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REVIEW 4 major objections 7 minor 74 references

LittleLearner: Language Models Under Pedagogically Controlled Knowledge Exposure

T0 review · 4 major / 7 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read The paper argues that a model's pretraining knowledge boundary, set by a K-5-filtered corpus, acts as a hard ceiling that scaling, post-training, and in-context learning cannot break through.

desk verdict A genuinely useful controlled-exposure resource whose strongest claim about the ceiling on post-training and ICL is still entangled with the post-hoc MathCAMPS evaluation filters. read the letter →

arxiv 2608.13545 v1 pith:5H2R2DL2 submitted 2026-08-13 cs.CL cs.AIcs.LG

Fanfei Li , Jana Zeller , Manuel Prada-Corral , Thaddäus Wiedemer , Prasanna Mayilvahanan , Ryan Cotterell , Wieland Brendel This is my paper · ORCID
classification cs.CLcs.AIcs.LG
keywords pretrainingdatafilteringknowledgeboundarycurriculum-constrainedcorpuscontrolledexposurepost-trainingin-contextlearningmodelscalingK-5education
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 establish that a language model's pretraining distribution, not later interventions, sets the boundary of what it can do. To show this, the paper constructs an 88B-token corpus restricted to U.S. kindergarten through grade 5 (K-5) material and trains a 5B-parameter model, LittleLearner, entirely on it. Across scaling, supervised fine-tuning followed by GRPO post-training, and few-shot in-context learning, the model improves within its K-5 scope but does not meaningfully move beyond it. If right, this gives researchers a controlled sandbox for studying knowledge acquisition, because prior exposure is known exactly rather than inferred after the fact.

What carries the argument

The mechanism that carries the argument is the multi-stage LittleCurriculum filter, which turns a large web-scale educational corpus into a sharply bounded K-5 corpus. It works in layers: an age-of-acquisition prefilter with frequency-based imputation removes texts whose vocabulary is learned after age 12; a lightweight text classifier and then a stronger classifier, trained on LLM-as-judge annotations grounded in curriculum standards, assign grade bands; a symbolic regular-expression stage removes mathematical notation such as equations, exponents, and integrals; and a final frequency-sampling stage drops documents concentrated with beyond-K-5 terms. Validation on a held-out curriculum-aligned benchmark and an external grade-labeled corpus is what makes the boundary interpretable and grounds the ceiling claims.

What would settle it

Train a matched 5B model on a version of the released corpus spiked with a small, measured fraction of grade-8 mathematics content, for example 1%, then evaluate it on the paper's grade-8 math questions. If accuracy stays at the original model's floor, the ceiling is not caused by content exposure alone; if it rises, the paper's attribution of the ceiling to the pretraining filter is falsified.

Watch

Extended reading notes

Core claim

The paper's central claim is that a deliberately restricted pretraining corpus creates a sharp, interpretable capability boundary, and that the boundary is set by the filter that built the corpus rather than by the model or by subsequent training. LittleLearner answers grade-school questions comparably to an unfiltered control, but on questions beyond grade 5 it collapses, producing plausible but wrong answers such as describing an out-of-scope quantum mechanics thought experiment as a literal cat with fabricated attributes. Scaling the model from 0.6B to 5B parameters improves in-scope and boundary performance but leaves grade-8 math at floor; SFT followed by GRPO post-training, even when the post-training data are unfiltered, does not close the gap; and few-shot demonstrations with hand-written reasoning traces give at most a small in-scope boost. The paper reads the consistent pattern as evidence that the pretraining filter, not the intervention, sets the effective capability ceiling in these tested settings.

Load-bearing premise

The filtering pipeline's measured leakage rates on validation sets, near-zero beyond-K-5 retention, 2.48% on an external corpus, and 0.09% phrase matches, are representative of the actual 88B-token corpus, so that the K-5 boundary is genuinely clean.

