pith. sign in

arxiv: 2601.09687 · v2 · submitted 2026-01-14 · ❄️ cond-mat.mes-hall · cond-mat.str-el

Disorder-induced strong-field strong-localization in 2D systems

Yi Huang , Sankar Das Sarma This is my paper

Pith reviewed 2026-05-16 14:25 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.str-el
keywords Anderson soliddisorder-induced localizationbilayer grapheneWigner crystallowest Landau levelstrong magnetic fieldrandom localized phaseSTM experiment
0
0 comments X

The pith

The random localized phase observed in bilayer graphene under strong magnetic fields is the disorder-induced Anderson solid.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Recent STM experiments in 2D bilayer graphene in a strong perpendicular magnetic field reveal three distinct phases in the lowest Landau level: an incompressible fractional quantum Hall liquid, a compressible hexagonal Wigner crystal with long-range order, and a random localized solid with no spatial order. The paper argues that the random localized phase at low filling factors matches the recently proposed disorder-dominated amorphous Anderson solid phase. This phase appears generically at a sample-dependent filling factor due to disorder effects. A sympathetic reader would care because it provides a theoretical identification for an experimentally seen phase that lacks crystalline order, linking it to strong localization mechanisms in 2D systems.

Core claim

In the lowest Landau level of 2D bilayer graphene under strong perpendicular magnetic fields, the spatially random localized phase at low filling factors is the disorder-dominated strongly localized amorphous Anderson solid phase, which appears generically at sample-dependent filling factors and features no spatial order.

What carries the argument

The Anderson solid, a disorder-dominated strongly localized amorphous phase, which identifies the observed random localized phase as distinct from the ordered Wigner crystal.

If this is right

  • The random localized phase is distinct from the Wigner crystal and appears due to disorder dominance at low fillings.
  • This Anderson solid phase occurs generically in such 2D systems at a filling factor that depends on the specific sample disorder.
  • The identification unifies the experimental observation with theoretical predictions for strong localization in the presence of disorder.
  • The phase remains compressible and shows no rotational symmetry breaking unlike the Wigner crystal.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Disorder can stabilize amorphous localized states in quantum Hall systems that would otherwise form crystals.
  • Tuning the disorder strength in future experiments could map the boundary between the Anderson solid and the Wigner crystal phases.
  • This suggests that similar random localized phases may appear in other 2D materials under strong fields when disorder is present.

Load-bearing premise

The experimentally observed random localized phase without spatial order directly corresponds to the theoretically proposed Anderson solid, even without quantitative matching of filling factors or spatial correlations.

What would settle it

Measuring the exact spatial correlation functions or the precise filling factor range of the random phase in the bilayer graphene experiment and comparing them quantitatively to predictions for the Anderson solid would confirm or refute the identification.

Figures

Figures reproduced from arXiv: 2601.09687 by Sankar Das Sarma, Yi Huang.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic for the zero temperature phase diagram of [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Density of states (DOS) for a 2D electron gas in a [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The schematic finite-temperature ( [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: conjectures that in the limit of zero disorder, the FQHE is restricted to a set of measure zero occurring pre￾cisely at odd-denominator filling factors. Both WC and FQHL are truncated by the disorder line, and if the dis￾order is strong, then neither would manifest itself (which is the situation in all samples prior to the 1982 discovery of FQHE). If the disorder is weak, however, many FQHE at many odd den… view at source ↗
read the original abstract

