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REVIEW 4 major objections 4 minor 26 references

Collective Phonon Mixing and Eigenvector Transport Under Isotope Substitution

T0 review · 4 major / 4 minor · reviewed 2026-08-02 · deepseek-v4-flash

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Pith's one-line read Isotope substitution in dense phonon systems rotates vibrational eigenvectors within coupled subspaces, so mode correspondence between isotopic endpoints cannot be inferred from frequency shifts alone.

desk verdict A useful eigenvector-tracking framework for isotope-substitution phonon problems, with a clean derivation and a nice convergence check, but the experimental validation rests on Γ-point modes without a q-grid check, and the quantitative predictor is never actually tested. read the letter →

arxiv 2602.20907 v1 pith:XMNLCSUO submitted 2026-02-24 cond-mat.mtrl-sci

Jeff Armstrong , Hamish Cavaye , Pankaj Sharma , Matthew E. Potter This is my paper · ORCID
classification cond-mat.mtrl-sci
keywords isotopesubstitutionphononeigenvectorseigenvectorcontinuationZIF-8inelasticneutronscatteringmodemixingavoidedcrossingsmetal-organicframeworks
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 replacing hydrogen with deuterium in a complex solid does more than rescale vibrational frequencies: in spectrally dense regions it rotates the shapes (eigenvectors) of the vibrations, so a mode at the starting isotope cannot be identified by matching frequencies at the endpoint. Using ZIF-8 as a test case, the authors show that inelastic neutron scattering intensity—weighted by hydrogen displacement—can flag which modes will shift predictably and which will undergo collective reorganisation. They introduce an adiabatic eigenvector-continuation scheme that tracks each mode through a continuous mass change, with overlap-based assignment and stability diagnostics, and find that apparent mode crossings on coarse grids are undersampling artefacts. The result reframes vibrational identity in framework materials as a continuous trajectory in eigenvector space rather than a frequency-ordered list.

What carries the argument

The machinery is the one-parameter family of mass-weighted dynamical matrices D(s) = M(s)^(-1/2) Φ M(s)^(-1/2), built by linearly interpolating the mass matrix between protiated and deuterated forms while keeping the force-constant matrix fixed. On a discrete grid in s, each eigenvector is continued by the maximum-overlap assignment rule, and the gap between the largest and second-largest overlap quantifies tracking stability. First-order perturbation theory supplies the transport amplitudes a_ji = (q_j^T δD q_i)/(ω_i^2 - ω_j^2), with the two amplification channels—small frequency denominators and large coupling matrix elements—explaining collective rotation and 'action at a distance' mixing

What would settle it

Compute the phonon dispersion of ZIF-8 on a dense q-point mesh and simulate the powder INS spectrum including q-dependence. If the simulated fingerprint-region spectrum changes substantially relative to the zone-centre-only calculation, or if the H/D eigenvector overlap statistics differ once finite-q modes are included, then the experimental validation and the tracked mode identities are undermined. A cleaner experiment: use oriented or single-crystal INS to resolve individual modes and check directly whether the 734 cm^-1 protiated mode's displacement character is actually transferred to the

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Extended reading notes

Core claim

The core claim is that mass substitution is a parametric Hermitian deformation of the mass-weighted dynamical matrix, and as the mass parameter s runs from hydrogen to deuterium, eigenvectors in spectrally congested regions rotate substantially within coupled subspaces; hence continuity of frequency ordering does not imply continuity of vibrational identity. In ZIF-8 the paper demonstrates a progression from near-ideal behaviour (416 to 374 cm^-1, preserved displacement pattern) to quantitative redistribution (639 to 546 cm^-1, altered amplitudes) to qualitative mixing (734 to 553 cm^-1, new methyl-rocking participation). Because one-phonon INS intensity is proportional to hydrogen displacem

Load-bearing premise

The paper assumes that the zone-centre normal modes computed by density functional theory are the same vibrations the powder neutron experiment measures—i.e., that phonon dispersion and the wavevector dependence of eigenvectors are negligible across the measured fingerprint region—yet no q-grid or dispersion check is reported.