Editorial extensions

If this is right

  • A model trained under K-5 exposure performs on par with an unfiltered model on in-scope math and factual questions, so the filtering does not destroy elementary competence.
  • Increasing model parameters from 0.6B to 5B yields strong in-scope gains but leaves fully out-of-scope grade-8 performance at floor, so scale does not by itself extend the knowledge boundary.
  • SFT plus GRPO post-training lifts in-scope math accuracy for both the restricted and unfiltered models but does not close the beyond-K-5 gap, even when the restricted model is post-trained on unrestricted data.
  • Few-shot in-context learning with hand-written chain-of-thought examples can steer output format but does not unlock new out-of-scope reasoning for this 5B model.
  • For the tested settings, the pretraining filter, not the later intervention, is the effective capability ceiling.

Reading between the lines

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

  • The same design can be reused to test whether other post-training paradigms, such as long-horizon reinforcement learning, verifier-guided search, or retrieval, can genuinely introduce new capabilities rather than elicit latent ones, since the model's prior is fully known.
  • The K-5 boundary is a content boundary, not a human-developmental claim; the model's skill ordering differs from curriculum progression, so any prerequisite reasoning should be tested against the filter's actual content rather than grade-level labels.
  • The ceiling result may be scale-dependent: at frontier scales with stronger in-context learning, the same filter might show more boundary flexibility, so the sandbox should be re-run at larger sizes before generalizing to all language models.
  • A direct way to test the mechanism is to spike a small fraction of out-of-scope math content into a filtered corpus and measure whether grade-8 accuracy rises; if it stays at floor, the ceiling is not solely about content exposure.
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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 / 7 minor

Summary. The paper introduces LITTLECURRICULUM, an 88B-token pretraining corpus derived from FineWeb-Edu and filtered to U.S. elementary-school (K-5) content via a multi-stage pipeline (Age-of-Acquisition pre-filtering, LLM-as-a-judge annotation with FastText/ModernBERT classifiers, symbolic filtering, and frequency sampling), together with LITTLELEARNER, a 5B-parameter model trained from scratch on this corpus. The filter is validated on CommonCoreText (0% Beyond-K-5 retention), on the external WeeBit corpus (2.48% retention), and via a 126-term n-gram audit of the retained corpus (0.09% of passages). LITTLELEARNER performs comparably to an unfiltered control within K-5 across language-complexity (CLEAR), math-familiarity (CoMTA), fact-retrieval (Jeopardy), and math-reasoning (MathCAMPS) measures, while degrading on Beyond-K-5 content. Three intervention studies—model scaling from 0.6B to 5B, SFT+GRPO post-training, and few-shot in-context learning—improve in-scope performance but do not close the Beyond-K-5 gap, and the paper concludes in Section 4.4 that the pretraining filter, rather than any tested intervention, sets the effective capability ceiling. The authors release the corpus and model as a developmentally restricted sandbox for controlled-exposure research.

Significance. The work is significant as a community resource: if the K-5 boundary is as clean as claimed, LITTLECURRICULUM and LITTLELEARNER enable controlled studies of knowledge acquisition, transfer, post-training, and in-context learning that are otherwise confounded by unknown pretraining exposure. Strengths include the release of corpus and model, a precision-first filter with staged validation, an external WeeBit check and a corpus-level n-gram audit, matched baselines for the main comparisons, honest disclosure of boundary fuzziness (e.g., the non-monotonic skill orderings in Section C.2.2), and careful pass@k analysis showing that the Beyond-K-5 gap persists at high sampling budgets. The headline negative result—that scaling, SFT+GRPO, and ICL amplify in-scope capability but do not extend the boundary—is interesting, falsifiable, and useful even if later work qualifies it. The main risk is that the intervention results rest on a single benchmark whose Beyond-K-5 split is partly constructed post hoc in Section C.2.1.