A recent STM experiment in 2D bilayer graphene [Y.-C. Tsui, et al., Nature 628, 287 (2024)], under a strong perpendicular magnetic field, has made a direct observation of the existence of three distinct filling-factor-dependent quantum phases in the lowest Landau level: the incompressible fractional quantum Hall liquid, a crystalline compressible hexagonal Wigner crystal with long-range order and rotational symmetry-breaking, and a random localized solid phase with no spatial order. We argue that the spatially random localized phase at low filling is the recently proposed disorder-dominated strongly localized amorphous "Anderson solid" phase [A. Babber, et al., arXiv:2601.03521], which appears generically at a sample-dependent filling factor.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The manuscript interprets recent STM observations in bilayer graphene under strong perpendicular magnetic fields as revealing three filling-factor-dependent phases in the lowest Landau level: an incompressible fractional quantum Hall liquid, a compressible hexagonal Wigner crystal with long-range order, and a spatially random localized solid with no order. It argues that the random localized phase at low filling corresponds to the disorder-dominated amorphous 'Anderson solid' proposed in the authors' prior work (arXiv:2601.03521), appearing generically at sample-dependent filling factors.

Significance. If the identification holds, the result would link an experimental random localized phase to a theoretically proposed disorder-induced strongly localized state, offering a framework for understanding sample-dependent behavior in 2D systems at strong fields. The manuscript contains no new derivations, simulations, or data analysis, so its contribution is purely interpretive; quantitative validation would be required to elevate its impact beyond a qualitative suggestion.

major comments (1)
  1. [Abstract] Abstract and main text: the central identification of the STM-observed random localized phase with the Anderson solid rests exclusively on shared qualitative traits (spatial randomness and absence of long-range order) but supplies no quantitative comparison of filling factors, disorder strengths, localization lengths, or two-point correlation functions against the parameters used in arXiv:2601.03521.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their thoughtful review and constructive comments on our interpretive manuscript. We address the major comment below, maintaining that the identification is appropriately qualitative given the nature of the available experimental data.

read point-by-point responses

  1. Referee: [Abstract] Abstract and main text: the central identification of the STM-observed random localized phase with the Anderson solid rests exclusively on shared qualitative traits (spatial randomness and absence of long-range order) but supplies no quantitative comparison of filling factors, disorder strengths, localization lengths, or two-point correlation functions against the parameters used in arXiv:2601.03521.

    Authors: We acknowledge that the central claim relies on qualitative correspondence between the STM observations (spatially random localized phase at low filling factors with no long-range order) and the disorder-induced Anderson solid predicted in our prior work (arXiv:2601.03521). The Tsui et al. experiment reports the existence of this phase and its sample-dependent filling-factor range but does not furnish quantitative metrics such as localization lengths, two-point correlation functions, or explicit disorder strengths. Our theoretical proposal emphasizes that the Anderson solid emerges generically at sample-dependent fillings due to disorder dominance, which is consistent with the experimental variability across samples. As the present manuscript is purely interpretive and introduces no new calculations or simulations, we do not attempt quantitative matching. We maintain that the qualitative alignment offers a coherent framework for the observed phases without overclaiming precision. revision: no

Circularity Check

1 steps flagged

Central identification of random localized phase as Anderson solid reduces to self-citation of prior proposal without quantitative matching

specific steps
  1. self citation load bearing [Abstract]
    "We argue that the spatially random localized phase at low filling is the recently proposed disorder-dominated strongly localized amorphous 'Anderson solid' phase [A. Babber, et al., arXiv:2601.03521], which appears generically at a sample-dependent filling factor."

    The identification is asserted by direct reference to the prior proposal without independent evidence or calculation in the current work; the mapping is justified only by the self-cited definition of the Anderson solid, reducing the central claim to the content of arXiv:2601.03521.

full rationale

The paper's core claim equates the STM-observed spatially random localized phase to the disorder-dominated Anderson solid solely via reference to the authors' prior arXiv:2601.03521 work. No new derivations, simulations, or parameter matching (filling factor, disorder strength, correlation functions) are supplied; the argument rests on shared qualitative features (absence of order, spatial randomness) already defined in the self-cited proposal. This makes the identification load-bearing on the self-citation chain, with the present manuscript functioning as interpretive commentary rather than independent derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The paper relies on the prior theoretical definition of the Anderson solid and qualitative features of the STM data without introducing new parameters or entities in the abstract.

pith-pipeline@v0.9.0 · 5421 in / 1147 out tokens · 17835 ms · 2026-05-16T14:25:21.566213+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 1 Pith paper

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

  1. Interplay of disorder and interaction in quantum Hall systems: from fractional quantum Hall liquids to Wigner crystals and amorphous solids

    cond-mat.mes-hall 2026-04 unverdicted novelty 4.0

    Simulations reveal that random charged impurities and short-range disorder drive quantum Hall systems from incompressible fractional liquids through locally ordered solids to amorphous states, with charged impurities ...