Editorial extensions

If this is right

  • In spectrally sparse regions, an isolated peak's INS intensity directly predicts the size of its deuteration frequency shift, because both derive from the same hydrogen-displacement projection.
  • In congested regions, comparing protiated and deuterated spectra reveals whether neighbouring modes share hydrogen displacement weight, thus whether collective eigenvector reorganisation will occur.
  • Mode correspondence between isotopic endpoints should be built from overlap-based eigenvector continuation, not frequency ordering; coarse-grid apparent crossings are undersampling artefacts and disappear on refinement.
  • Deuteration, including selective deuteration of specific groups, becomes a practical tool to deliberately shift frequencies or redesign vibrational displacement patterns in framework materials.

Reading between the lines

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

  • The same continuation machinery should carry over to other parametric perturbations of the dynamical matrix—pressure, strain, or chemical substitution—though there the potential surface also changes, making the mass-only interpolation an approximation rather than exact.
  • Because the paper works with zone-centre modes while INS averages over a powder, a q-resolved version of the tracking would show whether the observed mixing and long-range coupling persist away from the zone centre; this is a direct extension.
  • The identification of structural similarity (shared isotope-sensitive coordinates) as a strong coupling channel suggests selection rules for long-range eigenvector transport that could predict mixing without running the full interpolation.
  • The intensity-based predictor could be developed into a routine experimental check of force-field quality in framework materials, using a single protiated spectrum to anticipate the full deuteration response.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The paper studies the vibrational response of protiated and deuterated ZIF-8 using inelastic neutron scattering (INS) and DFT lattice dynamics. It argues that mass substitution acts as a continuous Hermitian deformation of the mass-weighted dynamical matrix, and that in spectrally dense regions the associated eigenvectors rotate substantially within coupled subspaces, so mode correspondence cannot be inferred from frequency shifts alone. The authors introduce an adiabatic eigenvector-continuation framework with overlap-based tracking and an overlap-gap stability diagnostic, apply it to the H→D interpolation, and report grid-convergence tests showing that apparent mode crossings mostly disappear with increasing interpolation resolution. They further interpret transport amplitudes and propose that INS peak intensities, being hydrogen-weighted, provide an experimental predictor of whether a mode will shift predictably or reorganize.

Significance. If the central claim holds, the paper offers a practical framework for tracking vibrational identity under isotopic substitution in complex materials with dense phonon manifolds, a setting where standard frequency-based assignment is ambiguous. The perturbation derivation in Appendix A is clean, the approach uses no fitted physical parameters for the main results, and the explicit grid-convergence analysis of apparent crossings is a valuable methodological contribution. The potential connection between INS intensity and mode stability is physically appealing and would be useful for interpreting isotope-substitution experiments. However, the experimental validation and several of the derived predictions rely on an unvalidated Γ-point approximation for a powder neutron spectrum, which is a load-bearing gap in the current manuscript.

