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REVIEW 5 major objections 6 minor 27 references

3D Magnetic Inverse Routine for Single-Segment Magnetic Field Images

T0 review · 5 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read A three-stage routine recovers a single wire segment's 3D pose and current from one magnetic field image, avoiding FFT's resolution limit.

desk verdict A plausible single-segment MFI inversion pipeline with one genuinely new closed-form relation, but the benchmark claim outruns an evaluation that is entirely in-distribution simulation. read the letter →

arxiv 2507.11293 v1 pith:WPDA6WLY submitted 2025-07-15 eess.IV cs.CV

J. Senthilnath , Chen Hao , F. C. Wellstood This is my paper · ORCID
classification eess.IVcs.CV
keywords magneticfieldimagingnon-destructivetestingsemiconductorpackagingcurrentreconstructionconvolutionalneuralnetworkpeak-to-peakdistanceparameteroptimization3Dinverseproblem
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 proposes a three-stage 3D Magnetic Inverse Routine (3D MIR) that turns a two-dimensional magnetic field image of a single current-carrying segment into the segment's five physical parameters: starting position, length, vertical depth, and current. The first stage uses a convolutional neural network to estimate the ratio $\beta = \ell/z_o$ and to classify the segment as an x- or y-oriented wire. The second stage converts the measured peak-to-peak field distance into a closed-form depth estimate, which yields initial values for all five parameters. The third stage refines these values with a simplex optimizer that minimizes a pixel-level chi-squared difference between the reconstructed and measured field. The authors report that this recovers the parameters with precision that improves with signal-to-noise and surpasses the lateral resolution of Fourier-transform-based inversion, which they present as a new benchmark for non-destructive testing in semiconductor packaging.

What carries the argument

The load-bearing object is a closed-form relation between the measured peak-to-peak distance $PP$ between the field's maximum and minimum and the unknown ratio $\beta = \ell/z_o$, given as equation (5) of the paper. That relation lets a single CNN prediction of $\beta$ turn an image-level measurement into a concrete depth $z_o$ and length $\ell$, from which the remaining parameters follow from the field extrema and a current estimate. A second CNN classifies x versus y orientation, and a simplex direct-search optimizer minimizes the pixel-level chi-squared objective (12) to refine the five parameters. The forward model is the magnetostatic field of a thin straight current segment, so the whole pipeline inherits the limits of that idealization.

What would settle it

Scan a lithographically patterned straight wire of known length and depth with a magnetic field imager, run 3D MIR, and check whether the recovered $z_o$, $\ell$, and $I$ match the known values within the claimed error; any systematic deviation that grows with wire width or with a parallel neighbor wire would show the thin-wire assumption breaks.

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Extended reading notes

Core claim

The central claim is that a learned scalar prior combined with a closed-form geometry relation makes the single-segment magnetic inverse problem solvable without an exhaustive search. Given only a $B_z$ image, the routine predicts $\beta = \ell/|z-z_o|$ and the segment orientation, then uses the analytic peak-to-peak identity $$PP = |z-z_o|\,\sqrt{(\$\beta$/2)^2+1}\,\sqrt{-1+\sqrt{1+8/((\$\beta$/2)^2+1)}}$$ to compute the depth and hence the length. With depth, orientation, and the field extrema coordinates, the in-plane position and current are fixed by simple formulas, and the five-parameter vector is then polished by a simplex optimizer against a forward model of the straight-wire field. On 500 simulated test images the optimized parameters align with ground truth, errors fall with increasing signal-to-noise, and normalized position errors drop below the established FFT lateral-resolution limit at high signal-to-noise. The orientation classifier reaches 100 percent accuracy on the test set.

Load-bearing premise

The whole pipeline trusts that simulated thin-wire field images with added noise stand in for real magnetic field images from semiconductor packages, so a real sensor's finite wire width, nearby conductors, and noise shape must still obey the closed-form peak-to-peak relation and the CNN's learned mapping.