Reference graph

Works this paper leans on

56 extracted references · 56 canonical work pages · cited by 1 Pith paper

  1. [1]

    Y.-C. Tsui, M. He, Y. Hu, E. Lake, T. Wang, K. Watan- abe, T. Taniguchi, M. P. Zaletel, and A. Yazdani, Direct observation of a magnetic-field-induced wigner crystal, Nature628, 287 (2024)

    work page 2024

  2. [2]

    Yoshioka, B

    D. Yoshioka, B. I. Halperin, and P. A. Lee, Ground state of two-dimensional electrons in strong magnetic fields and 1 3 quantized hall effect, Phys. Rev. Lett.50, 1219 (1983)

    work page 1983

  3. [3]

    V. S. Khrapai, A. A. Shashkin, M. G. Trokina, V. T. Dolgopolov, V. Pellegrini, F. Beltram, G. Biasiol, and L. Sorba, Filling factor dependence of the fractional quantum hall effect gap, Phys. Rev. Lett.100, 196805 (2008)

    work page 2008

  4. [4]

    B. E. Feldman, B. Krauss, J. H. Smet, and A. Yacoby, Unconventional sequence of fractional quantum hall states in suspended graphene, Science337, 1196 (2012), https://www.science.org/doi/pdf/10.1126/science.1224784

    work page doi:10.1126/science.1224784 2012

  5. [5]

    Z. Ge, C. Smith, Z. He, Y. Yang, Q. Li, Z. Xiang, J. Xiao, W. Zhou, S. Kahn, M. Erdi, R. Banerjee, T. Taniguchi, K. Watanabe, S. A. Tongay, M. A. Morales, S. Zhang, F. Wang, and M. F. Crommie, Visualizing the impact of quenched disorder on 2d electron wigner solids (2025), arXiv:2510.12009 [cond-mat.str-el]

    work page arXiv 2025

  6. [6]

    Babbar, Z.-J

    A. Babbar, Z.-J. Li, and S. D. Sarma, Wigner solid or anderson solid – 2d electrons in strong disorder (2026), arXiv:2601.03521 [cond-mat.mes-hall]

    work page arXiv 2026

  7. [7]

    P. W. Anderson, Absence of diffusion in certain random lattices, Phys. Rev.109, 1492 (1958)

    work page 1958

  8. [8]

    M. Shayegan, Case for the magnetic-field-induced two-dimensional wigner crystal, inPerspectives in Quantum Hall Effects: Novel Quantum Liquids in Low-Dimensional Semiconductor Structures, edited by S. Das Sarma and A. Pinczuk (Wiley-VCH, New York,

    work page

  9. [9]

    H. A. Fertig, Properties of the electron solid, inPerspec- tives in Quantum Hall Effects: Novel Quantum Liquids in Low-Dimensional Semiconductor Structures, edited by S. Das Sarma and A. Pinczuk (Wiley-VCH, New York,

    work page

  10. [10]

    A. A. Wilson, S. J. Allen, and D. C. Tsui, Evidence for a magnetic-field-induced wigner glass in the two- dimensional electron system in si inversion layers, Phys. Rev. B24, 5887 (1981)

    work page 1981

  11. [11]

    R. L. Willett, H. L. Stormer, D. C. Tsui, L. N. Pfeiffer, K. W. West, and K. W. Baldwin, Termination of the series of fractional quantum hall states at small filling factors, Phys. Rev. B38, 7881 (1988)

    work page 1988

  12. [12]

