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REVIEW 4 major objections 4 minor 1 cited by

Aligned Textual Scoring Rules

T0 review · 4 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The paper designs the Aligned Scoring Rule, a provably truthful textual scoring rule chosen to minimize mean squared error to a reference score, and reports that it outperforms truthful baselines on peer-grading data.

desk verdict A sensible, clean method for aligning proper textual scoring rules with reference scores, but the empirical properness claim has an unexamined hole wherever the QA oracle says 'Neither'. read the letter →

arxiv 2507.06221 v1 pith:LMLCV4HI submitted 2025-07-08 cs.AI cs.GT

Yuxuan Lu , Yifan Wu , Jason Hartline , Michael J. Curry This is my paper
classification cs.AIcs.GT
keywords properscoringrulestextualinformationelicitationLLM-as-judgepeergradingconvexoptimizationtruthfulGPTscorealignment
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 provably truthful (proper) scoring rule for open-ended text can be aligned with human preference: the Aligned Scoring Rule (ASR) is chosen to minimize the mean squared error to an exogenous reference score—the instructor score or an LLM-judge score—while remaining proper. This matters because standard LLM-as-judge scores are scalable but can be gamed, while textbook proper scoring rules are truthful but may reward text that does not match what a human grader values. On two real peer-grading datasets, the paper reports that ASR fits the reference score nearly as the identity function, beats the best constant score on MSE, and beats the non-aligned ElicitationGPT baselines on MSE, Pearson, and Spearman correlations. If the claim holds, open-ended peer review can be scored in a way that is simultaneously hard to manipulate and close to what an instructor would give.

What carries the argument

The mechanism has three parts. First, the textual reduction: a summarization oracle extracts summary points and a question-answering oracle maps each report to {0,1,⊥}, with ⊥ interpreted as the prior, so the improper text space becomes a finite numerical report space. Second, the hypothesis class of separate scoring rules: the total score is a weighted average of per-rubric-point single-dimensional proper scoring rules, each described by six numbers S(r,θ) for r∈{0,1,⊥} and θ∈{0,1}; properness is the finite constraint set of Definition 2.5. Third, the convex program that minimizes E[(S(r,θ)−reference)²] over these scores, subject to properness and boundedness. Because the objective and constraints are convex in the six variables per dimension, the optimal aligned rule can be found reliably and remains interpretable: near-linear score lines indicate rubric points that the reference score ignores.

What would settle it

Ask peer reviewers to state a probability for each rubric point (or flag hedged statements such as 'likely correct'), then test whether the posterior mean ever lies strictly between 0 and the prior, or between the prior and 1, rather than only at 0, 1, or the prior. Finding even one such instance would falsify Assumption 2.2, and the paper's proof that ASR is proper on the ternary report space would no longer cover the reported belief.

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Extended reading notes

Core claim

The Aligned Scoring Rule is a textual scoring rule that is proper by construction and aligned by optimization. Following the reduction from textual to numerical elicitation, a language model summarizes instructor reviews into a rubric of summary points and maps each peer review to a ternary vector (agree, disagree, or not applicable). The paper then minimizes the expected squared difference between a separate scoring rule—a weighted sum of single-dimensional proper scoring rules—and the reference score, subject to the linear properness constraints of Definition 2.5. The optimization is convex and solved by gradient descent. Empirically, a linear fit of the reference score on the ASR is almost the identity, and the ASR outperforms the best constant and both V-shaped ElicitationGPT baselines on all three alignment metrics, for both instructor and LLM-judge references.

Load-bearing premise

The design relies on Assumption 2.2, that a reviewer's belief about each rubric point is either certainty that it holds, certainty that it fails, or no information beyond the base rate; if reviewers hold intermediate degrees of belief, the optimized rule may no longer be strictly proper.

