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REVIEW 3 major objections 4 minor 31 references

MetaCaDI: A Meta-Learning Framework for Causal Discovery from Multiple Environments with Unknown Interventions

T0 review · 3 major / 4 minor · reviewed 2026-08-04 · deepseek-v4-flash

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Pith's one-line read MetaCaDI claims Bayesian meta-learning with a closed-form adaptation step can jointly infer a shared causal graph and unknown intervention targets from very few samples, outperforming existing methods on synthetic and gene-expression data.

desk verdict MetaCaDI is a solid, well-executed meta-learning adaptation of Bayesian causal discovery with unknown interventions; the new problem formulation and closed-form adaptation are genuine, but the identifiability argument is asserted rather than proven and a few reporting inconsistencies need fixing. read the letter →

arxiv 2510.22298 v2 pith:HARM4FCG submitted 2025-10-25 stat.ML cs.LG

Hans Jarett Ong , Yoichi Chikahara , Tomoharu Iwata This is my paper
classification stat.MLcs.LG
keywords causaldiscoverymeta-learningunknowninterventionsfew-shotlearningBayesianinferenceadditivenoisemodelsgraphrecoveryinterventiontargetprediction
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 tries to show that a long-standing impasse—causal discovery when intervention targets are unknown and each experiment has very few samples—can be broken by meta-learning. It proposes MetaCaDI, a Bayesian framework that learns a shared causal graph across many experiments and then adapts to a new, small dataset to predict which variables were intervened upon. The key move is making adaptation analytical: instead of gradient-based fine-tuning, the last layer of the interventional mechanism is fit by ridge regression in closed form. The paper reports that this outperforms existing methods on intervention-target prediction and is competitive on graph recovery, especially on realistic gene-expression simulation data. A sympathetic reader would care because the method targets settings where experiments are costly and targets are uncertain, such as CRISPR off-target effects or fault diagnosis.

What carries the argument

The central machinery is the factored variational objective combined with an analytical adaptation step. The intervention mechanism for each variable is written as a linear readout of a shared feature extractor applied to the variable's parents, so the task-specific weights are obtained in closed form by ridge regression. This closed-form solver replaces the gradient inner loop of standard meta-learning, making adaptation fast and stable. Around it sit a differentiable DAG sampler that guarantees acyclicity, a Gumbel-Softmax target sampler, and permutation-invariant pooling that makes the target-prediction feature invariant to data ordering.

What would settle it

Generate a meta-test dataset where the interventional mechanism is a nonlinear function of the parent features that is not in the span of the shared extractor (e.g., a sinusoid or a product interaction), and measure whether intervention-target AUROC drops to chance. A second test: train with one variable always intervened and never observed under its observational mechanism, then present a dataset where that variable is actually observational; if the model still predicts an intervention, the feature design is relying on leakage, and if it fails, the observational-mechanism assumption is expose

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Extended reading notes

Core claim

MetaCaDI's central claim is that joint inference of a shared causal DAG and per-environment intervention targets can be cast as a Bayesian meta-learning problem in which each dataset is a task, and that this formulation yields accurate few-shot predictions. The model factorizes the posterior into a task-shared graph distribution and task-specific target distributions, and it trains a network to output intervention-target logits from a permutation-invariant feature vector that combines observed values with predictions from observational and interventional mechanisms. The load-bearing novelty is that only the last layer of the interventional mechanism is task-specific, so adapting to a new dat

Load-bearing premise

The load-bearing premise is that any new intervention is representable as a linear readout of a shared feature extractor applied to the intervened variable's parents, and the paper also relies on an unproven transfer of infinite-sample identifiability to its variational objective.