    P. D. Ye, L. W. Engel, D. C. Tsui, R. M. Lewis, L. N. Pfeiffer, and K. West, Correlation lengths of the wigner- crystal order in a two-dimensional electron system at high magnetic fields, Phys. Rev. Lett.89, 176802 (2002)

    work page 2002

  13. [13]

    V. J. Goldman, M. Santos, M. Shayegan, and J. E. Cun- ningham, Evidence for two-dimensional quantum wigner crystal, Phys. Rev. Lett.65, 2189 (1990)

    work page 1990

  14. [14]

    H. C. Manoharan, Y. W. Suen, M. B. Santos, and M. Shayegan, Evidence for a bilayer quantum wigner solid, Phys. Rev. Lett.77, 1813 (1996)

    work page 1996

  15. [15]

    P. T. Madathil, C. Wang, S. K. Singh, A. Gupta, K. A. V. Rosales, Y. J. Chung, K. W. West, K. W. Baldwin, L. N. Pfeiffer, L. W. Engel, and M. Shayegan, Signatures of correlated defects in an ultraclean wigner crystal in the extreme quantum limit, Phys. Rev. Lett.132, 096502 (2024)

    work page 2024

  16. [16]

    C. Wang, P. T. Madathil, S. K. Singh, A. Gupta, Y. J. Chung, L. N. Pfeiffer, K. W. Baldwin, and M. Shayegan, Developing fractional quantum hall states at even-denominator fillings 1/6 and 1/8, Phys. Rev. Lett.134, 046502 (2025)

    work page 2025

  17. [17]

    C. Wang, A. Gupta, S. K. Singh, L. N. Pfeiffer, K. W. Baldwin, R. Winkler, and M. Shayegan, Competing 12 many-body phases at small fillings in ultrahigh-quality gaas two-dimensional hole systems: Role of landau level mixing, Phys. Rev. B111, 085429 (2025)

    work page 2025

  18. [18]

    Maki and X

    K. Maki and X. Zotos, Static and dynamic properties of a two-dimensional wigner crystal in a strong magnetic field, Phys. Rev. B28, 4349 (1983)

    work page 1983

  19. [19]

    P. K. Lam and S. M. Girvin, Liquid-solid transition and the fractional quantum hall effect, Phys. Rev. B30, 473 (1984)

    work page 1984

  20. [20]

    Levesque, J

    D. Levesque, J. J. Weis, and A. H. MacDonald, Crys- tallization of the incompressible quantum-fluid state of a two-dimensional electron gas in a strong magnetic field, Phys. Rev. B30, 1056 (1984)

    work page 1984

  21. [21]

    Ortiz, D

    G. Ortiz, D. M. Ceperley, and R. M. Martin, New stochastic method for systems with broken time-reversal symmetry: 2d fermions in a magnetic field, Phys. Rev. Lett.71, 2777 (1993)

    work page 1993

  22. [22]

    Zhu and S

    X. Zhu and S. G. Louie, Wigner crystallization in the fractional quantum hall regime: A variational quantum monte carlo study, Phys. Rev. Lett.70, 335 (1993)

    work page 1993

  23. [23]

    Zhu and S

    X. Zhu and S. G. Louie, Variational quantum monte carlo study of two-dimensional wigner crystals: Exchange, cor- relation, and magnetic-field effects, Phys. Rev. B52, 5863 (1995)

    work page 1995

  24. [24]

    Price, X

    R. Price, X. Zhu, S. Das Sarma, and P. M. Platzman, Laughlin-liquid–wigner-solid transition at high density in wide quantum wells, Phys. Rev. B51, 2017 (1995)

    work page 2017

  25. [25]

    R. K. Kamilla and J. K. Jain, Excitonic instability and termination of fractional quantum hall effect, Phys. Rev. B55, R13417 (1997)

    work page 1997

  26. [26]

    Yi and H

    H. Yi and H. A. Fertig, Laughlin-jastrow-correlated wigner crystal in a strong magnetic field, Phys. Rev. B 58, 4019 (1998)

    work page 1998

  27. [27]