Editorial extensions

If this is right

  • In peer grading, ASR can replace raw LLM-judge or instructor scores with a truthful score that still tracks them closely, reducing the incentive to add irrelevant statements or guess.
  • The convex program gives per-rubric-point score lines, so instructors can see which rubric points matter in the reference score and which are effectively ignored.
  • Because the LLM-judge reference correlates with the instructor score in the data, aligning to an LLM-judge reference offers a scalable path that requires no instructor scores at alignment time.
  • ASR converts a non-proper reference score into a proper one, so any future reference—including a better LLM judge—can be plugged into the same optimization.

Reading between the lines

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

  • If the claim is right, there is no inherent tension between truthful elicitation and preference alignment: any score a designer can produce, including a biased or noisy judge, can be turned into a truthful proxy, so the bottleneck shifts to the quality of the reference score itself.
  • The same optimization could be applied to other reference signals, such as rubric-specific rubrics or downstream outcome labels, provided a labelled dataset exists; the finite report space is what keeps the problem convex.
  • The know-it-or-not assumption is testable and is the most natural point of failure: one can ask graders for confidence levels and check whether their posterior means are ever strictly between 0, 1, and the prior. If they are, an approximately-proper variant or a larger report space would be needed.
  • A behavioral experiment could verify whether the improved alignment survives real strategic agents who know they are scored by ASR, since properness protects against misreporting beliefs but not against effort choice or collusion.
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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 the Aligned Scoring Rule (ASR), a textual scoring mechanism that combines the ElicitationGPT reduction of Wu & Hartline with a convex optimization over separate proper scoring rules to minimize the mean squared error to an external reference score (instructor or LLM-judge score). The authors formulate the optimization problem as a convex program with explicit properness constraints under a ternary report space {0,1,⊥}, prove convexity, and report experimental results on two peer-grading datasets showing that ASR achieves lower MSE and higher correlation with reference scores than two baselines, along with a case study for interpretability.

Significance. If the theoretical guarantee holds, the paper makes a useful contribution by casting alignment of proper scoring rules with human preferences as a convex program, building on Li et al. (2022) and Wu & Hartline (2024). The explicit properness constraints are formal and the convexity argument is clean under Assumption 2.2. The work also provides a concrete pipeline for implementing text elicitation with LLM oracles. However, the empirical support is thin (no out-of-sample evaluation, no error bars, no code/data release) and the implementation deviates from the theorem's assumptions, so the central claim of a provably truthful rule that aligns with human scores is only partially supported.

major comments (4)
  1. [Section 3.1, Footnote 1] The implementation scores ground-truth ⊥ by drawing the binary state from the prior, which is outside the conditions of Theorem 3.2. Under this scheme, an agent's expected payoff for report r_i is E_{θ~p_i} S(r_i, θ_i) regardless of her posterior q_i. By the second constraint of Definition 2.5, ⊥ is weakly optimal for every q_i, so an agent who knows θ_i has no strict incentive to report it. The question-answering prompt in Appendix A.1.2 explicitly allows 'Neither' outputs, so this event is not vacuous. The paper reports neither the frequency of ground-truth ⊥ nor a robustness analysis, so the claim of maintaining properness in the reported experiments is unsupported.
  2. [Section 2.2, Assumption 2.2] The assumption that posterior beliefs are always in {0,1,p_i} is not established. The paper's justification, that textual reports either express 0/1 or no information, concerns the report space, not the belief distribution. Without this assumption, the finite constraints in Definition 2.5 do not imply properness for agents with intermediate beliefs, and the optimized scoring rule can fail to be proper. Please provide evidence for this assumption or characterize the degree of improperness when it is violated.
  3. [Section 5.3, Table 1] The evaluation appears to be entirely in-sample: the ASR is fit on the same reference scores it is then evaluated against, and no train/test split, error bars, or significance tests are reported. The 'nearly-identity linear fit' in Figure 4 is expected from the fact that ASR minimizes MSE to the reference score, so it does not independently establish alignment. Without out-of-sample evaluation or a comparison on a holdout set, the performance advantage over baselines in Table 1 is not convincing.
  4. [Section 3.2, Corollary 3.4 and Appendix A] The paper states that the optimization is solved by gradient descent over samples, but Appendix A, which promises to describe 'the numerical solution to the convex optimization problem,' contains only the LLM prompts. Details such as the step size, number of iterations, initialization, convergence criteria, and how the constraints are enforced (e.g., projected gradient vs. penalty) are missing. Without these, the reported numbers in Table 1 cannot be reproduced or checked.
minor comments (4)
  1. [Section 5.2] The Pearson correlation of 0.5540 between Instructor Score and LLM-Judge Score is described as 'high'; by the thresholds given in Section 5.1, this is a moderate correlation, so the wording should be adjusted.
  2. [Section 2.1, Definition 2.4] The formula for the V-shaped scoring rule divides by (1-p) and is undefined at p=1; also the range [0,1/2] is claimed but the symmetric case for p∈(1/2,1] is only described in words. A complete piecewise definition would be clearer.
  3. [Section 3.2, Program 2] The objective uses 's' as the reference score; earlier the paper says reference scores are normalized to [0,1], but Section 5.1 states instructor scores are in [0,10]. Please clarify the normalization used in the objective and in Table 1.
  4. [Section 5.3, Footnote 3] There is a typo 'becausre'. Also, the description of how Spearman correlation is computed for the baselines versus ASR could be more explicit, since the footnote says the evaluation differs from Wu & Hartline (2024).