Editorial extensions

If this is right

  • For single straight wires, the routine yields a complete parameter set (position, length, depth, current) directly from one field image, with no reference image or human expert needed.
  • Parameter errors decrease as signal-to-noise increases, so the method is most reliable on high-signal-to-noise images where defect localization matters.
  • The reported normalized errors drop below the FFT-based lateral resolution limit at high signal-to-noise, suggesting the routine resolves features that Fourier inversion cannot.
  • Because the CNN supplies only a scalar ratio and orientation, the optimizer needs no global search; the reported computation time per image is a few seconds of refinement.
  • The x/y orientation classification is exact on the simulated test set, which removes the main discrete ambiguity of the inverse problem.

Reading between the lines

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

  • If the same peak-to-peak ratio trick can be derived for finite-width or multi-layer conductors, the architecture would extend naturally to full circuit current maps; such an extension is not in this paper but is the obvious next step.
  • The simulated training set uses an idealized thin-wire field with added noise, so accuracy on real magnetic images is an open empirical question; fine-tuning the CNN on measured fields with known ground truth would directly test the transfer.
  • A useful stress test would be to scan a lithographically defined straight wire of known depth and length, apply the routine, and compare recovered parameters; failure on that would indicate the thin-wire model is the limiting assumption.
  • The benchmark claim versus FFT assumes identical sensor geometry and noise; a matched comparison on the same data, rather than reference limits from the literature, would sharpen the claimed advantage.
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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 / 6 minor

Summary. The paper proposes a three-stage algorithm, 3D MIR, to invert a magnetic field image (MFI) of a single current-carrying segment into five parameters (x0, y0, z0, ℓ, I). A CNN predicts the ratio β = ℓ/z0 and the segment orientation (x or y); closed-form spatial constraints provide initial parameter estimates; a Nelder-Mead optimizer refines them by minimizing the pixel-level difference between the measured and reconstructed MFI using a Biot-Savart forward model. The method is evaluated on 500 simulated test images, with scatter plots and qualitative examples suggesting good recovery, and the authors claim it outperforms FFT-based inversion and 'sets a new benchmark.'

Significance. The idea of combining DL for coarse parameter regression, physics-based initialization, and numerical optimization for MFI inversion is plausible and potentially useful for semiconductor NDT. The paper is among the first to propose this combination for 3D MFI reconstruction, and the single-segment problem is a sensible first step. However, the current evidence is limited to a same-simulator test: the data are generated from the same Biot-Savart model used in the optimizer. There are no quantitative error metrics, no same-data comparison with an alternative method, and no real or mismatched data. Thus the claimed significance ('new benchmark') is not yet supported. The work's strength is the clear algorithmic pipeline and the in-distribution demonstration; its weakness is the absence of external validation.

