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Learn from What We HAVE: History-Aware VErifier that Reasons about Past Interactions Online

T0 review · 4 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read A history-aware verifier that scores action proposals—rather than a generator conditioned on past interactions—drops failure rates by 3–10x in the paper's experiments.

desk verdict A well-engineered generator-verifier pipeline for ambiguous manipulation with a sound but simple theory and consistent empirical gains, though the verifier's deployment accuracy is never measured and the headline numbers use privileged flow. read the letter →

arxiv 2509.00271 v2 pith:5742JHMB submitted 2025-08-29 cs.RO

Yishu Li , Xinyi Mao , Ying Yuan , Kyutae Sim , Ben Eisner , David Held This is my paper
classification cs.RO
keywords history-awareverifiergeneration-verificationambiguousmanipulationpartiallyobservableMDPdiffusionpolicyarticulatedobjectsonlinedisambiguationdenseactionfields
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's central claim is that a robot facing visually identical objects that behave differently should not try to make one history-conditioned action generator do everything; instead it should decouple generation from verification. The proposed system samples several candidate actions from an unconditional diffusion generator and lets a history-aware verifier—a scorer that looks at the current proposal plus the chain of past actions and their observed effects—pick the best one. The paper proves a theorem that whenever the verifier is better than random chance (accuracy pV > 0.5, or pV1 + pV0 > 1 in the dependent case), selecting among N sampled actions strictly improves expected reward over a single generator sample. Empirically, on articulated objects, ambiguous doors, and uneven-mass pick-up, this cuts failure rates by roughly 3–10x relative to the baselines tested, including a history-conditioned diffusion generator. If the claim holds, the practical message is that adding a moderately competent verifier to an existing proposal generator is a cheap and general way to handle ambiguity online.

What carries the argument

The carrying mechanism is the history-aware verifier (HAVE): an explicit dot-product attention layer in which the encoded proposed action is the query, the encoded history actions are keys, and encoded observation-flow results (the motion between before/after point clouds) are values, with an unconditional score token as a fallback when no similar history exists. It outputs a score from a small MLP. The theoretical identity doing the work is the expected-reward formula E[Rgt(aw/ver)] = (1-(1-Q)^N) pG pV/Q + (1-Q)^N pG(1-pV)/(1-Q), with Q = P(V(a)=1); simplifying it shows the verifier helps exactly when pV>0.5. The observation encoder uses 3D flow between consecutive observations (ground-trut

What would settle it

Measure the verifier's per-action accuracy pV on the deployment-time distribution—the same generator proposals, the same estimated flow tracker, unseen objects—using simulator ground-truth rewards. If pV is at or below 0.5 (or pV1+pV0 ≤ 1 in the dependent case) and HAVE still outperforms the generator alone, then the theorem's mechanism is not what is driving the gain; if pV exceeds 0.5, the theorem predicts HAVE must beat single-sample generation. A second check: compare HAVE's failure rate against the oracle verifier and generator-only curves in Fig. 6; if HAVE falls outside the interval bet

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Extended reading notes

Core claim

HAVE trains a verifier that takes an action proposal plus the history of (observation, action, outcome) triples and outputs a score in [-1,1]. At run time an unconditional diffusion generator proposes N actions, the verifier scores them, and the robot executes the top-scoring one. Theorem A states that for binary rewards with generator quality pG in (0,1), N>1, and verifier accuracy pV, verifier selection strictly improves expected reward over single-sample generation if and only if pV>0.5; the dependent-accuracy extension replaces this with pV1+pV0>1. The continuous-reward extension predicts gains growing roughly as sqrt(2 ln N) with a prefactor that grows with reward spread and shrinks wit

Load-bearing premise

The load-bearing premise is that the verifier, trained on privileged simulator-derived labels, remains better than random at scoring the actual distribution of generator proposals and estimated observation flows encountered at run time; the paper never measures verifier accuracy directly and reports no error bars on the main failure-rate tables.

