machine Learning, 14(3):1–159, 2020

    2020

  6. [14]

    Algebraic topology

    Allen Hatcher. Algebraic topology. Cambridge University Press, 2005

    2005

  7. [15]

    Could graph neural networks learn better molecular representation for drug discovery? A comparison study of descriptor-based and graph-based models

    Dejun Jiang, Zhenxing Wu, Chang-Yu Hsieh, Guangyong Chen, Ben Liao, Zhe Wang, Chao Shen, Dongsheng Cao, Jian Wu, and Tingjun Hou. Could graph neural networks learn better molecular representation for drug discovery? A comparison study of descriptor-based and graph-based models...

    2021

  8. [16]

    The weighted Euler curve transform for shape and image analysis

    Qitong Jiang, Sebastian Kurtek, and Tom Needham. The weighted Euler curve transform for shape and image analysis. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, pages 844–845, 2020

    2020

  9. [17]

    Bronstein, and Daniel Cremers

    Christian Koke, Yuesong Shen, Abhishek Saroha, Marvin Eisenberger, Bastian Rieck, Michael M. Bronstein, and Daniel Cremers. Graph networks struggle with variable scale. In ICLR Workshop ‘I Can’t Believe It’s Not Better: Challenges in Applied Deep Learning’, 2025

    2025

  10. [18]

    A fast and scalable computational topology framework for the Euler characteristic

    Daniel J Laky and Victor M Zavala. A fast and scalable computational topology framework for the Euler characteristic. Digital Discovery, 3(2):392–409, 2024

    2024

  11. [19]

    The Euler characteristic of a category

    Tom Leinster. The Euler characteristic of a category. Documenta Mathematica, 13:21–49, 2008

    2008

  12. [20]

    Extracting insights from the shape of complex data using topology

    Pek Y Lum, Gurjeet Singh, Alan Lehman, Tigran Ishkanov, Mikael Vejdemo-Johansson, Muthu Alagappan, John Carlsson, and Gunnar Carlsson. Extracting insights from the shape of complex data using topology. Scientific reports, 3(1):1236, 2013

    2013

  13. [21]

    alvaDesc: A tool to calculate and analyze molecular descriptors and fingerprints

    Andrea Mauri. alvaDesc: A tool to calculate and analyze molecular descriptors and fingerprints. In Ecotoxicologi- cal QSARs, pages 801–820. Springer, 2020

    2020

  14. [22]

    An invitation to the Euler characteristic transform

    Elizabeth Munch. An invitation to the Euler characteristic transform. The American Mathematical Monthly , 132(1):15–25, 2025

    2025

  15. [23]

    Elements of algebraic topology

    James R Munkres. Elements of algebraic topology. CRC press, 2018

    2018

  16. [24]

    A critical look at the evaluation of GNNs under heterophily: Are we really making progress? arXiv preprint arXiv:2302.11640, 2023

    Oleg Platonov, Denis Kuznedelev, Michael Diskin, Artem Babenko, and Liudmila Prokhorenkova. A critical look at the evaluation of GNNs under heterophily: Are we really making progress? arXiv preprint arXiv:2302.11640, 2023

    2023 arXiv

  17. [25]

    Topology meets machine learning: An introduction using the Euler characteristic transform

    Bastian Rieck. Topology meets machine learning: An introduction using the Euler characteristic transform. 2024

    2024

  18. [26]

    Differentiable Euler characteristic transforms for shape classification

    Ernst Röell and Bastian Rieck. Differentiable Euler characteristic transforms for shape classification. In International Conference on Learning Representations, 2024

    2024

  19. [27]

    The topology of molecular representations and its influence on machine learning performance

    Florian Rottach, Sebastian Schieferdecker, and Carsten Eickhoff. The topology of molecular representations and its influence on machine learning performance. Journal of Cheminformatics, 2025

    2025

  20. [28]

    Topological analysis of molecular dynamics simulations using the euler characteristic

    Alexander Smith, Spencer Runde, Alex K Chew, Atharva S Kelkar, Utkarsh Maheshwari, Reid C Van Lehn, and Victor M Zavala. Topological analysis of molecular dynamics simulations using the euler characteristic. Journal of Chemical Theory and Computation, 19(5):1553–1567, 2023

    2023

  21. [29]

    Katharine Turner, Sayan Mukherjee, and Doug M. Boyer. Persistent homology transform for modeling shapes and surfaces. Information and Inference: A Journal of the IMA, 3(4):310–344, 12 2014

    2014

  22. [30]

    Exposing the limitations of molecular machine learning with activity cliffs

    Derek Van Tilborg, Alisa Alenicheva, and Francesca Grisoni. Exposing the limitations of molecular machine learning with activity cliffs. Journal of Chemical Information and Modeling, 62(23):5938–5951, 2022. 10 V . Toscano et al

    2022

  23. [31]

    Dominik J. E. Waibel, Scott Atwell, Matthias Meier, Carsten Marr, and Bastian Rieck. Capturing shape information with multi-scale topological loss terms for 3D reconstruction. In Linwei Wang, Qi Dou, P. Thomas Fletcher, Stefanie Speidel, and Shuo Li, editors, Medical Image Com...

    2022

  24. [32]

    Applications of deep learning in molecule generation and molecular property prediction

    W Patrick Walters and Regina Barzilay. Applications of deep learning in molecule generation and molecular property prediction. Accounts of Chemical Research, 54(2):263–270, 2020

    2020

  25. [33]

    A review of molecular representation in the age of machine learning

    Daniel S Wigh, Jonathan M Goodman, and Alexei A Lapkin. A review of molecular representation in the age of machine learning. Wiley Interdisciplinary Reviews: Computational Molecular Science, 12(5):e1603, 2022

    2022

  26. [34]

    Pushing the boundaries of molecular representation for drug discovery with the graph attention mechanism

    Zhaoping Xiong, Dingyan Wang, Xiaohong Liu, Feisheng Zhong, Xiaozhe Wan, Xutong Li, Zhaojun Li, Xiaomin Luo, Kaixian Chen, Hualiang Jiang, et al. Pushing the boundaries of molecular representation for drug discovery with the graph attention mechanism. Journal of Medicinal Chem...

    2019

  27. [35]

    Graph neural networks: A review of methods and applications

    Jie Zhou, Ganqu Cui, Shengding Hu, Zhengyan Zhang, Cheng Yang, Zhiyuan Liu, Lifeng Wang, Changcheng Li, and Maosong Sun. Graph neural networks: A review of methods and applications. AI Open, 1:57–81, 2020. 11

    2020

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.