major comments (5)
  1. [Sec. 3.1, Sec. 2.3] The evaluation is an inverse-crime test: the 500 test images are simulated using the same infinitely-thin-wire Biot-Savart model (Eqs. 10–11) that is hard-coded into the forward model of the optimizer (Eq. 12). The paper does not report any test on a mismatched simulator (e.g., finite wire width, sensor averaging, correlated noise) or on real MFI data, and the conclusion (Sec. 4) states that the approach 'will be tested on real MFI data.' The abstract's claim that the method 'sets a new benchmark' is therefore not supported by the evidence in the paper. Please add an out-of-distribution test, a real-data example, or temper the claims to an in-distribution simulation study.
  2. [Sec. 3.3, Figs. 4-5] No quantitative accuracy metric is reported for the parameter recovery. Figures 4(c)-(g) and 5(a)-(b) are scatter plots and error-versus-S/N plots, but no aggregate statistics (e.g., root-mean-square error, mean absolute error, or coefficient of determination) are given for x0, y0, z0, ℓ, or I. In addition, the signal-to-noise ratio in Fig. 4(a) is never defined, and the paper acknowledges failures for 'cases when ℓ is too short' without quantifying the failure rate or magnitude. The central claim of 'high precision' requires reporting these numbers.
  3. [Sec. 2.1, Eq. (3)] The peak-to-peak relation in Eq. (3) is stated without derivation. This formula is the basis for the initial estimation of z0 and ℓ (Eqs. 5–6), and without a derivation or a reference the reader cannot assess its range of validity or approximation error. The derivation from Eq. (10) should be supplied.
  4. [Sec. 3.3, Fig. 5(b)] The comparison with FFT-based inversion is not a same-data benchmark. The red dashed line in Fig. 5(b) is taken from Refs. [11,12] and is not computed on the 500 test images. Moreover, it appears to compare a system resolution limit with per-image parameter errors (δxo/zo, etc.), which are different quantities. The claim that '3D MIR can outperform FFT' is therefore not demonstrated by the presented data.
  5. [Sec. 3.2, Fig. 3(c)] The CNN regression model's performance is not quantified. The paper reports 100% classification accuracy for segment type but only a scatter plot (Fig. 3(c)) for β prediction. Since β is a key input to the initial parameter estimates via Eqs. (5)–(6), the regression accuracy (e.g., R², MAE, or relative error) should be reported so that the initial-estimation stage can be assessed.
minor comments (6)
  1. [Sec. 2.1, Eq. (2)] Equation (2) describes a planar current sheet with thickness d, whereas the remainder of the paper uses a line-current model (Eqs. 10–11). Please reconcile or remove Eq. (2).
  2. [Sec. 2.2, Eq. (9)] Equation (9), the formula for the current I, is not typeset legibly; please correct the LaTeX so that the expression can be verified.
  3. [Sec. 2.1, Eqs. (3)-(5)] The notation in Eqs. (3)–(5) is confusing: z appears to be the sensor-plane coordinate in Eq. (3), while in Eqs. (10)–(12) z is the vertical distance. Please define the vertical coordinate convention explicitly.
  4. [Sec. 2.3] The optimization details are incomplete: the paper should state the Nelder-Mead initial simplex, convergence tolerance, and maximum number of iterations.
  5. [Fig. 3(c)] In Fig. 3(c), axis labels and a title are missing; the units of β should be given.
  6. [Abstract] The term 'single-segment MFI' is used without definition; please clarify what constitutes a single segment.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the 3D MIR estimates are produced by a CNN, closed-form image-geometry relations, and a forward-model fit; test data being generated from the same forward model is a generalization limitation, not a logical circularity.

full rationale

The derivation chain is not circular. Equations (3)-(5) are analytic consequences of the stated Biot-Savart model for an infinitely thin straight wire; the PP distance and CNN-predicted beta are image-derived inputs, not outputs of the optimizer. Equations (10)-(11) define the forward model used in the objective chi^2 (Eq. 12), and the Nelder-Mead optimizer adjusts xo, yo, zo, ell, and I to match data; no fitted parameter is relabeled as an independent prediction. The CNN was trained on separate simulated images and evaluated on 500 held-out images, so the beta and c predictions are not constructed from the test outputs. The main weakness is that the test MFIs are simulated with the same infinitely-thin-wire Biot-Savart model hard-coded in the inversion, so the reported accuracy is an in-distribution, 'inverse-crime' style validation; the conclusion even states the method 'will be tested on real MFI data.' This affects generalizability and the strength of the 'new benchmark' claim, but it is not circularity under the definition used here. The FFT benchmark from refs. [11,12] is a self-citation by a co-author, but it is an external published spatial-resolution result, not a premise that presupposes the present method's outputs, and it does not carry the parameter-recovery derivation.

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

The analytic derivation introduces no free parameters, but the method relies on a learned CNN surrogate, an unspecified noise model, and unspecified parameter ranges for the simulated dataset. The key physical axioms are the thin-wire Biot-Savart model, the unproven peak-to-peak relation, the single-segment isolation assumption, and the generalization of the CNN to real data.