Editorial extensions

If this is right

  • New experiments can be diagnosed from a handful of samples without retraining on the full data collection, which matters for sequential fault detection and real-time systems.
  • The shared graph recovered across environments can narrow the space of causal hypotheses even when no single experiment is large enough to identify it alone.
  • Because adaptation is closed-form, deployment on a new dataset is computationally cheap and avoids unstable inner-loop gradients.
  • The method's success on a noisy gene-expression simulator suggests the approach may transfer to real biological data where intervention targets are often unknown.
  • If the identifiability claim holds, the additive-noise plus meta-learning combination gives a principled posterior over graph and targets, not just a point estimate.

Reading between the lines

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

  • The closed-form adaptation recipe is more general than this paper: any mechanism that is linear in learned features over parents could be adapted this way, so the framework might extend to post-nonlinear or heteroscedastic noise models, which the paper lists as future work.
  • The reported intervention-target AUPRC values (0.094 on SERGIO) show the paper's success is mostly in ranking targets; exact identification of sparse interventions remains hard, so practical deployment would likely need careful thresholding or human confirmation.
  • If a variable is intervened in every training environment, its observational mechanism is never observed; the model must guess it from other variables, and target prediction for that variable may degrade—a testable failure mode the paper does not analyze.
  • There is a minor inconsistency between the abstract's '3 samples' and the main text's '10 data instances' for the few-shot setting; quantitative claims should be read against the main experimental protocol.
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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

3 major / 4 minor

Summary. The paper proposes MetaCaDI, a meta-learning framework for jointly inferring a shared causal DAG and per-dataset intervention targets from multiple interventional environments with unknown targets. The model uses a variational Bayesian formulation: a differentiable DAG sampler for the shared graph, a Gumbel-Softmax target predictor, and an ANM-based likelihood in which the interventional mechanism is a linear readout of a shared feature extractor. Task adaptation is done via a closed-form ridge regression solution rather than gradient-based inner-loop optimization. Experiments on synthetic GP-based data and SERGIO gene-expression simulations report strong performance in intervention target prediction and competitive graph recovery relative to JCI-PC, UT-IGSP, DCDI-G, BaCaDI, and MAML variants, especially with only 10 support samples per meta-test task.

Significance. If the claims hold, MetaCaDI is a meaningful step: it is the first to cast unknown-intervention target identification as a meta-learning problem, and the closed-form adaptation is a practical contribution that avoids costly bilevel optimization. The evaluation on held-out meta-test tasks with no ground-truth targets used in the predictor's training supports the core target-prediction claims, and the inclusion of several baselines and ablations strengthens the empirical picture. However, the paper's theoretical identifiability claim is asserted rather than proved, and the stated conditions are insufficient to guarantee identifiability in a realistic failure mode.