Editorial extensions

If this is right

  • If a verifier is only slightly better than chance (pV just above 0.5), selecting among N sampled actions already beats the generator alone; at pG=0.9, pV=0.9, N=2, failure rate drops from 10% to 3%.
  • The generator does not need to be conditioned on history at all: an unconditional diffusion generator plus the verifier outperforms a history-conditioned diffusion generator (20% to 2% failure on articulated objects).
  • Sampling efficiency is high: with the verifier, 5 proposals capture most of the benefit; failure rate continues to fall as N grows, at roughly linear compute cost per extra proposal.
  • The verifier suppresses previously failed modes: with one-step failure history, the selected action avoids the failed mode in 99.79% of trials on the multi-modal door dataset.
  • The generation-verification split transfers to other ambiguous manipulation settings (uneven-mass pick-up) and to hierarchical sub-goal selection in benchmark tabletop tasks where the verifier selects among high-level sub-goal predictions.

Reading between the lines

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

  • Because Theorem A only requires better-than-chance scoring, HAVE's logic should transfer to any POMDP with hidden state and observable outcome—not just mechanical ambiguity; the same generator-verifier split could be used for any policy family with sampled candidates.
  • The paper's own limitation—that the verifier inherits privileged simulator labels—suggests a direct test: train the verifier with only the observed outcome signal (e.g., door angle change or tilt) and re-measure whether pV stays above 0.5.
  • The oracle-verifier experiments in the paper indicate the remaining bottleneck is the generator's proposal distribution, so an inference-time loop that regenerates proposals conditioned on verifier scores could push failure rates toward the oracle level; the paper does not implement this.
  • The explicit-attention design, where the proposal acts as query over history-action keys and outcome-flow values, is a template for making learned verifiers robust to noisy observation estimates; the paper's robustness comparison supports that, but only within its environments.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper proposes HAVE, a history-aware verifier that scores action proposals produced by an unconditional diffusion generator, using past observations and actions to disambiguate manipulation outcomes. The central claim is twofold: (i) theoretically, selecting among N generator samples with a verifier whose per-action accuracy exceeds 0.5 improves expected action quality over single-sample generation (Theorem A, Sec. 4.2); (ii) empirically, a learned verifier outperforms history-conditioned generative baselines and prior methods on articulated objects, multimodal doors, uneven object pick-up, and a real door, reducing failure rates substantially (e.g., Table 1). The paper also includes held-out category experiments, ablations, sample-count analysis, classifier-guidance comparison, and a hierarchical policy extension in Appendix D.4.

Significance. If the central claim holds, the work makes a useful contribution: it provides a simple, explicit proof that a better-than-random verifier improves generator output, and it demonstrates a practical architecture for history-aware verification in ambiguous manipulation. The theoretical part is clean and the appendix contains a careful dependent-case extension (Theorem A') and a continuous-reward extension. The experimental scope is broad: three simulation domains, a real-robot door, held-out categories, and multiple ablations. The authors are also transparent in reporting the estimated-flow variant of their method and in stating limitations in Sec. 8. However, the theoretical guarantee is conditional on an unmeasured verifier accuracy, and the headline empirical gains rely on privileged ground-truth observation flow. Under deployment-time flow estimation, the advantage over the strongest baseline largely disappears in the articulated-object domain. These issues are load-bearing for the paper's main claims and need to be addressed before the paper can be recommended for acceptance.