free parameters (3)
  • CNN regression model weights for β prediction = not reported (trained on 5000 simulated images)
    The pipeline depends on a learned mapping from MFI to ℓ/z_o. Its test performance is only shown as a scatter plot, no numerical accuracy is given, and no weights are released.
  • Simulation noise level = unspecified (added to mimic real MFIs)
    All results depend on the noise model used to generate training and test images; without specifying the SNR distribution, the reported error-versus-S/N curves cannot be reproduced.
  • Parameter ranges for simulated dataset = unspecified (x_o, y_o, z_o, ℓ, I ranges not given)
    The range of lengths 'from short to long' and the depth and current values are not given, so the generalization envelope of the method is unknown.
assumptions (4)
  • domain assumption The thin-wire Biot-Savart model (Eq. 10-11) exactly describes the measured z-component of the magnetic field from a single current segment.
    Used throughout for forward reconstruction in Stage 3; real conductors have finite width and thickness and may have non-uniform current.
  • standard math The peak-to-peak distance formula (Eq. 3-5) is exact for the thin-wire model.
    Stated without derivation; it links the observable PP to the ratio β = ℓ/z_o and is the basis for z_o and ℓ estimation.
  • domain assumption The MFI image contains only the field from the target segment, measured on a plane at known height, with no other current sources.
    Single-segment assumption; multi-segment or return-path fields would corrupt the PP measurement and the CNN β prediction.
  • ad hoc to paper The CNN trained on simulated images will generalize to real MFI images.
    The paper's validation is entirely in-distribution (simulated test data from the same forward model); generalization to real sensor noise and geometry is assumed, not tested.

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Cite this review

Pith. "Pith review of 3D Magnetic Inverse Routine for Single-Segment Magnetic Field Images." pith.science (2026). https://pith.science/paper/WPDA6WLY

@misc{pith2026250711293,
  author       = {Pith},
  title        = {Pith review of: 3D Magnetic Inverse Routine for Single-Segment Magnetic Field Images},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WPDA6WLY}},
  note         = {Machine review of arXiv:2507.11293}
}
abstract

In semiconductor packaging, accurately recovering 3D information is crucial for non-destructive testing (NDT) to localize circuit defects. This paper presents a novel approach called the 3D Magnetic Inverse Routine (3D MIR), which leverages Magnetic Field Images (MFI) to retrieve the parameters for the 3D current flow of a single-segment. The 3D MIR integrates a deep learning (DL)-based Convolutional Neural Network (CNN), spatial-physics-based constraints, and optimization techniques. The method operates in three stages: i) The CNN model processes the MFI data to predict ($\ell/z_o$), where $\ell$ is the wire length and $z_o$ is the wire's vertical depth beneath the magnetic sensors and classify segment type ($c$). ii) By leveraging spatial-physics-based constraints, the routine provides initial estimates for the position ($x_o$, $y_o$, $z_o$), length ($\ell$), current ($I$), and current flow direction (positive or negative) of the current segment. iii) An optimizer then adjusts these five parameters ($x_o$, $y_o$, $z_o$, $\ell$, $I$) to minimize the difference between the reconstructed MFI and the actual MFI. The results demonstrate that the 3D MIR method accurately recovers 3D information with high precision, setting a new benchmark for magnetic image reconstruction in semiconductor packaging. This method highlights the potential of combining DL and physics-driven optimization in practical applications.

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Reference graph

Works this paper leans on

27 extracted references · 26 canonical work pages

  1. [1]

    INTRODUCTION The development of three-dimensional (3D) packaging in semiconductor manufacturing is crucial for advanced com- puter technology. However, non-destructive testing (NDT) of these structures becomes more challenging as package depth This study is supported by the Machine Learning Guided Failure Analy- sis & Diagnostic Capability Development for...

    work page Pith review arXiv 2025

  2. [2]

    Develop two CNN models to analyze the MFI: 1 CNN model acts as a regression model to estimate the param- eter β = ℓ/z and another CNN model acts as a classifi- cation model to classify the segment type c (x-segment or y-segment)

    work page

  3. [3]

    By leveraging spatial-physics-based constraints, our routine provides initial estimates for the current seg- ment’s position (xo, yo, zo), length (ℓ), current intensity (I), and the direction of current flow (positive or nega- tive)

    work page

  4. [4]

    We conducted extensive simulations to evaluate the proposed 3D MIR using single-segment magnetic images