major comments (4)
  1. [§4.4 and §C.2.1] The central claim of Section 4.4—that 'the pretraining filter, rather than the intervention, sets the effective capability ceiling'—is evaluated on MathCAMPS, but the Beyond-K-5 split used in Figures 7-9 is constructed by the post-hoc filters of Section C.2.1. In particular, standard 6.EE.B.7 is excluded explicitly because its items are 'structurally indistinguishable from grade-3 add/sub word problems,' which is precisely the class of crossover items where a K-5-pretrained model with post-training or ICL might most plausibly show out-of-scope gains, and standards with fewer than 30 unique gold answers (including perfect squares, cubes, and cube roots, which are grade-8 content) are dropped. Excluding these items from the aggregate Beyond-K-5 score makes the ceiling look harder than the pretraining filter alone would produce, so the attribution in Section 4.4 is not separable from the evaluation filter. The authors should report the aggregate Beyond-K-5 numbers for the scaling, post-training, and ICL experiments with 6.EE.B.7 re-included and, ideally, with the low-entropy standards re-included, as a sensitivity analysis.
  2. [§4, Figures 7-9] The three intervention claims are tested on a single benchmark: MathCAMPS. The Jeopardy, CLEAR, and CoMTA experiments characterize the base model's boundary but do not test scaling, post-training, or in-context learning, so the claim that 'each lever ... provides limited gains in Beyond-K-5' is supported by only one evaluation instrument. I ask the authors to run at least one additional Beyond-K-5 evaluation (for example, the Jeopardy or CoMTA protocol) for at least the post-training condition, or, failing that, to narrow the summary and abstract claims to the MathCAMPS setting. This is not a request for exhaustive evaluation, but the single-benchmark basis is thin for the paper's headline negative result.
  3. [§3.3, §B, Figure 7] The UNFILTERED control and the scaling runs are said to share LITTLELEARNER's training recipe, but the token budgets, number of epochs, and total compute for each model are not reported. If UNFILTERED, or the 0.6B and 1.3B models, saw different amounts of data than LITTLELEARNER, the divergences in Figures 3-8 cannot be attributed solely to the K-5 filter, because data quantity is a confound. The paper should state the exact token counts, step budgets, and data mixtures for every model in the comparisons.
  4. [§3.1.6, §A.5, §A.6] CommonCoreText is used during pipeline construction—for rule-based metric selection in Section A.1 and for the LLMJ 'precision-on-validation' prompt optimization in Section A.2—so the 0% Beyond-K-5 retention on CommonCoreText is a development-set result rather than an independent validation; the Figure 2 caption discloses this role, but the main text of Section 3.1.6 presents it as validation. The genuinely independent checks (WeeBit at 2.48% retention with 0.05% genuinely out-of-scope after manual inspection, and the 126-n-gram corpus scan at 0.09%) are reassuring but narrow relative to the claim that the 88B-token corpus respects the K-5 boundary. I recommend an additional corpus-level audit, such as a broader grade-6+ vocabulary or classifier-based scan of the released corpus, or an explicit statement of what the 126-n-gram audit can and cannot detect.
minor comments (7)
  1. [§3.3.1] The sentence 'This divergence can be attributed to pretraining data, since UNFILTERED shares LITTLELEARNER's training recipe but Gemma 2B's BPB' is garbled and should be rephrased.
  2. [§4.2 and Figure 8] The text claims 'no difference between LITTLELEARNER post-trained on K-5 data versus Beyond-K-5 data' in Beyond-K-5 performance, but Figure 8's legend ('Pretrain / Post-training K-5 / Unfiltered') does not clearly show the K-5-versus-unfiltered GRPO ablation; the figure should label each condition explicitly so the claimed null result is visible.
  3. [§3.1.2] The paper does not state how many samples were LLMJ-annotated or the accuracy of the trained FastText and ModernBERT classifiers on held-out LLMJ labels; these numbers are needed to assess classifier quality and to reproduce the pipeline.
  4. [§3.1.5 and §A.4] The frequency-sampling stage is underspecified: the minimum frequency threshold, the blocklist size, and the downsampling rule are not reported, even though this stage removes documents from the final corpus and could affect the boundary.
  5. [§C.2.2] The phrase 'diverge framing-dependent at Grade 7' is ungrammatical and should be rewritten, for example as 'diverge depending on the framing of the problem at Grade 7.'
  6. [Figure 1] Figure 1 labels 'ln(0) = -1' as an out-of-scope example, but ln(0) is undefined rather than equal to -1; since the paper is about mathematical boundaries, this is a distracting error.
  7. [§4.2 and §3.2] The naming of the post-training data variants is inconsistent between the text ('K-5 data versus Beyond-K-5 data') and the figure legends ('K-5 / Unfiltered'); the authors should use one terminology throughout.