major comments (4)
  1. [Sec. 4.2 (Theorem A), Sec. 5.1/B.2, Table 1] The theorem's improvement condition is pV > 0.5 on the actions being selected, but pV is never measured on the deployment proposal distribution. The verifier is trained on ground-truth/random/history action proposals (Sec. B.2), while at inference it scores actions sampled from a diffusion generator as 3D articulation flows converted to dense action fields (Sec. B.1). These are different distributions, so training accuracy need not transfer. Please report the verifier's accuracy, ranking accuracy, or a calibration curve on held-out generator proposals, and verify that pV > 0.5 (or pV1+pV0 > 1 in the dependent case) actually holds at deployment.
  2. [Sec. 6.1.1, Table 1; Sec. D.1, Table 3] The headline failure-rate reductions (6x, 10x, 3x) are for 'HAVE (Ours) + GT obs flow', which uses privileged ground-truth flow from the simulator. The deployable variant, 'HAVE (Ours) + Estimated obs flow', achieves A VGc = 6.7 on general articulated objects, which is not better than FlowBotHD w/CC (6.2). On held-out categories (Table 3), HAVE+DELTA (21.5) is also worse than FlowBotHD w/CC (14.8). Since the estimated-flow setting is the actual deployment condition, the central empirical claim is not established there. The estimated-flow results should be the primary metric, or the paper should clearly separate and discuss the gap.
  3. [Tables 1–3 and Appendix C.1] The main failure-rate tables report single numbers per category with no error bars, confidence intervals, or repeated-seed variance. Given the stochasticity of the diffusion generator and the fact that each object is tested only 5 times (or 3 for unseen uneven objects), differences such as 2.5 vs. 6.2 or 16.9 vs. 14.8 could be within sampling variation. Please provide standard errors or confidence intervals, and for the 'Oracle Verifier' and 'Oracle Sampler' rows specify the number of runs. This is needed to assess the robustness of the empirical advantage.
  4. [Appendix A.2 (Theorem A') and Sec. 8] The dependent-case extension relaxes independence but still assumes verifier accuracies pV1 and pV0 are uniform over actions and the reward is binary. The actual verifier is trained on a mixture of proposal types and scores real-valued dense action fields, so the theoretical guarantee does not directly certify the deployed system even if pV1+pV0 > 1 on the training mixture. The paper's own Limitations (Sec. 8) correctly notes the reliance on privileged supervision and the generator's expressiveness bound; a direct measurement of verifier accuracy on the deployment distribution would connect the theory to practice.
minor comments (4)
  1. [Abstract/Introduction] The abstract and introduction describe the generator as 'unconditional diffusion-based', but the generator in Fig. 12 and Sec. B.1 conditions on the current observation point cloud. Please clarify that it is unconditional with respect to history, not unconditional with respect to observation.
  2. [Sec. C.5] The text says the conditional diffusion baseline uses 'the vanilla transformer architecture in Appendix D.3'; this appears to be a typo for Appendix C.4. Please correct the cross-reference.
  3. [Sec. 5.3] The dense action field equation is described verbally; please give the explicit formula for the point-cloud channels, e.g., {d_i = d * exp(-c * ||p_i - p||^2)}. The scaling constant c is never specified or ablated. Since c is a free parameter and affects the representation, a value or sensitivity study would help.
  4. [Appendix E.1, Table 5] The 'Valid Rate' metric is useful, but it only measures avoidance of repeated failure modes; it does not quantify whether the verifier's score is well-calibrated or whether pV > 0.5. A short statement connecting this analysis to Theorem A's condition would improve the paper.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the theory is a conditional proof from explicit assumptions, and the empirical comparisons are benchmarked independently of the derivation.

full rationale

The paper's central theoretical result (Theorem A, Sec. 4.2 and Appendix A.1-A.2) is a conditional mathematical statement: under explicit assumptions (independence of generator and verifier errors, pG in (0,1), and pV > 0.5, or the dependent-case condition pV1 + pV0 > 1), selecting the verifier's highest-scored among N proposals has higher expected binary reward than one sample from the generator. The proof derives the improvement algebraically and proves the equivalence in both directions; neither the assumptions nor the conclusion are fitted to the paper's experimental outcomes, and the conclusion is not assumed. The continuous-reward extension in Appendix A.3 is likewise an analytic approximation with stated distributional assumptions. The empirical claims (Tables 1-3, Figures 2-6) compare the trained HAVE verifier against baselines on unseen instances and held-out categories using the same success/failure metric for all methods; these results are independent of the theorem and are not constructed from its parameters. The only self-citations ([30], [31]) are to the authors' prior systems used as building blocks (the action generator, 3D articulation flow representation) and as baselines; they do not carry the load-bearing argument that a verifier improves selection. The paper's own Limitations section acknowledges that the verifier is bounded by generator expressiveness and that training requires privileged ground-truth labels, which is a scope limitation rather than a circular step. The skeptic's concern that pV is never directly measured on the deployment-time proposal distribution is a legitimate empirical-validation gap, but the absence of such a measurement is not a case of a 'prediction' reducing to a fitted input, a self-definition, or a self-citation chain. The theorem's resemblance to well-known best-of-N selection properties is a novelty/positioning issue, not circularity. Therefore no significant circularity is found.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central method introduces three hand-chosen hyperparameters (sample count N, action field constant c, history length K). The theory rests on idealized assumptions about verifier accuracy, and training requires privileged simulation labels. No invented physical entities.