    An optimization process then adjusts the parameters (xo, yo, zo, ℓ, I) to minimize the difference between the reconstructed MFI and the actual MFI. We conducted extensive simulations to evaluate the proposed 3D MIR using single-segment magnetic images. The results demonstrate the method’s effectiveness in reconstructing magnetic images, with the CNN provi...

    work page

  5. [5]

    Figure 1 shows the schematic representation of the 3D MIR method

    3D MIR METHOD Our 3D MIR method operates in three stages for reconstruc- tion of magnetic images of current-carrying circuits into 3D representation of current flow. Figure 1 shows the schematic representation of the 3D MIR method. 2.1. Preliminaries Consider a current segment of lengthℓ that starts at(xo, yo, zo) and ends at (xo + ℓ, yo, zo). It carries ...

    work page

  6. [6]

    return: xo, yo, zo, ℓ, I

    Minimize objective function (χ2) (12) by Nelder–Mead method to optimize the parameters. return: xo, yo, zo, ℓ, I

    work page

  7. [7]

    β = M1(P) , c = M2(P)

    work page

  8. [8]

    The converged minimum χ2 value, along with the optimal fit parameters (xo, yo, zo, ℓ, I) and best fit imageBtest z are recorded

    to minimize iteratively, thereby reducing the difference between the reconstructed MFI (Btest z ) and the actual MFI (Bdata z ). The converged minimum χ2 value, along with the optimal fit parameters (xo, yo, zo, ℓ, I) and best fit imageBtest z are recorded. The residual image (best fit) shows hidden noise by reconstructing an image that closely matches th...

    work page

Show all 27 references
  1. [9]

    From P get the maximum value of magnetic field Bmax z = max(P), the maximum and minimum coordinates (xmin, ymin) (xmax, ymax),

  2. [10]

    if c is a x-segment then P P= |ymin − ymax| ; calculate zo by (5); calculate ℓ by (6); calculate xo, yo by (7); else if c is a y-segment then P P= |xmin − xmax| ; calculate zo by (5); calculate ℓ by (6); calculate xo, yo by (8)

  3. [11]

    Calculate I by (9); /* MFI reconstruction by initial estimates of the parameters */

  4. [12]

    if c is a x-segment then Reconstruct the magnetic field at (x, y) by (10) else if c is a y-segment then Reconstruct the magnetic field at (x, y) by (11) /* Parameter Optimization */

  5. [13]

    RESULTS A comprehensive analysis has been conducted to evaluate the performance of the 3D MIR on single-segment MFI. 3.1. Dataset and Implementation Data description. A total of 6100 simulated magnetic im- ages were segregated into three datasets for training, valida- tion and...

  6. [14]

    Further- more, to optimize the five parameters, we applied the Nelder- Mead optimization method implemented which is available in the SciPy Python package [10]

    for two independent processing steps: predicting β using a regression approach (where the last layer features a linear layer with a single output) and classifying c using classifica- tion approach (where the last layer features a linear layer with two output features followed ...

  7. [15]

    The 3D MIR method combines CNN, spatial-physics- based constraint and optimization techniques for parameter optimization

    CONCLUSION In this paper, we propose the 3D Magnetic Image Routine (3D MIR) to estimate parameters in single-segment magnetic im- ages. The 3D MIR method combines CNN, spatial-physics- based constraint and optimization techniques for parameter optimization. The trained CNN mod...

  8. [16]

    Non- destructive 3d failure analysis work flow for electrical failure analysis in complex 2.5 d-based devices com- bining 3d magnetic field imaging and 3d x-ray mi- croscopy,

    A. Orozco, E. Talanova, A. Jeffers, F. Rusli, B. Zee, W. Qiu, SMD ZulkifliAllen Gu, and J.A. Mora, “Non- destructive 3d failure analysis work flow for electrical failure analysis in complex 2.5 d-based devices com- bining 3d magnetic field imaging and 3d x-ray mi- croscopy,” i...

