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REVIEW 5 major objections 5 minor 1 cited by

Beyond Data Scarcity: A Frequency-Driven Framework for Zero-Shot Forecasting

T0 review · 5 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

Pith's one-line read Synthetic sine waves beat real data for zero-shot forecasts

desk verdict Plausible and useful empirical claim—synthetic harmonic training can beat real data—but the 'only sampling rate' framing is weakened by test-informed tuning of the anchor and harmonic count. read the letter →

arxiv 2411.15743 v1 pith:BSMMKZZA submitted 2024-11-24 cs.LG cs.AI

classification cs.LGcs.AI
keywords zero-shotforecastingfew-shotlearningsyntheticdatagenerationFourieranalysisperiodogramfrequencygeneralizationconfusiontimeseries
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 argues that deep forecasting models—both large foundation models and ordinary networks—struggle in the same systematic way: they get worse when the training set contains many frequencies beyond the target's (frequency confusion), and they fail to generalize to frequencies they never saw during training (poor frequency generalization). To exploit this diagnosis, the authors propose Freq-Synth, a synthetic-data generator that, given only the sampling rate of the target series, builds training examples from sums of sine waves whose frequencies are the fundamental and its harmonics. Trained on just 5,000 synthetic samples, several models achieve lower error than when trained on roughly a thousand times more real data, beating real-data training on 6 of 8 zero-shot benchmarks and improving few-shot fine-tuning as well. If this holds, zero-shot forecasting no longer demands vast corpora or huge foundation models.

What carries the argument

The load-bearing tool is the scaled periodogram, $P(\omega_j) = A_j^2$, which the paper uses to quantify how much of a signal's variance sits at each frequency, along with the two definitions it introduces: frequency confusion (performance degrades when the training set includes unrelated frequencies) and frequency generalization (ability to forecast unseen frequencies). The generative machinery is the pool of harmonics: given a fundamental frequency $\bar{\omega}$ estimated from the target's sampling rate, Freq-Synth samples frequencies from $\Omega = \{\bar{\omega}, 2\bar{\omega}, \ldots, h\bar{\omega}\}$, draws amplitudes from an exponential distribution and phases uniformly, and forms each variate as the sum of $l$ randomly chosen sines. This construction makes the training spectrum deliberately sparse and aligned with the presumed target spectrum, avoiding the confusion caused by extra frequencies.

What would settle it

Train Freq-Synth on a target series whose periodogram shows two or more comparable dominant peaks not related by integer multiples (e.g., a strong daily cycle plus a strong weekly cycle) and measure zero-shot error against real-data training: if the single-fundamental assumption is load-bearing, Freq-Synth should fail to match real data on such series, just as it already fails on the Exchange dataset.

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Extended reading notes

Core claim

The central claim is that the factor governing effective learning in zero-shot time series forecasting is frequency alignment: a model transfers well when the training data shares the target's dominant periodic components, and poorly when the training data introduces unrelated frequencies or omits the target's fundamental. The paper demonstrates this with controlled sine-wave experiments and periodogram correlations, then turns the diagnosis into a generator: Freq-Synth constructs a pool of sinusoids at the target's fundamental frequency and its harmonics, with random amplitudes and phases, and sums a random subset per variate to form multivariate series. Because it needs only the sampling rate of the target (mapped to a common natural frequency), the method is parameter-light and fast. Empirically, training on Freq-Synth data outperforms training on real data in 6/8 benchmark datasets in zero-shot evaluation, reduces MSE by roughly 10–20% in few-shot fine-tuning across three tested models, and outperforms other synthetic generators while using a fraction of the data.

Load-bearing premise

The method assumes the target series is dominated by a single fundamental frequency, estimated from its sampling rate, and that its harmonics; if the series has a broad or multi-dominant spectrum, the synthetic data cannot represent it and the claimed advantage disappears.

Editorial extensions

If this is right

  • Zero-shot forecasting can be performed with a tiny, fast-to-generate synthetic corpus, removing the need to collect and clean large real-world training sets.
  • Non-foundation models trained on Freq-Synth data can match or beat foundation models on several benchmarks, suggesting compute-heavy pretraining may not be necessary for these tasks.
  • Frequency alignment, not domain identity, is the main driver of transfer success in time series, so dataset selection for training should prioritize periodogram similarity over sector labels.
  • Few-shot fine-tuning also benefits: pre-training on synthetic data then fine-tuning on 10% of the target data outperforms fine-tuning from real-data pretraining on the tested models.