major comments (3)
  1. [§3.1, Remark 3.1] The identifiability claim is asserted by reference to non-Bayesian results (e.g., Brouillard et al. 2020), but the variational meta-learning objective in Eq. (7) is not shown to inherit those results. A concrete failure mode is present in the generative model of Eq. (2): if a variable X_i is intervened upon in every meta-training task, its observational mechanism f_i is never active in any reconstruction loss L_{R,t}, so Θ_obs for that variable is never updated. At meta-test, when X_i is not intervened, the task-adapted interventional mechanism f^I_i can fit the support data well while the untrained observational mechanism cannot, and the target predictor g_η(F_t) will spuriously classify X_i as intervened. The paper neither states nor verifies the necessary condition that each variable's observational mechanism is observed in at least one training task, nor reports whether the experimen
  2. [Abstract (arXiv metadata) vs. §5.1] The abstract states that MetaCaDI identifies intervention targets 'from as few as 3 samples,' but the full-text abstract, the experimental setup in §5.1, and all reported results use N_t'=10 observations for meta-test tasks. The '3 samples' claim is not supported by any experiment in the manuscript and appears to be an overstatement. Please reconcile this discrepancy and use the same number throughout.
  3. [§5.2, Causal Graph Discovery] The text claims MetaCaDI 'significantly outperforms state-of-the-art methods' in both intervention target prediction and graph recovery. However, for graph recovery the reported results are that MetaCaDI 'achieves better performance than BaCaDI and DCDI-G and proves to be highly competitive to JCI-PC and UT-IGSP.' No statistical significance is reported for E-SHD/E-SID against JCI-PC or UT-IGSP, and the figure does not show error bars for all methods (BaCaDI is averaged over fewer simulations). The central 'outperforms' claim for graph recovery is therefore weaker than stated. Please either provide significance tests for all graph metrics or temper the conclusion to 'competitive.'
minor comments (4)
  1. [§2.1] The notation for the structural equation is inconsistent: the text writes 'each variable X_i (j∈...)' and 'X_i (j∈...)' with a stray 'j' in the definition; also 'E_i ⊥ ⊥ E_j' should be made precise that independence holds for all i≠j. Please clean up the notation.
  2. [§4.2, Feature Design] The feature matrix C_t is defined as a 9-block concatenation, but the list only shows eight matrices: D_t, X̂_obs, D_t−X̂_obs, (D_t−X̂_obs)^2, X̂_int, D_t−X̂_int, (D_t−X̂_int)^2, and μ(D_t), σ(D_t). This appears to be 8 items, not 9. Please clarify whether μ and σ are two separate blocks or one block, and correct the description.
  3. [§5.1, Baselines] The paper notes that baselines use all 20 meta-test datasets while MetaCaDI uses only one, and frames this as a more demanding protocol. This is fine, but the sentence in §5.2 'Achieving competitive and often superior performance despite such challenging setup' is vague—please specify exactly which baselines are outperformed in which metrics and which are merely competitive.
  4. [Appendix references] Several results are deferred to appendices (e.g., graph AUROC/AUPRC, runtime comparison, hyperparameters) that are not included in the main text. For a self-contained submission, please either include the key numbers in the main text or ensure the appendices are available in the version under review.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: intervention-target predictions are held-out latent inferences, and the closed-form solver fits function weights, not the targets.

full rationale

The proposed derivation is self-contained rather than circular. In the generative model (Eq. 2), intervention indicators m_t are latent variables; the training objective (Eq. 7) maximizes an ELBO over query data without ground-truth target supervision, and meta-test targets are evaluated on held-out tasks. The closed-form solver (Eq. 6) fits the task-specific last-layer weights w_i of the interventional mechanism, not the intervention targets, and the predictor g_eta(F_t) in Eq. (3) uses features constructed from the mechanism predictions (Section 4.2) rather than from the target values being predicted, so no prediction reduces to a fitted input by construction. Remark 3.1's identifiability claim references external non-Bayesian identifiability results (Brouillard et al. 2020) rather than a self-citation chain; its brevity is a rigor/correctness concern, not circularity. The experimental comparison against JCI-PC, UT-IGSP, DCDI-G, and BaCaDI is an external benchmark, and I found no load-bearing self-citations or equations that are definitionally equivalent to the claimed outputs.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The method's novelty rests on meta-learning over a shared graph and task-specific targets. The ledger shows the key extra assumptions introduced by the paper: the factorization, the linear-readout intervention mechanism, and the transfer of identifiability. Experimental hyperparameters are largely unreported, which adds to the reproducibility burden.