    K. Yang, F. D. M. Haldane, and E. H. Rezayi, Wigner crystals in the lowest landau level at low-filling factors, Phys. Rev. B64, 081301 (2001)

    work page 2001

  28. [28]

    S. S. Mandal, M. R. Peterson, and J. K. Jain, Two- dimensional electron system in high magnetic fields: Wigner crystal versus composite-fermion liquid, Phys. Rev. Lett.90, 106403 (2003)

    work page 2003

  29. [29]

    A. C. Archer, K. Park, and J. K. Jain, Competing crystal phases in the lowest landau level, Phys. Rev. Lett.111, 146804 (2013)

    work page 2013

  30. [30]

    M. R. Peterson and J. K. Jain, Possible persistence of fractional quantum hall effect down to ultralow fillings, Phys. Rev. B68, 195310 (2003)

    work page 2003

  31. [31]

    Huang, S

    K. Huang, S. Das Sarma, and X. Li, Thermal ionization of impurity-bound quasiholes in the fractional quantum hall effect, arXiv preprint arXiv:2512.07769 (2025)

    work page arXiv 2025

  32. [32]

    F. C. Zhang, V. Z. Vulovic, Y. Guo, and S. Das Sarma, Effect of a charged impurity on the fractional quantum hall effect: Exact numerical treatment of finite systems, Phys. Rev. B32, 6920 (1985)

    work page 1985

  33. [33]

    E. H. Rezayi and F. D. M. Haldane, Incompressible states of the fractionally quantized hall effect in the presence of impurities: A finite-size study, Phys. Rev. B32, 6924 (1985)

    work page 1985

  34. [34]

    Yi-Thomas, Y

    S. Yi-Thomas, Y. Huang, J. D. Sau, and S. Das Sarma, Integer quantum hall effect: Disorder, temperature, lo- calization, floating, and plateau width, Phys. Rev. B111, 195305 (2025)

    work page 2025

  35. [35]

    K. v. Klitzing, G. Dorda, and M. Pepper, New method for high-accuracy determination of the fine-structure con- stant based on quantized hall resistance, Phys. Rev. Lett. 45, 494 (1980)

    work page 1980

  36. [36]

    D. C. Tsui, H. L. Stormer, and A. C. Gossard, Two- dimensional magnetotransport in the extreme quantum limit, Phys. Rev. Lett.48, 1559 (1982)

    work page 1982

  37. [37]

    Ando and Y

    T. Ando and Y. Uemura, Theory of Quantum Transport in a Two-Dimensional Electron System under Magnetic Fields. I. Characteristics of Level Broadening and Trans- port under Strong Fields, Journal of the Physical Society of Japan36, 959 (1974)

    work page 1974

  38. [38]

    Das Sarma and F

    S. Das Sarma and F. Stern, Single-particle relaxation time versus scattering time in an impure electron gas, Phys. Rev. B32, 8442 (1985)

    work page 1985

  39. [39]

    A. F. Ioffe and A. R. Regel, Prog. Semicond.4, 237 (1960)

    work page 1960

  40. [40]

    N. F. Mott, Conduction in non-crystalline materials, The Philosophical Magazine: A Journal of Theoretical Exper- imental and Applied Physics19, 835 (1969)

    work page 1969

  41. [41]

    Fukuyama and P

    H. Fukuyama and P. A. Lee, Pinning and conductivity of two-dimensional charge-density waves in magnetic fields, Phys. Rev. B18, 6245 (1978)

    work page 1978

  42. [42]

    H. Deng, Y. Liu, I. Jo, L. N. Pfeiffer, K. W. West, K. W. Baldwin, and M. Shayegan, Commensurability oscilla- tions of composite fermions induced by the periodic po- tential of a wigner crystal, Phys. Rev. Lett.117, 096601 (2016)

    work page 2016

  43. [43]

