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REVIEW 4 major objections 6 minor 101 references

Momentum-Selective Two-Component Excitations in Electron-Doped Mott Insulators

T0 review · 4 major / 6 minor · reviewed 2026-07-31 · grok-4.5

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Pith's one-line read Electron-doped Mott insulators host momentum-separated coherent and incoherent excitations that explain their mixed Fermi-liquid and strong-correlation spectra.

desk verdict Solid single-/two-hole VMC shows sign(t') reweights kinetic energy into a momentum-selective coherent channel; the finite-doping ARPES story is a hand-tuned phenomenological GF, not a controlled prediction. read the letter →

arxiv 2607.24936 v1 pith:5VAEVPBE submitted 2026-07-27 cond-mat.str-el cond-mat.supr-con

Zeyu Han , Can Cui , Jia-Xin Zhang , Zheng-Yu Weng This is my paper · ORCID
classification cond-mat.str-elcond-mat.supr-con
keywords t-t'-Jmodelelectron-dopedcupratesMottinsulatorphasestringquasiparticleFermiarcantinodaldichotomyvariationalMonteCarlo
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

Cuprate experiments show a sharp asymmetry: hole-doped materials form nodal Fermi arcs, while electron-doped ones first show antinodal electron pockets and only later develop nodal weight, yet both still display strong-correlation signatures. This paper claims that the t-t'-J model already contains the explanation. Its ground-state wave function always has two components—a coherent quasiparticle and an incoherent composite built from fractionalized pieces—and kinetic energy comes from both bare quasiparticle motion and resonance between the two. Variational Monte Carlo at the single-hole level shows that for hole doping (t'<0) the resonance dominates and sits at the nodes, whereas for electron doping (t'>0) the coherent channel is selectively enhanced at the antinodes while the nodes remain resonance-dominated. Extending that momentum-selective structure to finite doping with a two-fluid Green’s function reproduces the experimental spectral evolution and keeps both doping sides inside one doped-Mott framework.

What carries the argument

Two-component decomposition of the variational single-hole (and two-hole) wave function into orthogonal quasiparticle and incoherent pieces, rooted in the phase-string representation; kinetic energy is partitioned into bare quasiparticle hopping versus inter-component resonance, and a phenomenological two-fluid Green’s function carries the same separation to finite doping.

What would settle it

A controlled finite-doping spectral calculation, or simultaneous high-resolution nodal and antinodal ARPES, showing that antinodal coherent weight and nodal composite weight do not remain distinct components whose relative weights evolve with the sign of t' as claimed, or that the single-hole kinetic-energy ratio fails to rise selectively at the antinodes above t'/t ≈ 0.09.

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Extended reading notes

Core claim

The ground-state wave function of the t-t'-J model generically decomposes into a coherent quasiparticle component and an incoherent composite component. For t'<0 the low-energy kinetic energy is carried almost entirely by resonance between them and concentrates at the nodes. For t'>0 beyond a threshold, intrinsic quasiparticle propagation is selectively enhanced at the antinodes while the nodal region stays controlled by the incoherent composite, producing a momentum-space separation of the two components that accounts for the contrasting single-particle spectra of electron- and hole-doped cuprates.

Load-bearing premise

The jump from single- and two-hole cluster wave functions to finite doping is made with a phenomenological Green’s function whose component densities, recombination strength, and antiferromagnetic coupling are free parameters chosen to match spectra, not fixed by a controlled many-body calculation.

Editorial extensions

If this is right

  • Electron-doped spectra should retain a nodal–antinodal dichotomy in quasiparticle character even when long-range antiferromagnetism is absent.
  • The same incoherent composite sector produces both hole-doped Fermi arcs and the nodal weight that appears upon electron doping.
  • Superconducting Tc remains set by the spin-gap scale of the composite sector, so a larger local pair amplitude for t'>0 need not raise Tc.
  • Weaker non-Fermi-liquid transport on the electron-doped side follows from reduced weight of the composite component.