Circularity Check

1 steps flagged · score 2.0 of 10

Minor validation circularity: CommonCoreText is both a construction input and the headline 'held-out' validation set, though external WeeBit and n-gram checks independently support the corpus boundary.

  1. self definitional [Section 3.1.6 and Figure 2 caption]
    "We validate our pipeline using CommonCoreText, a held-out ground-truth dataset constructed from publicly available recommended reading materials and textbooks paired with grade-level labels ... The pipeline successfully reduces the retention of Beyond-K–5 content to 0% ... contrast Figure 2 caption: "CommonCoreText contains CCSS-aligned reading materials (see Section A.5) used during the construction of the filtering pipeline.""

    The paper's headline filter-precision result (0% Beyond-K–5 retention on CommonCoreText) is presented as a held-out validation, yet the Figure 2 caption states that CommonCoreText was used during construction of the filtering pipeline. Section A.1 confirms this: CommonCoreText was used to select AoA as the pre-filter metric, making the 0% retention on that benchmark partly a self-consistency check rather than an independent test of the boundary. The circularity is limited because the paper separately reports external support: WeeBit retention of 2.48% with manual inspection, and a corpus-wide n-gram audit finding matches in only 0.09% of retained passages.

full rationale

The paper's central interventions (scaling, SFT+GRPO, ICL) are tested on external benchmarks, chiefly MathCAMPS, CLEAR, CoMTA, and Jeopardy, and the results come from models trained from scratch under filtered versus unfiltered corpora. The claim that the pretraining filter sets the capability ceiling is an empirical finding of that controlled comparison, not an equation-level reduction of the output to its input. The MathCAMPS post-hoc filters (Section C.2.1) remove low-entropy items, gold-string-in-question items, and standard 6.EE.B.7, but those filters are applied identically to LITTLELEARNER and UNFILTERED and are not fitted to the intervention outcomes, so they do not make the ceiling claim tautological; at most they narrow the tested Beyond-K–5 band, which is a validity caveat rather than circularity. The one genuine circular step is the CommonCoreText validation overlap: the corpus is described as held out while the figure caption and Section A.1 show it was used during pipeline construction. Because the external WeeBit and n-gram checks provide independent support for the corpus boundary, and because the capability experiments are self-contained against external benchmarks, the overall circularity score is low (2). Self-citations in Section 2 motivate the framing but are not load-bearing for the empirical results.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

The central boundary results rest on the filtering pipeline's precision, which depends on hand-chosen thresholds (AoA age, symbol patterns, blocklists) and on domain assumptions linking curriculum standards to model knowledge. The model and corpus are released artifacts, not new physical entities.