Circularity Check

1 steps flagged · score 4.0 of 10

ASR's alignment metrics restate its own objective; properness constraints and baseline comparisons keep the core derivation from being fully tautological.

  1. fitted input called prediction [Section 3.2, Program 2; Section 5.3 'Nearly-Identity Linear Fit' and Table 1]
    "min {S_i}_{i∈[m]} E_{(r,θ,s)}[(Σ_{i∈[m]} S_i(r_i,θ_i) − s)^2] (Program 2). 'Our optimization objective minimizes the mean squared error (MSE) between ElicitationGPT score and the reference score (e.g. instructor score).' 'The first criterion to evaluate the effectiveness of our approach is to examine whether our ASR can effectively fit the original reference scores. Figure 4 illustrates the joint empirical distribution of the ASR scores and the reference scores, with a regression line predicting the reference score s from the ASR score S.'"

    Program 2 defines ASR as the minimizer of squared error to the reference score. The Section 5.3 evaluation then presents that same squared error (Table 1) and a near-identity regression of the reference on ASR as evidence that ASR 'fits' or 'predicts' the reference. This is the training objective restated, not an independent prediction: the low MSE and near-identity line are forced by the choice of objective. The comparison with non-aligned ElicitationGPT baselines and the independent properness constraints retain substantive content, so the circularity is partial rather than total.

full rationale

The central derivation has a genuine non-circular core: ASR is constrained to be proper (Definition 2.5 constraints in Program 2, inherited from the Wu & Hartline 2024 reduction), and the optimization over that constrained space is an independent theoretical and computational contribution. The empirical headline, however, is partly self-definitional. ASR is by definition the minimizer of MSE to the reference score, so reporting MSE, Pearson, and Spearman against that reference, plus a near-identity regression, is a report of the fitted objective. No train/test split is described, so the Table 1 numbers appear to be in-sample values of the very quantity being minimized. This reduces the 'aligns best with the reference' claim to construction, though not tautologically: the properness constraints and the comparison to non-fitted ElicitationGPT and constant baselines provide independent content. The self-citation of Wu & Hartline (2024) for Theorem 3.2 is load-bearing for the properness guarantee, but it is a stated-assumption theorem rather than a definitional equivalence, so I do not count it as a circular step; its unverified working-paper status is a correctness risk. Two further non-circular correctness risks are flagged: Assumption 2.2 (Know-it-or-not) is asserted from dataset observation without validation, and footnote 1 of Section 3.1 replaces ground-truth ⊥ by a prior draw, which is outside the conditions of Theorem 3.2 whenever the QA oracle outputs 'Neither' on the ground-truth side. These weaken the properness claim but do not make the derivation circular.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The method's guarantees are purchased with three unverified or data-dependent inputs: the know-it-or-not restriction on beliefs, the non-inverting LLM oracle, and the empirical priors and scoring values fitted to the reference data. These are the main uncharged assumptions.