Reading between the lines

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

  • If momentum locking of the two fluids only gradually softens with doping, intermediate-doping electron-doped samples should show hybrid damping rates that interpolate between Fermi-liquid and arc-like scattering.
  • Constructive NN–NNN interference for t'>0 that stabilizes antiferromagnetism predicts a slower collapse of the spin gap with doping than on the hole-doped side, testable by neutron or Raman spin-gap measurements.
  • Analogous two-component structures may appear in other doped Mott systems whenever next-nearest-neighbor hopping can partially bypass phase-string frustration.
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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 / 6 minor

Summary. The manuscript addresses the electron–hole asymmetry of cuprate single-particle spectra within the single-band t-t′-J model, using the phase-string representation. The controlled part of the work is a variational Monte Carlo (VMC) study of the single- and two-hole-doped model: the single-hole ground state is decomposed into a bare-quasiparticle component and an incoherent (twisted-hole) component, and the kinetic energy is split accordingly (Eqs. 15–17). For t′<0 the kinetic energy is dominated by inter-component resonance concentrated in the nodal region; for t′>0 beyond a threshold t′/t≈0.09 an intrinsic quasiparticle propagation channel activates selectively in the antinodal region (Figs. 3–4). The ansatz is benchmarked against DMRG on 8×8 clusters (App. E, Table II, Fig. ES12). Building on this, the authors propose a two-fluid ground state |Ψ_c⟩⊗|Ψ_G⟩ for t′>0 (Eq. 21b) and construct a phenomenological finite-doping Green's function — an RPA recombination channel (Eq. 30) plus a coherent channel (Eq. 33), with static AFM folding (Eq. 34) and a linear superposition (Eq. 36) — whose zero-energy spectra (Fig. 8) reproduce the experimental sequence: antinodal pockets at low doping, nodal pockets at intermediate doping, and a large Fermi surface at high doping.

Significance. If the controlled part holds, the paper identifies a concrete, physically transparent mechanism for the electron–hole asymmetry of the t-t′-J model: the sign of t′ controls whether the bare-quasiparticle hopping channel contributes constructively to the kinetic energy, and this contribution is momentum-selective (antinodal for t′>0). Strengths that deserve explicit credit: (i) the single-hole VMC ansatz is benchmarked against DMRG for both energies and the momentum-resolved quasiparticle weight Z_k (App. E), and the t′=0 dispersion is checked against Green-function Monte Carlo; (ii) the kinetic-energy decomposition in Eqs. (16)–(17) is a well-defined, ansatz-internal diagnostic, and the ratio C(k) in Fig. 4 provides a falsifiable momentum-resolved measure that other numerical methods (DMRG, DQMC) could test; (iii) the Bloch-wave control calculation (Sec. III C) cleanly demonstrates that the antinodal mode at t′>0 is conventional in character while the nodal mode at t′<0 is not. The finite-doping Green's function, by contrast, is explicitly phenomenological and its agreement with ARPES is at best illustrative; the paper is best read as a controlled single-/two-hole study plus a moti