free parameters (4)
  • ridge regularization λ = not reported in main text
    Regularizer in the closed-form solver (Eq. 5-6); controls adaptation strength and is central to the analytical adaptation claim.
  • loss weights λ_I, λ_H, λ_G = not reported in main text
    Weights for intervention sparsity, residual independence, and graph sparsity in Eq. (7); without values, replication is impossible.
  • embedding dimension k = not reported in main text
    Feature representation size for the Deep Sets pooling layers; directly affects the intervention target predictor.
  • hidden dimension d_h = not reported in main text
    Feature extractor output dimension for the interventional MLP in Eq. (4); central to the ridge adaptation.
assumptions (6)
  • domain assumption The data-generating graph G is a DAG and satisfies causal sufficiency (no unobserved confounders).
    Section 2.1; standard causal discovery assumption, but if violated, shared-graph inference and target identification are not valid.
  • domain assumption Each variable follows an Additive Noise Model X_i = f_i(PA_i) + ε_i with independent noise.
    Section 2.1; ensures direction identifiability but restricts the model class to ANMs.
  • domain assumption Every dataset is generated from the same shared causal graph under a hard or soft intervention on a distinct variable subset.
    Section 3.1; if datasets come from different graphs or have latent shifts, the shared graph posterior collapses.
  • ad hoc to paper The variational assumptions m_a ⟂ m_b | Φ and m_t' ⟂ D_train | Φ hold.
    Eq. (1); this factorization is the foundation of the meta-learning posterior and is justified only by stipulating that Φ is a sufficient statistic.
  • ad hoc to paper The interventional mechanism can be expressed as w_i^T h_{Θ'_int}(A_i ∘ X), a linear readout of a shared feature extractor.
    Eq. (4); this is what makes the closed-form ridge solution possible. If a new intervention changes the mechanism outside this class, adaptation and target prediction degrade.
  • ad hoc to paper Identifiability results for non-Bayesian continuous causal discovery transfer to the variational meta-learning objective.
    Remark 3.1; asserted by citing Brouillard et al. (2020), without showing that the variational objective, neural-network parameterization, and regularizers inherit those guarantees.

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Pith. "Pith review of MetaCaDI: A Meta-Learning Framework for Causal Discovery from Multiple Environments with Unknown Interventions." pith.science (2026). https://pith.science/paper/HARM4FCG

@misc{pith2026251022298,
  author       = {Pith},
  title        = {Pith review of: MetaCaDI: A Meta-Learning Framework for Causal Discovery from Multiple Environments with Unknown Interventions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HARM4FCG}},
  note         = {Machine review of arXiv:2510.22298}
}
read the original abstract

Uncovering the causal mechanisms of complex real-world systems remains a significant challenge, as these systems often entail high data collection costs and involve unknown interventions. We introduce MetaCaDI, the first framework to cast the identification of unknown interventions as a meta-learning problem, explicitly leveraging a jointly learned causal graph. MetaCaDI is a Bayesian framework that learns a shared causal structure across multiple environments and is optimized to rapidly adapt to new, few-shot intervention target identification tasks. A key innovation is our model's analytical adaptation, which uses a closed-form solution to bypass expensive and potentially unstable gradient-based bilevel optimization. Extensive experiments on synthetic and complex gene expression data demonstrate that MetaCaDI significantly outperforms state-of-the-art methods. It excels at identifying intervention targets from as few as 3 samples - where existing methods collapse to random chance - while robustly recovering the shared causal graph, proving its effectiveness in data-scarce scenarios.

Figures

Figures reproduced from arXiv: 2510.22298 by the authors.

Figure 1
Figure 1. Our meta-learning setup. Meta-training Phase: Given a collection of datasets Dtrain = {D1, . . . , DT }, MetaCaDI infers shared causal DAG adjacency matrix A from Dtrain, as well as intervention target mt for each Dt. Meta-test Phase: Using a new, small dataset D′ t ′ , MetaCaDI performs fine-tuning to infer its specific intervention targets. Separating the parameters into such two sets is central to our meta-learni… view at source ↗
Figure 2
Figure 2. Performance comparison on the SERGIO and Synthetic datasets, with results averaged over 20 independent sim [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

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Works this paper leans on

31 extracted references · 5 linked inside Pith

  1. [1]

    , " * write output.state after.block = add.period write newline

    ENTRY address archivePrefix author booktitle chapter edition editor eid eprint howpublished institution isbn journal key month note number organization pages publisher school series title type volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.a...

  2. [2]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in capitalize " " * FUNCT...