    M. K. Ma, K. A. Villegas Rosales, H. Deng, Y. J. Chung, L. N. Pfeiffer, K. W. West, K. W. Baldwin, R. Winkler, and M. Shayegan, Thermal and quantum melting phase diagrams for a magnetic-field-induced wigner solid, Phys. Rev. Lett.125, 036601 (2020)

    work page 2020

  44. [44]

    K. A. Villegas Rosales, S. K. Singh, M. K. Ma, M. S. Hossain, Y. J. Chung, L. N. Pfeiffer, K. W. West, K. W. Baldwin, and M. Shayegan, Competition between frac- tional quantum hall liquid and wigner solid at small fill- ings: Role of layer thickness and landau level mixing, Phys. Rev. Res.3, 013181 (2021)

    work page 2021

  45. [45]

    H. L. Stormer, Nobel lecture: The fractional quantum hall effect, Rev. Mod. Phys.71, 875 (1999)

    work page 1999

  46. [46]

    V. J. Goldman, J. K. Jain, and M. Shayegan, Nature of the extended states in the fractional quantum hall effect, Phys. Rev. Lett.65, 907 (1990)

    work page 1990

  47. [47]

    W. Pan, H. L. Stormer, D. C. Tsui, L. N. Pfeiffer, K. W. Baldwin, and K. W. West, Transition from an electron solid to the sequence of fractional quantum hall states at very low landau level filling factor, Phys. Rev. Lett.88, 176802 (2002)

    work page 2002

  48. [48]

    H. W. Jiang, R. L. Willett, H. L. Stormer, D. C. Tsui, L. N. Pfeiffer, and K. W. West, Quantum liquid versus electron solid aroundν=1/5 landau-level filling, Phys. Rev. Lett.65, 633 (1990)

    work page 1990

  49. [49]

    V. J. Goldman, M. Shayegan, and D. C. Tsui, Evidence for the fractional quantum hall state atν= 1 7, Phys. Rev. Lett.61, 881 (1988)

    work page 1988

  50. [50]

    Y. J. Chung, D. Graf, L. W. Engel, K. A. V. Rosales, P. T. Madathil, K. W. Baldwin, K. W. West, L. N. Pfeif- fer, and M. Shayegan, Correlated states of 2d electrons near the landau level fillingν= 1/7, Phys. Rev. Lett. 128, 026802 (2022)

    work page 2022

  51. [51]

    D. C. Tsui, H. L. St¨ ormer, A. C. Gossard, and W. Wieg- mann, Two-dimensional electrical transport in gaas- alxga1−xAs multilayers at high magnetic fields, Phys. Rev. B21, 1589 (1980)

    work page 1980

  52. [52]

    H. L. Stormer, A. Chang, D. C. Tsui, J. C. M. Hwang, A. C. Gossard, and W. Wiegmann, Fractional quantiza- 13 tion of the hall effect, Phys. Rev. Lett.50, 1953 (1983)

    work page 1953

  53. [53]

    Z.-W. Zuo, A. C. Balram, S. Pu, J. Zhao, T. Jolicoeur, A. W´ ojs, and J. K. Jain, Interplay between fractional quantum hall liquid and crystal phases at low filling, Phys. Rev. B102, 075307 (2020)

    work page 2020

  54. [54]

    B. I. Shklovskii and A. L. Efros,Electronic Properties of Doped Semiconductors(Springer, Berlin, 1984)

    work page 1984

  55. [55]

    S. Das Sarma, Localization, metal-insulator transitions, and quantum hall effect, inPerspectives in Quantum Hall Effects: Novel Quantum Liquids in Low-Dimensional Semiconductor Structures, edited by S. Das Sarma and A. Pinczuk (Wiley-VCH, New York, 1996) pp. 1–36

    work page 1996

  56. [56]

    Imry and S.-k

    Y. Imry and S.-k. Ma, Random-field instability of the ordered state of continuous symmetry, Phys. Rev. Lett. 35, 1399 (1975)

    work page 1975