major comments (4)
  1. [Sec. IV B, Fig. 8, Eq. (36)] The central finite-doping claim — that the two-fluid Green's function 'accounts for' the experimental electron-doped spectral evolution — is load-bearing for the paper's second stated question (b), but the construction has at least three free knobs per panel: the sector partition n_c̃=δ/2 (which the text itself describes as 'merely a convenient choice and does not carry intrinsic physical significance'), the recombination vertex λ (0.1J in Fig. 8, but 0.06J in the otherwise analogous hole-doped Fig. 7), and a per-doping AFM folding schedule J_cp = 0.4J, 0.25J, 0 at δ = 0.06, 0.14, 0.20. With three adjustable parameters per panel, reproducing three qualitative features (antinodal pockets, nodal pockets, large FS) is weak evidence for the mechanism rather than a prediction. The authors should either (a) provide a sensitivity analysis showing the qualitative sequence is robust over a substa
  2. [Sec. IV B.2, Eq. (36)] The text concedes that the linear superposition G^e = G^{e,qp}_fold + G^{e,com}_fold 'does not strictly preserve the local sum rule for total spectral weight.' This is not a cosmetic issue: the spectral-weight sum rule is one of the few exact constraints available at finite doping, and a Green's function that violates it can manufacture apparent pocket weight or Fermi-surface area that has no physical meaning. The authors should quantify the violation (e.g., report the integrated weight ∫dω A^e(k,ω) versus the exact value for representative k points or as a k-average), and/or construct the superposition with explicit weight factors w_qp(k), w_com(k) chosen to restore the sum rule, showing that the qualitative features of Fig. 8 survive.
  3. [Sec. III A, Fig. 3; Conclusion] The threshold t′/t = 0.09 for the activation of the coherent antinodal channel is quoted as a sharp number in the abstract-level claims and the Conclusion, but Fig. 3 shows that the kinetic-energy curves exhibit 'abrupt jumps... from level crossings' on a 12×12 open-boundary cluster. Level crossings on a finite OBC cluster are generically size-dependent, so the threshold value (and possibly its sharpness) may be a finite-size artifact. Since the two-fluid picture of Sec. IV is premised on this channel being active at physical t′/t ≈ 0.2–0.3, the authors should either demonstrate size convergence of the threshold (e.g., 8×8 vs 12×12 vs 16×16, or twisted boundary conditions to move the crossing points) or state clearly that 0.09 is an estimate whose precise value is not controlled. This is a bounded, feasible addition within the existing VMC machinery.
  4. [Sec. III C, Eq. (21b)] The factorized form |Ψ_{t′>0}⟩ = |Ψ_c⟩ ⊗ |Ψ_G⟩ is presented as the synthesis of the VMC results, but the VMC calculations are performed at the single- and two-hole level, where '⊗' has no operative meaning — there is no density of coherent carriers to factorize. Eq. (21b) is therefore an ansatz extrapolated to finite doping, not a result of Sec. III. This matters because the entire two-fluid counting (δ = n_c + n_c̃) and the independent-mode language of Sec. IV B rest on it. The authors should state explicitly that Eq. (21b) is a hypothesis motivated by the single-hole diagnostics, and ideally provide at least one finite-doping consistency check (e.g., a two-hole or few-hole calculation showing additive behavior of E_K^qp, or a VMC energy comparison of the factorized form against an unfactorized ansatz at small finite δ).
minor comments (6)
  1. [Sec. II A] Typo: 'open boundary conditionss' (extra s). Also Eq. (25) ends with a stray comma.
  2. [Sec. IV A vs IV B] λ = 0.06J is used for the hole-doped Fermi arc (Fig. 7) but λ = 0.1J for all electron-doped panels (Fig. 8). If this difference is physically motivated (e.g., doping- or sign-dependence of the recombination vertex), it should be stated; otherwise a common value would make the comparison cleaner.
  3. [Fig. 3] The axis labels are missing from the reproduced figure; please ensure the published version labels the ordinate (energies in units of J?) and identifies the three curves with a legend rather than only in the caption.
  4. [Sec. III B] The state-selection rule for C(k) ('the eigenstate whose energy lies closest to ω(k) and carries the largest spectral weight') is ambiguous when these two criteria select different states; please specify the tie-breaking procedure.
  5. [Fig. 8] The pink/blue color coding distinguishing quasiparticle from composite weight is defined only in the caption; a legend or an explicit statement of how the two contributions are separated when plotting −Im(G_qp + G_com) (which is not additive in the spectral function after folding) would help the reader.
  6. [Sec. I / Sec. V A] The comparison with the DQMC study of Ref. [37] (momentum-dependent damping as the origin of the dichotomy) is mentioned but not engaged quantitatively; a sentence on whether the two pictures are complementary or competing would strengthen the discussion. Also, Ref. [37] and Ref. [39] are arXiv preprints; please update if published.