    2018

  9. [17]

    A breakthrough in res- olution and scan speed: Overcome the challenges of 3d x-ray imaging workflows for electronics package failure analysis,

    Allen Gu, Gerhard Krampert, Susan Candell, Masako Terada, and Thomas Rodgers, “A breakthrough in res- olution and scan speed: Overcome the challenges of 3d x-ray imaging workflows for electronics package failure analysis,” in 2023 IEEE International Symposium on the Physical a...

    2023

  10. [18]

    Scanning SQUID microscopy of inte- grated circuits,

    S. Chatraphorn, E.F. Fleet, F.C. Wellstood, L.A. Knauss, and T.M. Eiles, “Scanning SQUID microscopy of inte- grated circuits,” Applied Physics Letters , vol. 76(16), pp. 2304–2306, 2000

    2000

  11. [19]

    Integra- tion of SQUID microscopy into FA flow,

    R. Dias, L. Skoglund, Z. Wang, and D. Smith, “Integra- tion of SQUID microscopy into FA flow,” International Symposium for Testing and Failure Analysis, vol. 30859, pp. 77–81, October 2001

    2001

  12. [20]

    Lo- calizing power to ground shorts in a chips-first mcm by scanning SQUID microscopy,

    WE Vanderlinde, ME Cheney, EB McDaniel, KL Skin- ner, LA Knauss, BM Frazier, and HM Christen, “Lo- calizing power to ground shorts in a chips-first mcm by scanning SQUID microscopy,” in 2000 IEEE Interna- tional Reliability Physics Symposium Proceedings. 38th Annual (Cat. No. ...

    2000

  13. [21]

    Failure analysis on resistive opens with scanning SQUID microscopy,

    S Hsiung, KV Tan, AJ Komrowski, DJD Sullivan, J Gaudestad, A Orozco, E Talanova, and LA Knauss, “Failure analysis on resistive opens with scanning SQUID microscopy,” in 2004 IEEE International Re- liability Physics Symposium. Proceedings . IEEE, 2004, pp. 611–612

    2004

  14. [22]

    Efficientnet: Rethinking model scaling for convolutional neural networks,

    Mingxing Tan and Quoc Le, “Efficientnet: Rethinking model scaling for convolutional neural networks,” in International conference on machine learning . PMLR, 2019, pp. 6105–6114

    2019

  15. [23]

    A simplex method for function minimization,

    John A Nelder and Roger Mead, “A simplex method for function minimization,” The computer journal , vol. 7, no. 4, pp. 308–313, 1965

    1965

  16. [24]

    PyTorch 2: Faster Machine Learning Through Dynamic Python Bytecode Transformation and Graph Compilation,

    Jason Ansel, Edward Yang, Horace He, Natalia Gimelshein, Animesh Jain, Michael V oznesensky, Bin Bao, Peter Bell, David Berard, Evgeni Burovski, Geeta Chauhan, Anjali Chourdia, Will Constable, Alban Des- maison, Zachary DeVito, Elias Ellison, Will Feng, Jiong Gong, Michael Gsc...

    2024

  17. [25]

    SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python,

    Pauli Virtanen, Ralf Gommers, Travis E. Oliphant, Matt Haberland, Tyler Reddy, David Cournapeau, Evgeni Burovski, Pearu Peterson, Warren Weckesser, Jonathan Bright, St ´efan J. van der Walt, Matthew Brett, Joshua Wilson, K. Jarrod Millman, Nikolay Mayorov, Andrew R. J. Nelson,...

    2020

  18. [26]

    Noise and spatial resolution in SQUID microscopy,

    S Chatraphorn, EF Fleet, FC Wellstood, and LA Knauss, “Noise and spatial resolution in SQUID microscopy,” IEEE transactions on applied superconductivity , vol. 11, no. 1, pp. 234–237, 2001

    2001

  19. [27]

    Rela- tionship between spatial resolution and noise in scan- ning superconducting quantum interference device mi- croscopy,

    S Chatraphorn, EF Fleet, and FC Wellstood, “Rela- tionship between spatial resolution and noise in scan- ning superconducting quantum interference device mi- croscopy,” Journal of applied physics, vol. 92, no. 8, pp. 4731–4740, 2002

    2002

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