major comments (4)
  1. [Appendix A.2; Section II.B; Fig. 1] The paper states that all modes are Γ-point normal modes (Appendix A.2) and uses Fig. 1 to validate the DFT force constants against TOSCA powder INS data. TOSCA measures a Brillouin-zone average; the one-phonon intensity in Eq. (5) and the eigenvector overlaps in Eq. (3) are q-dependent in general. No q-grid, dispersion bandwidth, or zone-boundary check is reported anywhere. If the 200–1200 cm−1 modes of ZIF-8 have appreciable dispersion, the measured peaks are not necessarily the same objects as the tracked Γ-point eigenmodes, and the experimental validation and all mode-correspondence statistics are undermined. This is fixable by adding a q-point convergence study or at least a dispersion estimate in the fingerprint region, but it is load-bearing for the central empirical claim.
  2. [Section III.E and Figs. 4–6] The text reports that at N_s = 10,000 there are still 13 apparent crossings, and that targeted refinement in s∈[0.2,0.35] reduces this number to 3. The authors then state that representative modes are chosen that do not undergo apparent crossings, so mode continuity is ensured for the studied modes. This is a selection, not a demonstration of full correspondence: the residual crossings are located in the most congested regions, which are precisely the regions where the paper claims its framework resolves ambiguity. The claim that the evolution is consistent with avoided-crossing behaviour is therefore not fully established for the entire spectrum. The authors should either resolve all residual crossings, or explicitly state the scope of the tracking claim and explain why the remaining cases do not affect the conclusions.
  3. [Eq. (5) and Section III.C] Equation (5) is written as I_i(Q,ω) ∝ exp(−2W(Q)) |Q·e_i,H|^2 / ω_i, but the experiment is a powder measurement. For a powder, the intensity involves an orientational average over Q directions, so the simple statement that 'the measured peak intensity provides a direct experimental measure of hydrogen displacement weight' needs a derivation or at least a justification that the powder average preserves the proportionality to the hydrogen displacement amplitude. Without this, the predictive claim connecting INS intensity to the diagonal perturbation in Eq. (4) is not rigorously established, even at the Γ-point.
  4. [Section III.G and Fig. 7] The 'action at a distance' example is interpreted as a large coupling matrix element acting despite a comparatively large spectral denominator. The text does not provide the numerical values of the relevant N_ji and (ω_i^2−ω_j^2) terms along the interpolation path, so the reader cannot verify that the coupling is indeed structural rather than accidental near-degeneracy at some intermediate s. A short table or trajectory of these quantities would make the interpretation quantitative and falsifiable.
minor comments (4)
  1. [Throughout] There are several typographical issues: 'endpont' (Section III.B), 'sugggest thereofre' (Conclusions), 'Chemsitry Divison' and 'assitance' (Acknowledgments), and 'V ASP' in the DFT methods. These should be corrected.
  2. [Eqs. (13)–(14)] The notation O_i^(1)(s_k) and O_i^(2)(s_k) is defined verbally but the index j^(1) is not made explicit before use. A compact formal definition of j^(1)(i,s_k) would improve readability.
  3. [Section III.F, Eq. (17)] In the two-level effective model, V_ij(s) is introduced but not defined in terms of the original dynamical matrix. It would be helpful to state that it is the off-diagonal matrix element of D(s) in the q_i,q_j basis, or otherwise relate it to the transport amplitudes a_ji.
  4. [Fig. 2 and Fig. 3] The overlap map in Fig. 2 would benefit from a color scale (the caption says the color axis, but the axis is not labeled with values). In Fig. 3, the choice of 'representative' modes should be made reproducible by specifying the selection criterion, since the captions state the illustrations are representative examples.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central derivation rests on an external INS/DFT benchmark and standard perturbation identities, with self-citations only as background.

full rationale

I walked the derivation chain from the mass-weighted dynamical matrix (Eq. 1) through the perturbative frequency shift (Eq. 4), eigenvector mixing (Eqs. 7-8), and the adiabatic continuation (Eqs. 9-16). The force constants are obtained from PBE-D3 DFPT and the calculated INS spectra are compared with TOSCA data (Fig. 1) as an external benchmark; the calculations are not fitted to the spectra. The perturbation identities in Appendix A are derived from standard Hermitian first-order perturbation theory and are not empirical inputs. The overlap-based tracking rule (Eqs. 12-14) is an explicit matching criterion, and the paper uses it to quantify eigenvector rotation; it does not present the criterion itself as an independent physical prediction. The only fitted quantities are the descriptive convergence curves in Appendix B, which are not used to generate the main physical conclusions. Self-citations (refs 5, 6-10) provide background context and are not load-bearing. The main caveat—a Gamma-point-only comparison to powder TOSCA spectra without a reported q-grid—is a validation gap and a correctness risk, not a circular step, because the measured spectra are independent data used to test the dynamical matrix rather than to define its output.