Circularity Check

4 steps flagged · score 5.0 of 10

Single-hole VMC is non-circular; finite-doping ARPES 'explanation' is a phenomenological two-fluid GF with free n_c̃, λ, and J_cp tuned panel-by-panel to the experimental sequence that motivated the work.

  1. fitted input called prediction [Sec. IV B §§1–3; Eq. (36); Fig. 8 caption]
    "we take the density n_˜c to be δ/2 (δ=n_c + n_˜c), which is merely a convenient choice and does not carry intrinsic physical significance. ... the linear combination in Eq. (36) serves as a phenomenological superposition intended to illustrate the momentum-selective low-energy band structure, rather than strictly preserving the local sum rule for total spectral weight. ... with J_cp = 0.4J, 0.25J, and 0. Here, J is the superexchange coupling strength, and λ is set to 0.1J for all three panels."

    The finite-doping spectra that 'account for' electron-doped ARPES are produced by freely choosing the coherent/composite partition, the vertex λ, and a doping-dependent AFM folding schedule, then superposing two Green’s functions without a sum rule. Those knobs are adjusted so that low-δ antinodal pockets, intermediate-δ nodal+antinodal pockets, and high-δ large FS appear—the same sequence listed as experimental motivations (i)–(vi). Agreement is therefore partly built into the construction rather than predicted from the single-hole VMC alone.

  2. fitted input called prediction [Abstract; Introduction final paragraph; Sec. IV opening]
    "Motivated by such a structure and guided by experimental observations, we propose a phenomenological Green’s function at finite doping, yielding spectral features consistent with experiments."

    The abstract and framing present the phenomenological GF as the finite-doping answer to question (b) and as yielding experimental consistency, while the body states the construction is guided by those same observations and uses unconstrained parameters. Calling the output a result that accounts for the data overstates what is a tuned illustration.

2 more flagged steps
  1. self citation load bearing [Sec. IV A–B; App. B Table I; Eqs. (26)–(34); Refs. [45,53,54]]
    "building upon the phase-string formulation of the t–J model [43–45], we propose a two-component description... The doping-dependent mean-field parameters for the ˜c propagator are determined by self-consistently solving the saddle-point equations given in Appendix B. ... Following Refs. [45, 53], the mean-field effective Hamiltonian H=H_h+H_a+H_b is written as..."

    Composite-sector dispersions, pairing amplitudes, and the RPA recombination structure that fix where nodal weight sits are imported from the authors’ prior phase-string mean-field and Green’s-function papers, not re-derived or independently constrained at finite doping in this work. Combined with free λ and J_cp, the nodal composite arc is largely an output of that self-cited saddle-point apparatus plus hand-tuned scattering, not a new first-principles finite-doping calculation.

  2. ansatz smuggled in via citation [Sec. III D / Eq. (21); Sec. II A Eqs. (4)–(5); synthesis before Sec. IV]
    "Synthesizing the insights from the foregoing analysis with the t′=0 ground-state wave function [Eq. (5)], a unified picture emerges... |Ψ_{t′<0}⟩=|Ψ_G⟩, |Ψ_{t′>0}⟩=|Ψ_c⟩⊗|Ψ_G⟩. ... the ground state can be expressed as [45, 53]: |Ψ_G⟩≡e^{iΘ̂}|Φ_G⟩, |Φ_G⟩=P̂|Φ_˜c⟩⊗|Φ_b⟩."