  3. [3]

    Bergmann, T.; and Hartwigsen, G. 2021. Inferring Causality from Noninvasive Brain Stimulation in Cognitive Neuroscience. Journal of Cognitive Neuroscience, 33: 195--225

    2021

  4. [4]

    F.; Torr, P

    Bertinetto, L.; Henriques, J. F.; Torr, P. H. S.; and Vedaldi, A. 2018. Meta-learning with differentiable closed-form solvers. ArXiv, abs/1805.08136

    arXiv 2018

  5. [5]

    Brouillard, P.; Lachapelle, S.; Lacoste, A.; Lacoste-Julien, S.; and Drouin, A. 2020. Differentiable Causal Discovery from Interventional Data. In Larochelle, H.; Ranzato, M.; Hadsell, R.; Balcan, M.; and Lin, H., eds., Advances in Neural Information Processing Systems, volume 33, 21865--21877. Curran Associates, Inc

    2020

  6. [6]

    Charpentier, B.; Kibler, S.; and G \"u nnemann, S. 2022. Differentiable DAG Sampling. ArXiv, abs/2203.08509

    arXiv 2022

  7. [7]

    Dhir, A.; Ashman, M.; Requeima, J.; and van der Wilk, M. 2024. A Meta-Learning Approach to Bayesian Causal Discovery. ArXiv, abs/2412.16577

    arXiv 2024

  8. [8]

    Dibaeinia, P.; and Sinha, S. 2020. SERGIO: A Single-Cell Expression Simulator Guided by Gene Regulatory Networks. Cell Systems, 11(3): 252--271.e11

    2020

Show all 31 references
  1. [9]

    Eaton, D.; and Murphy, K. 2007. Exact Bayesian structure learning from uncertain interventions. In Meila, M.; and Shen, X., eds., Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics, volume 2 of Proceedings of Machine Learning Researc...

    2007

  2. [10]

    Eberhardt, F.; Glymour, C.; and Scheines, R. 2005. On the Number of Experiments Sufficient and in the Worst Case Necessary to Identify All Causal Relations Among N Variables. In Conference on Uncertainty in Artificial Intelligence

    2005

  3. [11]

    Eberhardt, F.; and Scheines, R. 2007. Interventions and Causal Inference. Philosophy of Science, 74(5): 981--995

    2007

  4. [12]

    Finn, C.; Abbeel, P.; and Levine, S. 2017. Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks. In International Conference on Machine Learning

    2017

  5. [13]

    agele, A.; Rothfuss, J.; Lorch, L.; Somnath, V. R.; Sch\

    H\"agele, A.; Rothfuss, J.; Lorch, L.; Somnath, V. R.; Sch\"olkopf, B.; and Krause, A. 2023. BaCaDI: Bayesian Causal Discovery with Unknown Interventions. In Ruiz, F.; Dy, J.; and van de Meent, J.-W., eds., Proceedings of The 26th International Conference on Artificial Intelli...

    2023

  6. [14]

    M.; Peters, J.; and Sch\" o lkopf, B

    Hoyer, P.; Janzing, D.; Mooij, J. M.; Peters, J.; and Sch\" o lkopf, B. 2008. Nonlinear causal discovery with additive noise models. In Koller, D.; Schuurmans, D.; Bengio, Y.; and Bottou, L., eds., Advances in Neural Information Processing Systems, volume 21. Curran Associates, Inc

    2008

  7. [15]

    S.; and Poole, B

    Jang, E.; Gu, S. S.; and Poole, B. 2016. Categorical Reparameterization with Gumbel-Softmax. ArXiv, abs/1611.01144

    2016 arXiv

  8. [16]

    Kool, W.; van Hoof, H.; and Welling, M. 2020. Ancestral Gumbel-Top-k Sampling for Sampling Without Replacement. Journal of Machine Learning Research, 21(47): 1--36

    2020

  9. [17]

    J.; Mnih, A.; and Teh, Y

    Maddison, C. J.; Mnih, A.; and Teh, Y. W. 2016. The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables. ArXiv, abs/1611.00712

    2016 arXiv

  10. [18]