free parameters (2)
  • Empirical priors p_i per summary point = Empirical frequency of summary point i in instructor reviews
    Estimated from the cluster of ground-truth reviews and used both to map a ⊥ report to the prior and in the properness constraints of Definition 2.5.
  • Six scoring values S_i(r, theta) per dimension (optimized) = Solutions of Program 2 by gradient descent
    The ASR score is the minimizer of MSE to the reference score, so the experimental alignment numbers are properties of a fitted function, not an out-of-sample prediction.
assumptions (4)
  • domain assumption Know-it-or-not posterior beliefs (Assumption 2.2): each marginal posterior belief is either 0, 1, or the prior p_i.
    Justifies restricting report space to {0, 1, ⊥} and the simplified properness characterization; if beliefs are continuous, the properness guarantee does not follow from Definition 2.5.
  • domain assumption Question-answering oracle is perfect on the ground-truth side and non-inverting on the report side (Definition 3.1, Theorem 3.2).
    The provable properness of ElicitationGPT and hence ASR depends on Pr[ŕ_i ≠ r_i | R] ≤ 1/2; this is never measured in the experiments.
  • domain assumption The textual state space is adequately represented by m binary summary points produced by the summarization oracle.
    If the summary rubric misses or conflates dimensions, the optimized scoring rule is proper for the wrong state space and alignment can be spurious.
  • standard math Convexity and convergence of gradient descent for Program 2 (Corollary 3.4).
    Objective and constraints are linear or quadratic in the 6m variables; standard convex optimization results apply.

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Cite this review

Pith. "Pith review of Aligned Textual Scoring Rules." pith.science (2026). https://pith.science/paper/LMLCV4HI

@misc{pith2026250706221,
  author       = {Pith},
  title        = {Pith review of: Aligned Textual Scoring Rules},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LMLCV4HI}},
  note         = {Machine review of arXiv:2507.06221}
}
read the original abstract

Scoring rules elicit probabilistic predictions from a strategic agent by scoring the prediction against a ground truth state. A scoring rule is proper if, from the agent's perspective, reporting the true belief maximizes the expected score. With the development of language models, Wu and Hartline (2024) proposes a reduction from textual information elicitation to the numerical (i.e. probabilistic) information elicitation problem, which achieves provable properness for textual elicitation. However, not all proper scoring rules are well aligned with human preference over text. Our paper designs the Aligned Scoring rule (ASR) for text by optimizing and minimizing the mean squared error between a proper scoring rule and a reference score (e.g. human score). Our experiments show that our ASR outperforms previous methods in aligning with human preference while maintaining properness.

Figures

Figures reproduced from arXiv: 2507.06221 by the authors.

Figure 1
Figure 1. The V-shaped scoring rule, the optimal scoring rule in Li et al. (2022). The [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. An example of a single-dimensional scoring rule for know-it-or-not reports. Each report in the [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Joint distribution (instructor score vs. LLM-Judge score) [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Reference Scores vs. ASR: The green dotted line represents the linear regression fitting reference score from ASR. On both plots, the linear relationship is almost the identity function. (a) Reference: Instructor Score Method Squared Loss Pearson Corr Spearman Corr ASR…
Figure 5
Figure 5. Figure 5: The visualization of ASR on one assignment in the algorithm class using instructor score as the reference. The score of r = ⊥ for each dimension has been shifted to zero. 13 [PITH_FULL_IMAGE:figures/full_fig_p013_5.png]
Figure 6
Figure 6. Figure 6: Joint distribution (instructor score vs. LLM-Judge score using [PITH_FULL_IMAGE:figures/full_fig_p022_6.png]
Figure 7
Figure 7. Figure 7: Reference Scores vs. ASR: The green dotted line represents the linear regression fitting reference score from ASR. On both plots, the linear relationship is almost an identity function. 23 [PITH_FULL_IMAGE:figures/full_fig_p023_7.png]