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

No physical parameters are fitted to data; the DFT setup uses standard PBE-D3 with no adjustable electronic parameters, and the convergence fits in Appendix B are descriptive only. The central claim rests on domain assumptions: harmonicity, unchanged force constants under isotope substitution, adequacy of Γ-point DFT modes for powder INS, and the one-phonon INS intensity model. The Γ-point assumption is the least validated. No invented physical entities are introduced.

assumptions (6)
  • domain assumption Born–Oppenheimer / frozen force constants: isotopic substitution changes the mass matrix M but leaves Φ unchanged
    Section I, Eq. (1); stated 'to first order' and used throughout the perturbation and continuation framework.
  • domain assumption Harmonic approximation applies to ZIF-8 vibrational eigenproblem at 10 K
    Sections II.B and III.A; the agreement with INS is taken as validation, but anharmonicity is not quantified.
  • domain assumption Γ-point normal modes faithfully represent the powder-averaged TOSCA INS spectrum
    Appendix A.2 ('All modes considered in this work correspond to Γ-point normal modes'); no q-grid or dispersion check is reported.
  • domain assumption One-phonon incoherent INS intensity formula, Eq. (5) with Debye–Waller factor, describes measured peak areas
    Section III.C; used to connect intensity to hydrogen displacement; not quantitatively validated in this paper.
  • standard math First-order perturbation theory for a real-symmetric one-parameter family D(s)
    Appendix A; standard and correctly derived.
  • domain assumption No exact degeneracies along the interpolation path; maximum-overlap discretization converges to the continuous adiabatic branch
    Section III.D–E; the grid-refinement evidence supports this but it remains an assumption about the spectrum of ZIF-8.

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Cite this review

Pith. "Pith review of Collective Phonon Mixing and Eigenvector Transport Under Isotope Substitution." pith.science (2026). https://pith.science/paper/XMNLCSUO

@misc{pith2026260220907,
  author       = {Pith},
  title        = {Pith review of: Collective Phonon Mixing and Eigenvector Transport Under Isotope Substitution},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XMNLCSUO}},
  note         = {Machine review of arXiv:2602.20907}
}
read the original abstract

Isotopic substitution modifies nuclear masses without altering the electronic potential energy surface to first order and is therefore often interpreted as a simple rescaling of vibrational frequencies. In solids with dense phonon manifolds, however, mass substitution acts as a parametric Hermitian deformation of the mass-weighted dynamical matrix, generating a continuous family of eigenproblems whose eigenvectors can undergo substantial rotation within coupled subspaces. Here we investigate protiated and deuterated ZIF-8 using inelastic neutron scattering and density functional theory lattice-dynamics calculations. While many vibrational modes exhibit near-ideal mass scaling and preserve their character across isotopic endpoints, modes embedded in spectrally congested regions display pronounced redistribution of vibrational character that cannot be inferred from frequency shifts alone. Because inelastic neutron scattering intensity is directly weighted by hydrogen displacement amplitude, spectral sparsity and congestion provide experimental indicators of predictable frequency renormalisation or susceptibility to qualitative eigenvector reorganisation under deuteration. To establish physically meaningful mode correspondence, we develop an adiabatic eigenvector-continuation framework with overlap-based tracking and explicit stability diagnostics. These results show that vibrational identity in complex framework materials is best understood as a continuous trajectory in eigenvector space and provide a general framework for analysing isotope-induced spectral flow in dense phonon systems.

Figures

Figures reproduced from arXiv: 2602.20907 by the authors.