    The finite-doping two-fluid ansatz |Ψ_c⟩⊗|Ψ_G⟩ is obtained by grafting the new VMC observation (extra coherent channel for t'>0) onto the authors’ prior fractionalized ground-state representation |Ψ_G⟩. The subsequent Green’s functions (resonance bubble vs intrinsic QP Dyson series) are diagrammatic transcriptions of that ansatz, so the momentum-selective two-fluid structure at finite doping is assumed by construction once Eq. (21) is written, not independently derived from a finite-doping variational principle.

full rationale

The load-bearing microscopic claim—that the single-hole t–t'–J ground state admits a two-component decomposition and that t'>0 beyond a threshold selectively activates bare-quasiparticle kinetic energy in the antinodal region—is obtained from a variational Monte Carlo computation (Sec. III, Eqs. 14–17, Figs. 3–4) with DMRG benchmarks (App. E). That chain does not reduce to its inputs by definition and is not circular. Circularity appears only in the bridge from that single-hole structure to finite-doping spectra (Sec. IV B, Fig. 8). There the authors write a two-fluid Green’s function whose sector partition is set by hand to n_c̃=δ/2 ('merely a convenient choice and does not carry intrinsic physical significance'), whose recombination vertex λ is chosen (0.06J–0.1J), and whose AFM folding J_cp is scheduled per doping panel (0.4J→0.25J→0). Eq. (36) is explicitly a non-sum-rule-preserving linear superposition 'intended to illustrate' the experimental nodal/antinodal sequence listed as motivating facts (i)–(vi) in the Introduction. Mean-field inputs for the composite sector are taken from the authors’ prior phase-string saddle-point equations (App. B, Table I; Refs. [45,53,54]). The resulting spectral panels are therefore consistency illustrations under free knobs, not parameter-free predictions forced by the VMC. Score 5 reflects genuine independent VMC content plus a partial, acknowledged phenomenological fit on the finite-doping claim that the abstract still presents as yielding features 'consistent with experiments.'

Assumptions & free parameters 5 free parameters · 6 assumptions · 3 invented entities

The central finite-doping narrative rests on the phase-string fractionalization framework (prior Weng et al.), a variational two-component ansatz validated mainly at one- and two-hole level, and a phenomenological two-fluid GF whose sector densities and couplings are not derived from a finite-doping saddle point. Several numbers are chosen to illustrate ARPES-like plots rather than predicted.

free parameters (5)
  • recombination vertex λ = 0.06J–0.1J (chosen per figure)
    Effective dressed vertex for fractionalization/recombination in the RPA GF; set by hand (e.g. 0.06J, 0.1J) to shape spectral weight in Figs. 7–9.
  • AFM folding strength J_cp = 0.4J, 0.25J, 0 across doping panels
    Coupling of carriers to static Néel order in Eq. (34); reduced with doping by hand (0.4J, 0.25J, 0) to weaken folding in Fig. 8.
  • composite density partition n_c̃ = n_c̃ = δ/2
    Fraction of doped carriers assigned to the incoherent composite sector; taken as δ/2 with explicit statement that the choice is convenient, not derived.
  • mean-field phase-string parameters (μ_b, Δ_b, μ_a, Δ_a, χ_a, γ) = Table I values at δ=0.06, 0.14, 0.20
    Saddle-point inputs from App. B / Table I that fix the composite propagator; standard within the authors' prior MF but still model parameters of the effective theory.
  • spectral broadening η = 0.05J
    Lorentzian width in single-hole spectral function Eq. (19).
assumptions (6)
  • domain assumption Phase-string sign structure and twisted-hole representation correctly capture the low-energy Hilbert space of the 2D t-J model.
    Sec. II A and App. A; foundation imported from prior Weng et al. work, not re-derived from first principles here.
  • domain assumption Single- and two-hole VMC ground states on ~12×12 open clusters faithfully represent the momentum-selective kinetic channels that survive at finite doping.
    Sec. III; the finite-doping story is motivated directly by these few-hole results.
  • ad hoc to paper For t'>0 the ground state factorizes as |Ψ_c⟩ ⊗ |Ψ_G⟩ with an independent coherent quasiparticle fluid coexisting with the fractionalized sector.
    Eq. (21b); postulated synthesis of the VMC observations, not a proven many-body factorization at finite density.
  • ad hoc to paper RPA resummation of recombination/fractionalization diagrams plus static AFM folding adequately describes the single-particle spectrum at finite doping.
    Sec. IV, Eqs. (28)–(36); phenomenological bridge from few-hole physics to ARPES.
  • domain assumption Particle-hole mapping with sign flip of t' correctly places electron-doped cuprates in the t'>0 hole-language t-t'-J model.
    Sec. II B and App. C; standard but essential for the asymmetry narrative.
  • standard math Standard variational Monte Carlo and DMRG methodology on finite lattices with the stated ansatz.
    Sec. III and App. E.
invented entities (3)
  • Momentum-selective two-fluid ground state |Ψ_c⟩ ⊗ |Ψ_G⟩ for t'>0
    purpose: Encode coexistence of an independent coherent antinodal quasiparticle fluid with the common fractionalized/incoherent sector.
    Introduced in Eq. (21) as the organizing structure for electron doping; not an extra orbital but a correlation-driven decomposition.
  • Composite / twisted fermion c̃ and vortex e^{iΩ} recombination channel
    purpose: Provide the incoherent component and the resonance-induced nodal propagation (Fermi arcs).
    Core of the phase-string representation (prior work, reused throughout Secs. II–IV); falsifiable only indirectly via spectral and current patterns.
  • Phenomenological two-channel electron Green's function G^{e,qp} + G^{e,com} with AFM folding
    purpose: Produce doping evolution of electron-doped ARPES spectra from the two-fluid picture.
    Sec. IV B; constructed to match experiment with free couplings rather than derived from a finite-doping variational principle.