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Scoring Rules! Statistical and Strategic Alignment for Text Evaluation Metrics

    cs.AI 2026-08 conditional novelty 6.0 of 10

    Statistical alignment with human ratings does not imply strategic alignment: LLM-as-a-Judge is highly correlated but easily manipulated, while a new statement-level mutual-information metric is robust to manipulation.

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32 extracted references · 32 canonical work pages · cited by 1 Pith paper

  1. [1]

    Carefully read the entire review comment

    work page

  2. [2]

    These should be comments that assess the quality, strengths, weaknesses, and suggestions

    Extract all evaluative statements from the review. These should be comments that assess the quality, strengths, weaknesses, and suggestions. Ignore purely descriptive or meaningless statements. Ignore statements purely about specific scores and ratings

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  3. [3]

    Each entry should be a single sentence in a single line containing a distinct evaluation from the review

    Create an indexed list of these evaluative statements. Each entry should be a single sentence in a single line containing a distinct evaluation from the review. - You should clearly convey the sentiment behind an evaluative statement

    work page

  4. [4]

    Split and Rewrite each evaluative statement into several abstract and concise statements, abandoning the specific expression

    After creating the indexed list. Split and Rewrite each evaluative statement into several abstract and concise statements, abandoning the specific expression. - Make your entry abstract and concise. - Always use ”part A / B / C” in the output to refer parts, even if the input says ”part a / b / c” or ”part 1 / 2 / 3”. - If an evaluative statement contains...

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  5. [5]

    Maintain the same subject matter and key elements of the original statement

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  6. [6]

    Change the emotional tone or sentiment to its opposite (e.g., positive to negative, approval to disapproval)

    work page

  7. [7]

    Use similar language structure when possible, but modify words to reflect the opposite sentiment

    work page

  8. [8]

    Ensure the new statement is coherent and makes sense in isolation

    work page

Show all 32 references
  1. [9]

    Make the new statement as concise as possible. Here is the list of evaluative statements: <evaluative statements> EV ALUATIVESTATEMENTS </evaluative statements> For each statement in the list, create an opposite version following the guidelines above. Present your results in t...

  2. [10]

    First, read the list of opinion pairs provided: <opinion pairs>OPINION PAIRS</opinion pairs>

  3. [11]

    Pairs in the same cluster should address roughly the same aspects of the subject matter

    Next, cluster the unique pairs based on their similarity in topic or theme in <clustering> tag. Pairs in the same cluster should address roughly the same aspects of the subject matter. Follow these steps:

  4. [12]

    Each cluster description must be specific: - You should cluster opinion pairs discussing different parts in different clusters

    You need to first draft a set of cluster descriptions in the <draft> tag. Each cluster description must be specific: - You should cluster opinion pairs discussing different parts in different clusters. - The description should clearly indicate the target of evaluation, avoidin...

  5. [13]

    Split clusters that contain more than one parts or aspects

    Then, based on these descriptions, analyze the following aspects in the <analysis> tag: - Splitting and merging clusters: Merge clusters that are redundant. Split clusters that contain more than one parts or aspects. - New clusters: Look for opinions that are not covered by an...

  6. [14]

    After completing this analysis, redefine the cluster descriptions based on your findings and repeat the entire process

  7. [15]

    You should follow this output format: <clustering> <epoch 1> <draft>[Your draft cluster descriptions] </draft> <analysis>[Your analysis here]</analysis> </epoch 1> <epoch 2>

    Perform this iteration a total of four times, wrapping the results of each iteration inside <epoch i> tags, where i represents the iteration number. You should follow this output format: <clustering> <epoch 1> <draft>[Your draft cluster descriptions] </draft> <analysis>[Your a...