Reading between the lines

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

  • If frequency confusion is as widespread as the paper suggests, the common practice of mixing many heterogeneous datasets for pretraining may actively hurt forecasting performance; a natural extension is to filter or reweight pretraining corpora by periodogram similarity to the deployment frequencies.
  • The closest-common-frequency heuristic for mapping sampling rates to fundamentals could be replaced by a direct periodogram estimate on a handful of target samples, which would extend Freq-Synth to irregularly sampled or non-natural frequencies, as the paper hints in its appendix.
  • The 6/8 success rate may be sensitive to the evaluation suite: applying the same protocol to a broader set of benchmarks with diverse spectral shapes would clarify whether the reported advantage is a general law or specific to this set of eight datasets.
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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

5 major / 5 minor

Summary. This paper proposes a Fourier-analysis view of zero-shot and few-shot time series forecasting, introducing the notions of frequency confusion and frequency generalization, and then presents Freq-Synth, a synthetic data generator that creates sinusoidal training series from the target dataset's sampling rate. The method is evaluated by training six forecasting models (TTM, Timer, UniTime, Moment, GPT4TS, PatchTST) on Freq-Synth data versus a large real-data training pool, on eight LTSF benchmarks, and is compared with other synthetic generators (TimesFM, ForecastPFN, KernelSynth). The authors report that Freq-Synth outperforms real-data training in 6/8 datasets on average MSE/MAE, helps in few-shot fine-tuning, and is substantially cheaper to generate than competing synthetic baselines.

Significance. If the central claims hold, Freq-Synth would be a meaningful practical contribution: a lightweight, easy-to-code synthetic generator that needs only the target sampling rate could reduce the data and compute requirements of zero-shot and few-shot forecasting. The paper's strengths include the breadth of the evaluation (six model families, eight benchmarks, horizon lengths 96-720), the inclusion of a code snippet and an explicit generation-time comparison (0.1 s vs. 138 min for KernelSynth), and the diagnostic experiments on frequency confusion and frequency generalization, which are clearly explained and potentially useful for future work. However, the zero-shot protocol as reported leaves room for target-dependent tuning of the fundamental-frequency anchor and the harmonic count, and one baseline (TimesFM) is a self-implementation; these issues currently limit the strength of the headline 6/8 claim.

major comments (5)
  1. [Sec. 4.2, App. B.1, Table 4] The central zero-shot claim that Freq-Synth needs only the target's sampling rate is not established by the current protocol. Table 4 defines the fundamental frequency as 'depends on dataset, see B.1', and App. B.1 describes only a 'closest common frequency' heuristic without specifying a unique mapping; for example, 15-minute data could be anchored to 1/96, 1/672, or 1/2880, and hourly data to 1/24, 1/168, or 1/720. Because the anchor is chosen per dataset, the comparison in Table 1 may use target-frequency information beyond the sampling rate, information that the real-data baseline does not receive. Please provide a fixed, a priori rule that maps each sampling rate to exactly one fundamental frequency, or restrict the claim accordingly.
  2. [Sec. 5.1, App. C.1, Fig. 5] The harmonic count h is effectively selected using the evaluation benchmarks. The main protocol uses three harmonic groups (h=1,2,3), but Fig. 5 reports MSE on ETTm1, ETTh2, ETTh1, Traffic, Weather, and Electricity as a function of h, and the choice h=3 is justified by those test-set results. Since the real-data baseline has no analogous test-informed tuning, this does not demonstrate a genuine zero-shot advantage. Please specify a fixed h, or a validation-based selection rule, before reporting the 6/8 comparison, and preferably show sensitivity to h with the chosen rule.
  3. [Sec. 5.2, App. D.3] The TimesFM synthetic-data baseline is a self-implementation: App. D.3 states 'we provided results based on our implementation as the original implementation is not available.' The reported 12.7% MSE reduction over TimesFM in the known-sampling-rate block rests on this unvalidated baseline. Please either use the official TimesFM checkpoint, or clearly mark the comparison as an approximation and provide enough implementation detail to reproduce and assess it.
  4. [Tables 1-3] The three-seed averages are reported without standard deviations or confidence intervals. Several per-dataset margins are small (e.g., ETTh2 and ETTm2 in Table 1), and the 6/8 claim is an aggregate statement; without variance information the reader cannot assess whether the observed wins are within noise. Please report seed-wise results or error bars for the main comparisons.
  5. [Sec. 4.2, App. B.4, App. E.1] The assumption that the target distribution is dominated by a single fundamental frequency and its harmonics is acknowledged to fail on Exchange and Weather, and the method's failures on those datasets are explicitly documented. However, the abstract and conclusion state the method improves zero-shot forecasting generally. The stated scope should be narrowed to datasets satisfying the single-fundamental assumption, or the method should be evaluated on a broader set of multi-dominant datasets to determine where the approach breaks down.
minor comments (5)
  1. [App. B.2, Sec. 5.2, Table 7] The method is sometimes called 'Synth-Freq' and sometimes 'Fq-Synth' while the introduction uses 'Freq-Synth'; please use one name consistently throughout.
  2. [Fig. 2] The x-axis labels ('0-0.5', '0.5-0.9', '0.9-', 'first choice second choice 3rd choice') are not explained in the caption; please clarify how the periodogram PCC bins and the 'choice' categories are defined.
  3. [Eq. (2)] The phase formula 'tan^-1(bj/aj)' should specify the quadrant-aware arctangent (atan2) or restrict the phase to a branch, since the standard arctangent does not recover the correct quadrant for all amplitude signs.
  4. [Table 4 vs. Listing 1] Table 4 sets n=50,000 and A'=5, while Listing 1 uses n=250 and A_avg=1; please state which parameter settings produce the reported results and harmonize the code snippet with the table, or explain that the listing is only an illustrative skeleton.
  5. [Sec. 5.2] The sentence 'Freq-Synth trains on a fraction (i.e.,1/14) of the data ForecastPFN, TimesFM, and Synth-Freq use' should state precisely which data volumes are compared and what '1/14' refers to; as written, the comparison is ambiguous.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: Freq-Synth's design choices are empirical inputs, and its claims are tested against held-out real-data benchmarks.