Figure 1
Figure 1. FIG. 1. Experimental INS spectra (top) and neutron [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Mass-weighted overlap map for modes between 300 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Mass-weighted displacement patterns for representa [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (5 more)
Figure 5
Figure 5. Figure 5: FIG. 5. Grid-resolution dependence of spurious mode cross [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 4
Figure 4. Figure 4: FIG. 4. Normalized probability distributions [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Continuously tracked phonon modes calculated on [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Interaction amplitudes [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]

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Works this paper leans on

26 extracted references

  1. [1]

    Let u(t) ={u aα(t)} denote the Cartesian displacement vector, whereu aα is the displacement of atomaalong Cartesian directionα∈ {x, y, z}

    Harmonic lattice dynamics and physical displacement fields We consider a system ofNatoms with equilibrium positions{R a}. Let u(t) ={u aα(t)} denote the Cartesian displacement vector, whereu aα is the displacement of atomaalong Cartesian directionα∈ {x, y, z}. Within the harmonic approximation, the potential en- ergy expanded about equilibrium is V(u) =V ...

  2. [2]

    Normal modes and mass-weighted coordinates We seek harmonic solutions of the form u(t) =u i eiωit,(A5) whereu i is a time-independent displacement pattern and ωi is the angular frequency of modei. Substitution yields the generalised eigenvalue problem Φ ui =ω 2 i M ui.(A6) Introducing mass-weighted displacement vectors qi ≡M 1/2ui,(A7) 10 transforms the p...

  3. [3]

    This induces a perturbation of the dynamical matrix D→D+δD,(A12) through the mass-weighting in Eq

    Isotope substitution as a mass perturbation Isotope substitution modifies the atomic masses while leaving the force-constant matrix unchanged to first or- der, M→M+δM,Φfixed.(A11) HereδMis diagonal and nonzero only on substituted degrees of freedom. This induces a perturbation of the dynamical matrix D→D+δD,(A12) through the mass-weighting in Eq. (A9)

  4. [4]

    (A9), we write D(M) =M −1/2 Φ M−1/2.(A13) UnderM→M+δM, the first-order change is δD=δ(M −1/2)Φ M−1/2 +M −1/2 Φδ(M −1/2),(A14) where we have usedδΦ= 0

    Derivation of the mass-induced perturbationδD Starting from Eq. (A9), we write D(M) =M −1/2 Φ M−1/2.(A13) UnderM→M+δM, the first-order change is δD=δ(M −1/2)Φ M−1/2 +M −1/2 Φδ(M −1/2),(A14) where we have usedδΦ= 0. Define the dimensionless diagonal matrix G≡M −1/2 δM M−1/2.(A15) For a diagonal mass matrix, the first-order variation of M−1/2 is δ(M−1/2) =−...

  5. [5]

    (A19) Substituting into Eq

    First-order perturbation theory for frequencies and eigenvectors At a fixed interpolation point, the unperturbed eigen- problem is D qi =ω 2 i qi,q T i qi = 1.(A18) After a small mass perturbation, we write D→D+δD, ω 2 i →ω 2 i +δω 2 i ,q i →q i +δq i. (A19) Substituting into Eq. (A18) and retaining only first- order terms gives Dδq i +δD q i =ω 2 i δqi +...

  6. [6]

    (A26) The corresponding first-order mixing amplitude is de- fined as aji = Nji ω2 i −ω 2 j

    Mode-resolved coupling and mixing amplitudes The physically fundamental scalar coupling induced by the mass perturbation between modesjandiis Nji =q T j δD qi. (A26) The corresponding first-order mixing amplitude is de- fined as aji = Nji ω2 i −ω 2 j . (A27) With this definition, δqi = X j̸=i aji qj.(A28) 11 Appendix B: Convergence fit functions and param...