free parameters (7)
  • AoA age threshold = 12 years
    Documents in which more than 5% of words have AoA above 12 are dropped (Section 3.1.1); chosen for precision, not derived.
  • AoA imputation model = linear coefficients of log Zipf frequency on AoA
    Missing AoA values for about 10% of vocabulary are imputed using a linear model trained on the Kuperman et al. AoA data (Section 3.1.1).
  • LLMJ prompt set and grade bands = four grade bands (K-5, 6-8, 9-12, OOS)
    The LLM-judge classifies samples into these bands; prompts were optimized with DSPy/OpenEvolve, with ties broken toward higher grade (Section A.2).
  • Classifier decision thresholds = not reported
    FastText and ModernBERT classifiers are trained on LLMJ labels, but the operating thresholds for retention are not given in the paper (Sections 3.1.2 and 3.1.3).
  • Symbolic filter pattern set = fixed regex list, e.g., equations, exponents, roots
    Documents are dropped upon any match to chosen notation families (Section 3.1.4).
  • Frequency sampling blocklist thresholds = not reported
    Terms with positive contrastive log-ratio are blocklisted, and documents containing them are downsampled to reach the 88B-token target (Section 3.1.5).
  • MathCAMPS evaluation filters = drop standards with <30 unique gold answers; drop questions with verbatim gold answer; exclude 6.EE.B.7
    Post-hoc filtering of the evaluation set in Section C.2.1 affects the reported Beyond-K-5 accuracy.
assumptions (6)
  • domain assumption AoA scores are a valid proxy for the grade level of a document's content.
    Used as the first filter stage to align texts with age bands (Section 3.1.1).
  • domain assumption Common Core State Standards and NGSS define the K-5 knowledge boundary.
    Used to construct LLMJ prompts, to curate CommonCoreText, and to split Jeopardy and MathCAMPS into in-scope and out-of-scope (Sections 3.1, 3.3, C.2).
  • domain assumption FineWeb-Edu contains enough K-5 material to serve as the source corpus.
    The 88B-token corpus is filtered from FineWeb-Edu (Section 3.1).
  • domain assumption Bits-per-byte on unseen text reflects the model's familiarity with that content.
    Used in CLEAR and CoMTA validation to claim unfamiliarity beyond K-5 (Section 3.3.1).
  • domain assumption LLM-judge annotations by Gemini 3 Flash are accurate enough to train the downstream classifiers.
    Single-judge setup is used after ablations; no human agreement rate is reported (Section A.2).
  • domain assumption Pass@k with k up to 1024 is sufficient to expose latent capabilities.
    Used to conclude that the Grade-8 plateau is a capability ceiling, not a sampling artifact (Section C.2.3).

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Cite this review

Pith. "Pith review of LittleLearner: Language Models Under Pedagogically Controlled Knowledge Exposure." pith.science (2026). https://pith.science/paper/5H2R2DL2

@misc{pith2026260813545,
  author       = {Pith},
  title        = {Pith review of: LittleLearner: Language Models Under Pedagogically Controlled Knowledge Exposure},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5H2R2DL2}},
  note         = {Machine review of arXiv:2608.13545}
}
read the original abstract

Modern language models are trained on heterogeneous web-scale text corpora. Consequently, studying knowledge and skill acquisition is difficult, as prior exposure to related content is hard to characterize. To address this challenge, we introduce LITTLECURRICULUM, a curated 88B-token pretraining corpus tailored to U.S. elementary school material, explicitly excluding concepts, facts, and vocabulary taught above Grade 5. Training a 5B-parameter LLM from scratch on LITTLECURRICULUM yields LITTLELEARNER, a model with sufficient language competence for open-ended evaluation, yet with clear knowledge and capability boundaries mapped to interpretable curriculum guidelines. We release LITTLECURRICULUM and LITTLELEARNER as a developmentally restricted sandbox to study how models acquire, represent, and use data under a well-defined training scope. We illustrate the sandbox's utility in a first suite of experiments on injecting new knowledge through post-training and in-context learning. These methods let LITTLELEARNER better utilize existing knowledge, but do not raise out-of-scope capabilities. Our findings underscore the value of this controlled environment for future investigations.

Figures

Figures reproduced from arXiv: 2608.13545 by the authors.