full rationale

The paper's derivation chain is not circular. Freq-Synth constructs synthetic training data from a fundamental frequency derived (App. B.1) from the target sampling rate, and its effectiveness is evaluated by training models on this synthetic data and testing on held-out real-world LTSF benchmarks (Sec. 5.1). The central comparison—synthetic versus real-data training—is an external, falsifiable empirical test: the real-data baselines are trained on Monash and PEMS data, and the evaluation metrics come from the standard test splits, not from the training objective or the generator's parameters. The Sec. 4.1 finding that periodogram alignment aids transfer is itself an empirical measurement on real models, and Freq-Synth implements that observation as a design heuristic rather than defining the target performance in terms of the generator. The paper explicitly acknowledges failure cases (App. B.4 and E.1, e.g., Exchange), which would not be possible if the claimed advantage were forced by construction. The only substantive concern—that the 'closest common frequency' anchor and harmonic count are under-specified and could in principle be tuned using evaluation data—is a protocol-weakness issue, not an equation-level circularity, and the main experiments fix h=1,2,3 (Tab. 4) and use sampling-rate-derived anchors. No load-bearing self-citations or imported uniqueness theorems appear.

Assumptions & free parameters 8 free parameters · 4 assumptions · 0 invented entities

The central method has eight hand-chosen free parameters plus a per-dataset fundamental frequency; no new invented entities. The main domain assumption is spectral dominance by a single fundamental and harmonics.

free parameters (8)
  • A' (expected amplitude of sine waves) = 5 in Table 4; A_avg=1 in Listing 1 code
    Sampled from an exponential distribution; controls amplitude scale. Inconsistent between table and code.
  • m (pool size) = 100
    Number of sine waves in the harmonic pool; hand-chosen.
  • h (maximum harmonic number) = 1, 2, 3 (three datasets)
    Selected from ablation on the same evaluation benchmarks; tuning on test data is a concern.
  • l (sines summed per variate) = 10
    Controls inter-variate correlation; hand-chosen.
  • n (signal length) = 50,000
    Fixed length for generated series; hand-chosen.
  • d (number of variates) = 5
    Number of channels per synthetic sample; hand-chosen.
  • fundamental frequency per target dataset = dataset dependent (e.g., 1/24 hourly, 1/96 15-minute)
    Estimated from the sampling rate via a closest-common-frequency heuristic; this is the key input that encodes target information.
  • Synthetic dataset size = 5,000 train + 5,000 validation samples
    Chosen in Sec. 5.1; ablations show no clear trend with dataset size.
assumptions (4)
  • standard math Every finite real time series can be represented as a sum of sines and cosines (Fourier representation), Eq. 1.
    Used throughout as the analysis and generation basis.
  • domain assumption Target time series are dominated by one fundamental frequency plus a small number of harmonics.
    Stated in Sec. 4.2; Freq-Synth only generates harmonics of a single fundamental.
  • ad hoc to paper Sampling rate maps to fundamental frequency via the closest common natural period (daily, weekly, monthly).
    App. B.1; this heuristic fails for unnatural fundamental frequencies such as 1/100.
  • domain assumption Synthetic harmonic-sine data transfers to real distributions in zero-shot settings.
    The central transfer assumption behind Freq-Synth; supported only empirically and not for all datasets.