free parameters (3)
  • N (number of action proposals per timestep) = 30 for articulated objects, 20 for uneven pick-up, 5 for MimicGen
    Chosen by the authors; the theoretical analysis requires N>1 and the method's gains grow with N. The specific values are hand-picked hyperparameters, not fitted to data.
  • c (dense action field scaling constant) = not stated numerically in text
    Appears in the dense action field computation d_i = d * exp{-c * ||p_i - p||^2_2} (Sec 5.3). Hand-chosen; affects the action representation fed to the verifier.
  • Max history length K at inference = varies across experiments (1-30; 5 used for timing)
    The verifier conditions on up to K past interactions; E.2 shows performance improves with K up to a point. Hand-chosen.
assumptions (4)
  • domain assumption The environment is a distribution over POMDPs with unknown transition function T sampled from PT (Sec 2).
    Defines the problem: history is needed to infer the latent dynamics. Reasonable but constrains scope.
  • ad hoc to paper Generator and verifier accuracies are independent, and pV is uniform over actions (Sec 4.2, Assumptions 1-3).
    Used to derive Theorem A. The paper relaxes independence in A.2, but the main statement relies on it.
  • ad hoc to paper In the continuous case, verifier score Y = X + epsilon with epsilon ~ N(0, sigma_V^2) independent of X (Appendix A.3, Assumption 2).
    Needed for the Gaussian extreme value analysis; idealized model of verifier noise.
  • domain assumption Privileged simulator knowledge (ground-truth action and per-task reward) is available to label training data (Sec 5.1 and Limitations).
    The verifier is trained on scores simulated from privileged information; limits applicability to the real world without simulation.

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Cite this review

Pith. "Pith review of Learn from What We HAVE: History-Aware VErifier that Reasons about Past Interactions Online." pith.science (2026). https://pith.science/paper/5742JHMB

@misc{pith2026250900271,
  author       = {Pith},
  title        = {Pith review of: Learn from What We HAVE: History-Aware VErifier that Reasons about Past Interactions Online},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5742JHMB}},
  note         = {Machine review of arXiv:2509.00271}
}
read the original abstract

We introduce a novel History-Aware VErifier (HAVE) to disambiguate uncertain scenarios online by leveraging past interactions. Robots frequently encounter visually ambiguous objects whose manipulation outcomes remain uncertain until physically interacted with. While generative models alone could theoretically adapt to such ambiguity, in practice they obtain suboptimal performance in ambiguous cases, even when conditioned on action history. To address this, we propose explicitly decoupling action generation from verification: we use an unconditional diffusion-based generator to propose multiple candidate actions and employ our history-aware verifier to select the most promising action by reasoning about past interactions. Through theoretical analysis, we demonstrate that employing a verifier significantly improves expected action quality. Empirical evaluations and analysis across multiple simulated and real-world environments including articulated objects, multi-modal doors, and uneven object pick-up confirm the effectiveness of our method and improvements over baselines. Our project website is available at: https://liy1shu.github.io/HAVE_CoRL25/

Figures

Figures reproduced from arXiv: 2509.00271 by the authors.