  8. [16]

    For each cluster, generate an opinion pair as the cluster representative

    Complete your final cluster descriptions. For each cluster, generate an opinion pair as the cluster representative. - Ensure the opinion pair discusses exactly the core idea of the cluster description. - The opinion pair should be brief and omit details. - Do not use ”need” or...

  9. [17]

    Reprint the index of the opinion pair in <index> tag

  10. [18]

    Copy the text of the opinion pair in <opinion pair> tag

  11. [19]

    Carefully read and understand both the positive and negative opinions

  12. [20]

    For each relevant statement, determine whether it supports the positive opinion, the negative opinion, or neither, and specify whether the support is explicit or partial

    List all possibly relevant statements in the comment one by one in the <statements> tag. For each relevant statement, determine whether it supports the positive opinion, the negative opinion, or neither, and specify whether the support is explicit or partial. - Focus on the or...

  13. [21]

    - If their are conflicts, classify as the direction with stronger support

    Apply the following rules to determine the final conclusion in the <rubric> tag: - If only one direction is supported, classify as that direction, even if it is only partially supported. - If their are conflicts, classify as the direction with stronger support. - If no stateme...

  14. [22]

    - Only contain ”Positive”, ”Negative”, or ”Neither” in the tag! Do not use words like ”Correct”, ”Incorrect”, ”Clear”, ”Unclear”

    Restate your choice of whether the review supports the positive, the negative, or neither in the <conclusion> tag. - Only contain ”Positive”, ”Negative”, or ”Neither” in the tag! Do not use words like ”Correct”, ”Incorrect”, ”Clear”, ”Unclear”. Present your analysis and conclu...

  15. [23]

    Express the same aspect across different parts as separate points

    Identify the points in the instructor’s review in the <evaluation process> tag. Express the same aspect across different parts as separate points. For each point in the instructor’s review:

  16. [24]

    Reprint the text of this point from the instructor’s review

  17. [25]

    - Objective content includes factual assessments, such as the correctness of the assignment or proofs

    Judge whether the content of this point is subjective or objective. - Objective content includes factual assessments, such as the correctness of the assignment or proofs. - Subjective content includes aspects like clarity or style

  18. [26]

    - Consider subjective elements and minor discrepancies less impactful on the overall score

    Identify the importance of this point: - Give more weight to critical elements like the correctness of the assignment or proofs. - Consider subjective elements and minor discrepancies less impactful on the overall score

  19. [27]

    Extract all relevant text of this point from the peer review

  20. [28]

    Content: Does the peer review cover the same main topics of this key point? b

    Assess the following aspects: a. Content: Does the peer review cover the same main topics of this key point? b. Accuracy: Are the peer reviewer’s observations and critiques accurate when compared to the instructor’s key point? c. Depth: Does the peer review provide an appropri...

  21. [29]

    Judge the overall quality of the peer review on this point

  22. [30]

    - highlighting the alignments or misalignments between the peer review and the instructor’s review

    According to your evaluation, offer a comprehensive assessment of this peer review in the <assessment> tag, supported by justification. - highlighting the alignments or misalignments between the peer review and the instructor’s review. - Taking into account both the importance...

  23. [31]

    - 0-1: Totally wrong or meaningless review: The review is irrelevant, incoherent, or shows a complete misunderstanding of the material

    After the assessment, first provide your reasoning, then assign a score from 0 to 10 based on the rubric, enclosed in the <scoring> tag. - 0-1: Totally wrong or meaningless review: The review is irrelevant, incoherent, or shows a complete misunderstanding of the material. - 2-...

  24. [32]

    Output your final score again in the <final score> tag, with only the number. Present your final evaluation in the following format: <evaluation process>Point 1: [Description] - Instructor’s review: [Reprint text of this point from the instructor’s review] - Objective/subjecti...

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