Figure 1
Figure 1. LITTLECURRICULUM and LITTLELEARNER provide a pedagogically grounded sandbox for studying model behavior under precise data constraints. LITTLECURRICULUM is an 88B-token pretraining corpus filtered from FineWeb-Edu [1] to only contain elementary school (K–5) data. On it, we train a 5B model: LITTLELEARNER. Together, they form a well-curated sandbox to study scaling, post-training, educational science and more. ∗Equal… view at source ↗
Figure 2
Figure 2. The filtering yielding LITTLECURRICULUM conservatively enforces the K–5 boundary. Per-stage retention of K–5 and Beyond-K–5 documents on CommonCoreText (left) and WeeBit (right). CommonCoreText contains CCSS-aligned reading materials (see Section A.5) used during the construction of the filtering pipeline. WeeBit is an external benchmark with grade-level labels. On both benchmarks the pipeline achieves a Beyond-K–5 … view at source ↗
Figure 3
Figure 3. LITTLELEARNER is increasingly un￾familiar with more difficult text, as shown by increasing bits-per-byte (BPB) [46] on CLEAR [44]. Samples are binned by the peda￾gogical Bradley-Terry easiness score [45]. Elementary Algebra Trigonometry Calculus 1.4 1.6 1.8 2.0 2.2 BPB (↓ better) LittleLearner Unfiltered Gemma 2B [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (12 more)
Figure 5
Figure 5. Figure 5: LITTLELEARNER answers K–5 sci￾entific questions but collapses on Beyond-K– 5. Pass@1 accuracy on Jeopardy science ques￾tions [48] split by NGSS-aligned grade scope. K 1 2 3 4 5 6 7 8 Grade 0 20 40 60 80 100 Accuracy ↑ LittleLearner Unfiltered Gemma 2B [PITH_FULL_IMAGE…
Figure 7
Figure 7. Figure 7: Scaling model parameters help performance within K–5, and at the boundary, but does not recover performance well in Beyond-K–5 Performance of three differently sized LITTLELEARNERs and UNFILTERED models on MathCAMPS. Shaded regions correspond to 95% CIs. See [PITH_FUL…
Figure 8
Figure 8. Figure 8: Post-training on unfiltered content increases K–5 capabilities but does not overcome the Beyond-K–5 gap Performance on MathCAMPS for LITTLELEARNER and UNFILTERED and their post-trained versions after SFT and GRPO. Whiskers represent 95% CIs. Direct Few-shot Explanation…
Figure 9
Figure 9. Figure 9: In-context learning does not recover Beyond-K–5 capabilities LITTLELEARNER evaluated on MathCAMPS with Few Shot evaluation (giving three example traces for each problem category) slightly improves K–5 performance, but not Beyond-K–5. Adding explanations has no effect o…
Figure 10
Figure 10. Figure 10: Age-of-Acquisition gives the clearest signal for underlying Grade band Evaluating different rule-based metrics on our CommonCoreText reveals that AoA is the best fit. K5 refers to K–5, K8 to middle school, K12 to high school and OOS to out-of-scope, i.e. beyond school…
Figure 11
Figure 11. Figure 11: At higher word coverage Word Freq Zipf gives the best trade-off between more word coverage and alignment to AoA A.2 LLM-J LLM-J Setup Our LLM-J pipeline classifies a text snippet into one of four grade bands (elementary school, middle school, high school, out-of-scope…
Figure 12
Figure 12. Figure 12: No tested LLM-J method on Gemini 3 Flash vastly outperforms any other Since no tested LLM-J method vastly outperforms the others, we train classifiers on different labeled datasets and go with the setup yielding the best performing classifier. Refer to [PITH_FULL_IMA…
Figure 13
Figure 13. Figure 13: The single-judge Gemini setup (1) outperforms cross-model agreement on both accuracy (↑) and under-classification (↓) 0 5 10 15 20 25 30 Under-classification (%) 25 30 35 40 45 50 Accuracy (%) 1 2 3 4 5 6 K 5 (elementary) 6 8 (middle school) 9 12 (high school) OOS 0 2…
Figure 14
Figure 14. Figure 14 [PITH_FULL_IMAGE:figures/full_fig_p018_14.png]
Figure 15
Figure 15. Figure 15: LITTLELEARNER diverges more strongly on higher grade arithmetic problems (left); LITTLELEARNER and UNFILTERED do not follow CCSS learning paths (right) LITTLELEARNER and UNFILTERED evaluated at pass@1 (estimated from 1024 samples) on MathCAMPS along learning paths in …
Figure 16
Figure 16. Figure 16: The gap between LITTLELEARNER and UNFILTERED on Beyond-K–5 remains stable for higher sampling budgets Performance of LITTLELEARNER and UNFILTERED on MathCAMPS at higher pass@k. Shaded regions indicate 95% CIs. that more K–5 aligned framing does help LITTLELEARNER’s pe…
Figure 17
Figure 17. Figure 17: Scaling model parameters help performance within K–5, and at the boundary, but does not recover performance well in Beyond-K–5 Performance of three differently sized LITTLELEARNERs and UNFILTERED models on MathCAMPS. Shaded regions correspond to 95% CIs. C.2.3 Pass@k …

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.