Figure 1
Figure 1. HAVE Architecture: the proposed and history actions are encoded through a PointNet++ for 3D geometric understanding, and self-attention layers for sequential reasoning. History results are encoded similarly. Together they pass through an explicit attention layer to obtain the final score. We represent the observation encoder Eobs(oi−1, oi) as follows: First, we compute the flow from each point in observation oi−1 to… view at source ↗
Figure 2
Figure 2. Multi-modal Door Dataset Performance: The left plot shows an example of a con￾structed multi-modal door in simulation with the same geometry but different opening directions. The right bar plot demonstrates the efficacy metric Failure Rate and the efficiency metric Steps to Open from which we can see our method’s improvements over baselines and ablation architectures. 6.1.3 Real World Ambiguous Door We apply our met… view at source ↗
Figure 3
Figure 3. Real World Ambiguous Door Performance: The left side is the visual appearance of the ambiguous door and the 4 modes it opens. We collect 5 trials for each mode. From the bar plot we can see that HAVE demonstrates a more stable and efficient opening process. 7 [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (26 more)
Figure 4
Figure 4. Figure 4: Visualization of action sequence (dots) and theoretical center of mass range (bars): “Conditional Diffusion” takes 5 steps to succeed, while HAVE (Ours) takes only 3 steps and each attempt is within the theoretical center of mass range. In [PITH_FULL_IMAGE:figures/ful…
Figure 5
Figure 5. Figure 5: Comparison between Vanilla Transformer and HAVE: Robustness to noisy observation flow. Architecture. We compare our architecture with a vanilla transformer baseline where the action tokens (aˆemb, {aemb,i} t i=1) and observation tokens ({fi} t i=1) are concatenated cor…
Figure 6
Figure 6. Figure 6: Time and Accuracy vs Number of Samples: On the left, we plot the time used for gen￾erator and verifier w.r.t the number of generated samples (with verifier history length = 5); On the right, we plot the failure rate w.r.t sample count, comparing HAVE with an oracle ver…
Figure 7
Figure 7. Figure 7: Expected and Simulated Reward w.r.t. Sample Number: We can see the expected and simulated improvements the verifier introduces with different generator and verifier accuracy. A.2 Discrete Reward with Dependent Generator Verifier Accuracies We can also extend the theory…
Figure 8
Figure 8. Figure 8: Simulation Results (Normal Reward): We plot the simulated improvements and the theoretical improvements against different N, σG, and σV . The default values for parameters that are fixed are N = 50, σG = 1.0, and σV = 0.5. We also numerically simulate improvements with…
Figure 9
Figure 9. Figure 9: Simulation Results (Gaussian Mixture Model Reward): We plot the simulated im￾provements and the theoretical improvements against different N, σG and σV . The default values for parameters that are fixed are N = 20, σG = 1.0 and σV = 0.5. 0 20 40 60 80 100 Number of can…
Figure 10
Figure 10. Figure 10: Simulation Results (Uniform Reward): We plot the simulated improvements and the theoretical improvements against different N, and σV . The default values for parameters that are fixed are N = 20 and σV = 0.5. Verifier Pairwise Accuracy We also demonstrate the effect o…
Figure 11
Figure 11. Figure 11: Simulation Results (w.r.t. Verifier Pairwise Accuracy): We plot the simulated im￾provements and the theoretical improvements against different N, and pV . The default values for parameters that are fixed are N = 20 and pV = 0.8. Using the above theoretical and numeric…
Figure 12
Figure 12. Figure 12: Action Generator Architecture Following Li et al. [30], we construct our ac￾tion generator with a PointNet++ [28] encoder EΘ and a Diffusion Transformer (DiT) [35] de￾noiser DΦ as shown in [PITH_FULL_IMAGE:figures/full_fig_p020_12.png]
Figure 13
Figure 13. Figure 13: Point Cloud as Result (Ablation) Architecture: We pass the observations sequence directly through a self-attention layer without extracting observation flow from observation pairs. 21 [PITH_FULL_IMAGE:figures/full_fig_p021_13.png]
Figure 14
Figure 14. Figure 14: Vanilla Transformer (Ablation) Architecture: We concatenate the PointNet++ en￾coded action features and result features and pass through an end-to-end transformer. C.5 Conditional Diffusion To compare HAVE with end-to-end history-aware conditional diffusion without ve…
Figure 15