    Mariani, L.; Monni, C.; Pezz \`e , M.; Riganelli, O.; and Xin, R. 2018. Localizing Faults in Cloud Systems. 2018 IEEE 11th International Conference on Software Testing, Verification and Validation (ICST), 262--273

    2018

  11. [19]

    M.; Magliacane, S.; and Claassen, T

    Mooij, J. M.; Magliacane, S.; and Claassen, T. 2020. Joint Causal Inference from Multiple Contexts. Journal of Machine Learning Research, 21(99): 1--108

    2020

  12. [20]

    Pearl, J. 2009. Causality: Models, Reasoning and Inference. USA: Cambridge University Press, 2nd edition. ISBN 052189560X

    2009

  13. [21]

    M.; Janzing, D.; and Sch \"o lkopf, B

    Peters, J.; Mooij, J. M.; Janzing, D.; and Sch \"o lkopf, B. 2014. Causal Discovery with Continuous Additive Noise Models. Journal of Machine Learning Research, 15(58): 2009--2053

    2014

  14. [22]

    Siddiqi, S.; Kording, K.; Parvizi, J.; and Fox, M. 2022. Causal mapping of human brain function. Nature Reviews Neuroscience, 23: 1--15

    2022

  15. [23]

    Snell, J.; Swersky, K.; and Zemel, R. 2017. Prototypical networks for few-shot learning. In Proceedings of the 31st International Conference on Neural Information Processing Systems, NIPS'17, 4080–4090. Red Hook, NY, USA: Curran Associates Inc. ISBN 9781510860964

    2017

  16. [24]

    Squires, C.; Wang, Y.; and Uhler, C. 2020. Permutation-Based Causal Structure Learning with Unknown Intervention Targets. In Peters, J.; and Sontag, D., eds., Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI), volume 124 of Proceedings of Machi...

    2020

  17. [25]

    Tian, J.; and Pearl, J. 2001. Causal Discovery from Changes. In Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence, UAI '01, 512–521. San Francisco, CA, USA: Morgan Kaufmann Publishers Inc. ISBN 1558608001

    2001

  18. [26]

    Varici, B.; Shanmugam, K.; Sattigeri, P.; and Tajer, A. 2022. Intervention target estimation in the presence of latent variables. In Cussens, J.; and Zhang, K., eds., Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence, volume 180 of Proceedin...

    2022

  19. [27]

    Wu, H.; Shi, W.; and Wang, M. 2024. Developing a novel causal inference algorithm for personalized biomedical causal graph learning using meta machine learning. BMC Medical Informatics and Decision Making, 24

    2024

  20. [28]

    A.; Marx, A.; and Vreeken, J

    Xu, S.; Mian, O. A.; Marx, A.; and Vreeken, J. 2022. Inferring cause and effect in the presence of heteroscedastic noise. In International Conference on Machine Learning, 24615--24630. PMLR

    2022

  21. [29]

    Zaheer, M.; Kottur, S.; Ravanbhakhsh, S.; P\' o czos, B.; Salakhutdinov, R.; and Smola, A. J. 2017. Deep Sets. In Proceedings of the 31st International Conference on Neural Information Processing Systems, NIPS'17, 3394–3404. Red Hook, NY, USA: Curran Associates Inc. ISBN 9781510860964

    2017

  22. [30]

    Zhang, K.; and Hyv \"a rinen, A. 2009. On the identifiability of the post-nonlinear causal model. In Proc. 25th Conference on Uncertainty in Artificial Intelligence (UAI2009)

    2009

  23. [31]

    Y.; Wang, X.-G.; Huang, Q.-S.; and Yang, S.-H

    Zhang, X.-H.; Tee, L. Y.; Wang, X.-G.; Huang, Q.-S.; and Yang, S.-H. 2015. Off-target Effects in CRISPR/Cas9-mediated Genome Engineering. Molecular Therapy - Nucleic Acids, 4: e264

    2015

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Reviewed August 4, 2026 · model on record in the stance chip above.