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Pith. "Pith review of Momentum-Selective Two-Component Excitations in Electron-Doped Mott Insulators." pith.science (2026). https://pith.science/paper/5VAEVPBE

@misc{pith2026260724936,
  author       = {Pith},
  title        = {Pith review of: Momentum-Selective Two-Component Excitations in Electron-Doped Mott Insulators},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5VAEVPBE}},
  note         = {Machine review of arXiv:2607.24936}
}
abstract

Experimental studies reveal a striking asymmetry in low-energy single-particle excitations between electron- and hole-doped cuprates. Electron-doped cuprates display a nontrivial dichotomy: Fermi-liquid-like behavior (suggesting weaker electronic correlations) coexists with correlation-driven features typical of hole-doped systems. This dual nature challenges a unified description within a doped Mott insulator framework. The present work addresses this issue by establishing that the ground-state wave function of the $t$-$t'$-$J$ model generically possesses a two-component structure, comprising a coherent quasiparticle and an incoherent composite component. The kinetic energy arises from both the intrinsic propagation of the coherent quasiparticle and the resonance between these components. Using variational Monte Carlo at the level of a single hole, we show that for hole doping ($t'<0$), this resonance between components dominates and concentrates in the nodal region at low energies. This emergent propagation induced by resonance can be physically interpreted as originating from the recombination of fractionalized degrees of freedom, which drives various phenomena associated with strong correlations. Conversely, for electron doping ($t'>0$), the coherent quasiparticle propagation, which exhibits conventional properties of a Fermi liquid, is selectively enhanced in the antinodal region at low energies. This produces a separation in momentum space for systems with electron doping: the antinodal spectral weight at low energies is governed by the coherent quasiparticle, fundamentally differing from the nodal region, which remains dominated by the incoherent composite component. Motivated by such a structure and guided by experimental observations, we propose a phenomenological Green's function at finite doping, yielding spectral features consistent with experiments.

Figures

Figures reproduced from arXiv: 2607.24936 by the authors.

Figure 1
Figure 1. FIG. 1. Distinct evolution of Fermi surfaces (FS) away from half-filling ( [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Panels (a)–(e) illustrate a hopping process around [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Kinetic energy components [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Quasiparticle dispersion [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Expectation value of the hole-hole correlator [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Positive bias single-particle spectral function [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Fermi arc spectrum at hole-doping level [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Zero-energy single-particle spectra at finite doping. (a, b) Spectra for doping levels [PITH_FULL_IMAGE:figures/full_fig_p016_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Constant-energy contours ( [PITH_FULL_IMAGE:figures/full_fig_p018_9.png]

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