Figure 15. Figure 15: Conditional Diffusion Architecture: We first embed the histories and inject the embed￾ding as a condition into DiT in the denoiser. D Experiment Results and Details D.1 Held-out Articulated Categories Following the protocol of Eisner et al. [31], we split PartNet-Mobi…
Figure 16
Figure 16. Figure 16: Articulated Objects Categories Legend: We show the icon-to-text correspondence for better interpretation of the table. D.2 Uneven Object Pick-up We constructed the training ambiguous rod dataset with 17 rod replicates of the same size and assigned the mass center rand…
Figure 17
Figure 17. Figure 17: Uneven Object Dataset Examples: From left to right, we show examples of the visual appearance of rod, knife, complex bookmark and irregular bookmark in our uneven object dataset. and the model first tries push left (push is also executed by pull from the back) which d…
Figure 18
Figure 18. Figure 18: Real World Analysis (Example 1): HAVE suppresses the failure mode “push left” despite it being frequently generated from the generator and opens the door. No Movement Push Left Pull right Pull left Slightly Open Open [PITH_FULL_IMAGE:figures/full_fig_p025_18.png]
Figure 19
Figure 19. Figure 19: Real World Analysis (Example 2): HAVE takes 3 steps to explore towards the correct open action without repeating failure modes. Sub-goal Generation for Multi-stage Tasks. We consider manipulation tasks in MimicGen [37] using a robot manipulator with 2-finger grippers.…
Figure 20
Figure 20. Figure 20: Experimental environments from MimicGen [37]: The left image in each sub figure shows an initial state of the environment, and the right image shows the goal state. conditional denoising diffusion model that generates noise-free actions for execution. For the point cl…
Figure 21
Figure 21. Figure 21: Failure History Analysis (Average Scores): Verifier score analysis under different failure histories. Actions matching failure modes receive lower scores, showing the verifier’s ability to learn from failure histories. We plot the distribution of normalized score (nor…
Figure 22
Figure 22. Figure 22: Failure History Analysis (Examples): Verifier predictions for each mode under one￾step failure history on two example doors, showing score suppression of previously failed modes. Success History (Articulated Objects) : To test the verifier’s ability to utilize success…
Figure 23
Figure 23. Figure 23: Successful History Analysis: Given a successful history, we use the verifier to evaluate action proposals on a new state (geometrically very different from the history observation) of the same object. (1) With a fixed ground-truth direction, the score heatmap for vary…
Figure 24
Figure 24. Figure 24: Uneven Object Verifier Analysis (Example 1): HAVE narrows the action space each step by leveraging information from failures, leading to a faster success. Similarly in [PITH_FULL_IMAGE:figures/full_fig_p028_24.png]
Figure 25
Figure 25. Figure 25: Uneven Object Verifier Analysis (Example 2): HAVE learns from history, its selected actions stay mostly within the theoretical range at each step. E.2 Verifier Performance w.r.t History Length We experiment in all three articulated objects environments with different …
Figure 26
Figure 26. Figure 26: Max History Length Analysis: Performance improves with longer history up to a point, but excessive context can introduce redundancy and instability. E.3 HAVE with Conditional Generators We compared the performance of HAVE when paired with either an unconditional or a …
Figure 27
Figure 27. Figure 27: Performance of HAVE with Unconditional and Conditional Generators: The better expressiveness of the unconditional generator allows HAVE to achieve best performance on complex tasks like ’Articulated Objects’, while conditional generator achieves better performance for…
Figure 28
Figure 28. Figure 28: Classifier Guidance Performance: We plot the Success Rate (↑) with and without classifier guidance, and compare them with HAVE. 30 [PITH_FULL_IMAGE:figures/full_fig_p030_28.png]
Figure 29
Figure 29. Figure 29: Classifier-Free Guidance Scale Analysis: We plot the Normalized Distance (↑) against different classifier-free guidance scale, and the performance of HAVE and FlowBot3D as reference. E.6 Generalization with Different Verifier Capacity We test the generalization abilit…

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Cited by 1 Pith paper

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Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.