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Cite this review

Pith. "Pith review of Beyond Data Scarcity: A Frequency-Driven Framework for Zero-Shot Forecasting." pith.science (2026). https://pith.science/paper/BSMMKZZA

@misc{pith2026241115743,
  author       = {Pith},
  title        = {Pith review of: Beyond Data Scarcity: A Frequency-Driven Framework for Zero-Shot Forecasting},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BSMMKZZA}},
  note         = {Machine review of arXiv:2411.15743}
}
read the original abstract

Time series forecasting is critical in numerous real-world applications, requiring accurate predictions of future values based on observed patterns. While traditional forecasting techniques work well in in-domain scenarios with ample data, they struggle when data is scarce or not available at all, motivating the emergence of zero-shot and few-shot learning settings. Recent advancements often leverage large-scale foundation models for such tasks, but these methods require extensive data and compute resources, and their performance may be hindered by ineffective learning from the available training set. This raises a fundamental question: What factors influence effective learning from data in time series forecasting? Toward addressing this, we propose using Fourier analysis to investigate how models learn from synthetic and real-world time series data. Our findings reveal that forecasters commonly suffer from poor learning from data with multiple frequencies and poor generalization to unseen frequencies, which impedes their predictive performance. To alleviate these issues, we present a novel synthetic data generation framework, designed to enhance real data or replace it completely by creating task-specific frequency information, requiring only the sampling rate of the target data. Our approach, Freq-Synth, improves the robustness of both foundation as well as nonfoundation forecast models in zero-shot and few-shot settings, facilitating more reliable time series forecasting under limited data scenarios.

Figures

Figures reproduced from arXiv: 2411.15743 by the authors.

Figure 1
Figure 1. We show an example of frequency confusion, where adding more frequencies gradually [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Transfer learning performance bars for various frequency-based alignments between the [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. We construct a pool of sine waves that are harmonics to a given fundamental frequency [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: Zero-shot performance of pre-trained models on signals with one and two harmonics (top [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: The influence of the number of harmonics on the ZS performance per dataset, where each [PITH_FULL_IMAGE:figures/full_fig_p016_5.png]
Figure 6
Figure 6. Figure 6: Ablation of dataset size and number of variates. The colorbar represents the average MSE [PITH_FULL_IMAGE:figures/full_fig_p017_6.png]
Figure 7
Figure 7. Figure 7: Forecast depiction of a 1/24 periodic series with different harmonics [PITH_FULL_IMAGE:figures/full_fig_p019_7.png]
Figure 8
Figure 8. Figure 8: Forecast depiction of a 1/25 periodic series with different harmonics [PITH_FULL_IMAGE:figures/full_fig_p020_8.png]
Figure 9
Figure 9. Figure 9: Zero-shot performance of pre-trained models on signals with 1 to 4 harmonics. The models [PITH_FULL_IMAGE:figures/full_fig_p020_9.png]
Figure 11
Figure 11. Figure 11: Top: Periodogram of the frequency range (0, 0.25] for the datasets Exchange, Traffic, and Electricity visualized from left to right. Bottom: A random example from each dataset. tion matrix [PITH_FULL_IMAGE:figures/full_fig_p021_11.png]

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Forward citations

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Reference graph

Works this paper leans on

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    Chronos: Learning the language of time series

    Abdul Fatir Ansari, Lorenzo Stella, Caner Turkmen, Xiyuan Zhang, Pedro Mercado, Huibin Shen, Oleksandr Shchur, Syama Sundar Rangapuram, Sebastian Pineda Arango, Shubham Kapoor, et al. Chronos: Learning the language of time series. arXiv preprint arXiv:2403.07815,

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    Each channel is standardized, according to the LTSF protocol (Nie et al., 2023; Wu et al., 2021; Zhou et al., 2021), however, this may not be required depending on the use case or the model, since many models include instance normalization (Nie et al.,

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    Finding an accurate early forecasting model from small dataset: A case of 2019-nCoV novel coronavirus outbreak

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    A survey on deep learning based time series analysis with frequency transformation

    Kun Yi, Qi Zhang, Longbing Cao, Shoujin Wang, Guodong Long, Liang Hu, Hui He, Zhendong Niu, Wei Fan, and Hui Xiong. A survey on deep learning based time series analysis with frequency transformation. arXiv preprint arXiv:2302.02173,

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    In our implementation, we used a lookback of 96 and a horizon of 720, hence a sample length of 816 was used for training

    From all three comprised datasets, we sample all together 5,000 samples each of the lookback and horizon of interest. In our implementation, we used a lookback of 96 and a horizon of 720, hence a sample length of 816 was used for training. The reason we employ sampling is due to the stationarity of each xj in x, where the same patterns are repeated along ...