  7. [7]

    C. L. Bull, N. P. Funnell, C. J. Ridley, C. R. Pulham, P. L. Coster, J. P. Tellam, and W. G. Marshall, Crys- tEngComm21, 5872 (2019)

    2019

  8. [8]

    Y. Wu, X. Liu, A. Radulescu, L. Porcar, A. Krause- Heuer, H. Jiang, H. Yang, Y. Ke, T. Darwish, and Z. Luo, Nanoscale17, 3798 (2025)

    2025

Show all 26 references
  1. [9]

    H. Aoki, H. Ogawa, and M. Takenaka, Langmuir37, 196 (2021)

    2021

  2. [10]

    Colognesi, S

    D. Colognesi, S. D. Panfilis, F. Formisano, M. ´A. Gonz´ alez, S. Rudi´ c, and A. Santonocito, Chemical Physics597, 112773 (2025)

    2025

  3. [11]

    Armstrong, S

    J. Armstrong, S. Banerjee, V. Sch¨ unemann, J. A. Wolny, and P. J. Sadler, The Journal of Physical Chemistry Let- ters12, 658 (2021)

    2021

  4. [12]

    J. Mor, S. K. Sharma, J. Bahadur, S. Kancharlapalli, and J. Armstrong, Langmuir41, 26770 (2025)

    2025

  5. [13]

    Bahadur, S

    J. Bahadur, S. K. Sharma, S. Kancharlapalli, J. Mor, J. Armstrong, and D. Sen, The Journal of Physical Chem- istry Letters16, 5496 (2025), epub 2025-05-27

    2025

  6. [14]

    K. T. Butler, P. Vervoorts, M. G. Ehrenreich, J. Arm- strong, J. M. Skelton, and G. Kieslich, Chemistry of Ma- terials31, 8366 (2019)

    2019

  7. [15]

    Filippov, J

    S. Filippov, J. B. Grinderslev, M. S. Andersson, J. Arm- strong, M. Karlsson, T. R. Jensen, J. Klarbring, S. I. Simak, and U. H¨ aussermann, The Journal of Physical Chemistry C123, 28631 (2019)

    2019

  8. [16]

    Kieslich, J

    G. Kieslich, J. M. Skelton, J. Armstrong, Y. Wu, F. Wei, K. L. Svane, A. Walsh, and K. T. Butler, Chemistry of Materials30, 8782 (2018)

    2018

  9. [17]

    R. S. Pinna, S. Rudi´ c, S. F. Parker, J. Armstrong, M. Zanetti, G. ˇSkoro, S. P. Waller, D. Zacek, C. A. Smith, M. J. Capstick, D. J. McPhail, D. E. Pooley, G. D. Howells, G. Gorini, and F. Fernandez-Alonso, Nuclear In- struments and Methods in Physics Research Section A: Acc...

    2018

  10. [18]

    5286/isis.instrument.2527(2026), instrument DOI for TOSCA, ISIS Neutron and Muon Source

    TOSCA inelastic neutron scattering instrument at the ISIS neutron and muon source,https://doi.org/10. 5286/isis.instrument.2527(2026), instrument DOI for TOSCA, ISIS Neutron and Muon Source

    2026

  11. [19]

    Arnold and et al., Nucl

    O. Arnold and et al., Nucl. Instrum. Methods Phys. Res., Sect. A764, 156 (2014)

    2014

  12. [20]

    Kresse and J

    G. Kresse and J. Furthm¨ uller, Phys. Rev. B54, 11169 (1996)

    1996

  13. [21]

    Kresse and J

    G. Kresse and J. Furthm¨ uller, Comput. Mater. Sci.6, 15 (1996)

    1996

  14. [22]

    J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett.77, 3865 (1996)

    1996

  15. [23]

    Kresse and D

    G. Kresse and D. Joubert, Phys. Rev. B59, 1758 (1999)

    1999

  16. [24]

    Grimme, S

    S. Grimme, S. Ehrlich, and L. Goerigk, J. Comput. Chem.32, 1456 (2011)

    2011

  17. [25]

    Dymkowski, S

    K. Dymkowski, S. F. Parker, F. Fernandez-Alonso, and S. Mukhopadhyay, Physica B551, 443 (2018)

    2018

  18. [26]

    R. M. Hanson, J. Appl. Crystallogr.43, 1250 (2010)

    2010

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