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    • Timer (Liu et al., 2024d) employs a GPT-style architecture, originally designed for a range of tasks such as imputation, anomaly detection, and forecasting

    is a pre-trained model with a light-weight architecture which utilizes diverse resolution sampling with the implementation of patches of different 17 lengths and resolution prefix tuning, allowing the model to encode sampling rate specific information. • Timer (Liu et al., 2024d) employs a GPT-style architecture, originally designed for a range of tasks s...

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    For example, TTM’s superior inference speed compared to other models (Ekambaram et al., 2024)

    Performance and time efficiency: these works offer a thorough comparison to other comparable methods and showed better overall performance including faster inference or training time. For example, TTM’s superior inference speed compared to other models (Ekambaram et al., 2024)

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    This training setup is similar to the one employed in (Ekambaram et al., 2024)

    is also included for training. This training setup is similar to the one employed in (Ekambaram et al., 2024). In Tab. 5, we provide details regarding the selected datasets for training and testing. To ensure that certain large datasets do no dominate training, we limit the maximum number of examples per dataset to 500,000 for training and validation. Sel...

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    18 Table 5: Details on the considered datasets. Dataset RepositoryChannelsMin/max channel lengthSampling rate Sector Usage ETTh1 LTSF 7 17,420 hourly Energy EvaluationETTh2 LTSF 7 17,420 hourly Energy EvaluationETTm1 LTSF 7 69,680 15 minutes Energy EvaluationETTm2 LTSF 7 69,68...

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    Each recorded result represents an average of three random seeds

    Training with Real data from Monash and PEMS repos- itories. Each recorded result represents an average of three random seeds. Red and black bolds represents lowest score in the line and lowest score per model respectively. Model TTM Timer UniTime Moment GPT4TS PatchTST Naive ...

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    Known Sampling Rate Unknown Sampling RateFq-SynthFM PFN S-NaiveFq-Synth NatFq-Synth MixKer-SynthFM PFN NaiveMSE MAEMSE MAEMSE MAEMSE MAEMSE MAEMSE MAEMSE MAEMSE MAEMSE MAEMSE MAE PatchTST ETTh1 0.407 0.4100.496 0.4690.816 0.5910.513 0.4340.640 0.5360.709 0.5620.700 0.5530.769 ...

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    For ETTm2 and Weather the results show otherwise, however, for dataset sizes 10,000 and 5,000, a comparable alternative is given for somed >1

    for each dataset size. For ETTm2 and Weather the results show otherwise, however, for dataset sizes 10,000 and 5,000, a comparable alternative is given for somed >1. With respect to the dataset size, our experiments suggest an unclear pattern. For Weather, ETTm1, ETTm2, a smal...

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    We train the baseline models in Tabs

    bench- mark datasets. We train the baseline models in Tabs. 1 and 3 on a subset of datasets from the Monash repository (Godahewa et al., 2021). Specifically, we select the datasets that have a minimum length of 1,000 timesteps, in order to enable a training configuration of ho...

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    UniTime: A language-empowered unified model for cross-domain time series forecasting

    Xu Liu, Junfeng Hu, Yuan Li, Shizhe Diao, Yuxuan Liang, Bryan Hooi, and Roger Zimmermann. UniTime: A language-empowered unified model for cross-domain time series forecasting. In Proceedings of the ACM on Web Conference 2024, pp. 4095–4106, 2024a. Yong Liu, Tengge Hu, Haoran Z...

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    TTMs: Fast multi-level tiny time mixers for improved zero- shot and few-shot forecasting of multivariate time series.arXiv preprint arXiv:2401.03955,

    Vijay Ekambaram, Arindam Jati, Nam H Nguyen, Pankaj Dayama, Chandra Reddy, Wesley M Gifford, and Jayant Kalagnanam. TTMs: Fast multi-level tiny time mixers for improved zero- shot and few-shot forecasting of multivariate time series.arXiv preprint arXiv:2401.03955,

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