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Quenching of Nonrelativistic p-Wave Spin Splitting by Reduced c-f Coupling in CeNiAsO

Xinnuo Zhang,1 , ∗ Zhicheng Jiang,1 , ∗ Shibo Shen,2 , ∗ Jian Yuan,3 , ∗ Junseo Yoo,4 Xun Ma,1 Mao Ye,5 , 6 Jishan Liu,5 , 6 Zhengtai Liu,5 , 6, † Changyoung Kim,4 Yanfeng Guo,3 , 7, ‡ Yilin Wang,2 , 8, § and Dawei Shen1 ,

arXiv:2606.02420v2 [cond-mat.str-el] 12 Jun 2026

1 National Synchrotron Radiation Laboratory and School of Nuclear Science and Technology,

University of Science and Technology of China, Hefei, 230026, China 2 School of Emerging Technology, University of Science and Technology of China, Hefei 230026, China

3 State Key Laboratory of Quantum Functional Materials, School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China 4 Department of Physics and Astronomy, Seoul National University, Seoul 08826, Republic of Korea

5 Shanghai Synchrotron Radiation Facility, Shanghai Advanced Research Institute,

Chinese Academy of Sciences, Shanghai 201210, China 6 National Key Laboratory of Materials for Integrated Circuits, Shanghai Institute of Microsystem and Information Technology,

Chinese Academy of Sciences, Shanghai 200050, China

7 ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University, Shanghai 201210, China 8 Hefei National Laboratory, Hefei 230088, China

The application of spin-space group symmetries to noncollinear antiferromagnets has led to the prediction of odd-parity, nonrelativistic spin splittings, making the physical realization of a practical p-wave magnet a central pursuit in spintronics. The layered heavy-fermion oxypnictide CeNiAsO has been widely regarded as a prototypical platform to verify this paradigm. Here, we investigate the electronic structure of single-crystal CeNiAsO using high-resolution, ultra-low-temperature and resonant angle-resolved photoemission spectroscopy (ARPES), and ab − initio calculations. Across the consecutive magnetic transitions into the ordered phases, our spectroscopic data reveal neither the expected band folding associated with a spin density wave nor any observable p-wave spin split- ting, demonstrating that the conduction bands retain full degeneracy. By tracking the temperature dependence of the Ce 4f spectral weight via resonant ARPES, we find negligible c-f hybridiza- tion near the Fermi level within magnetically ordered states, confirming that the Ce 4f electrons reside close to the localized limit. Our findings establish a clear many-body constraint on the pro- jection of real-space magnetic symmetries onto momentum-space electronic bands, demonstrating that symmetry classifications constitute a necessary framework but are not a sufficient condition for nonrelativistic spin splittings in the presence of strong electronic correlations. The realization of nonrelativistic spin splittings inde- pendent of spin-orbit coupling (SOC) has emerged as a central frontier in quantum magnetism and spintron- ics [1–6]. This paradigm was initiated by altermagnets, where collinear antiferromagnetic (AFM) structures un- lock an even-parity (d- or g-wave) spin splitting at the electron-volt scale for high-efficiency spin currents [5, 7– 16]. Stimulated by this, spin-space group (SSG) [17–23] based classifications have generalized this phenomenon to noncollinear (NCL) magnetic structures that break spatial inversion symmetry while preserving a general- ized time-reversal symmetry, predicting odd-parity p- wave magnets [24–32]. It shifts the spin-polarized Fermi surfaces asymmetrically in momentum space, satisfying E(k, σ⊥ ) = E(−k, −σ⊥ ) and generating a unique p-wave spin texture with opposite polarizations on opposing sides of the Fermi surface [Fig. 1(a)]. Acting as a nonrel- ativistic counterpart to relativistic Rashba/Dresselhaus SOC, these profiles are governed by strong exchange en- ergy scales and highly attractive for nonrelativistic Edel- stein responses and for engineering unconventional triplet pairing toward topological superconductivity [33–48]. The heavy-fermion oxypnictide CeNiAsO has been proposed as a promising platform to host p-wave spin splitting driven by its coplanar NCL AFM order on Ce- sites [24, 32–36, 49–54]. To date, however, a direct momentum-resolved spectroscopic verification of such odd-parity spin splitting remains entirely elusive across all candidate materials. Although SSG symmetry classi- fications establish the necessary condition for odd-parity magnets, the spin-splitting in actual materials strongly depends on the assumed well-defined single-particle band structures in momentum space. In strongly corre- lated heavy-fermion f -electron materials, this single- particle framework must confront the intrinsic many- body competition between the local-moment behavior of f -electrons and the phase-coherent hybridization with the conduction c-electrons. To enable the momentum- space spin splitting, the correlated 4f electrons must ei- ther form coherent, dispersive bands that split directly, or develop a sufficiently strong c-f exchange coupling to transfer the odd-parity magnetic potentials to the itin- erant conduction bands. Both scenarios dictate a phase- coherent c-f entanglement, leaving the validity of static symmetry predictions in the presence of strong electronic correlations an open but crucial question.

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0 5 10 15 0.010 0.011 0.012 χ ( e m u / m o l / O e ) 0 100 2 00 300 0.004 0.008 0.012 0.016 χ ( e m u / m o l / O e ) T ( K) B = 1 T (f) Ce O As Ni (a) (b) (c) (d) kx ky [C2 ⊥| τ] (e) d R / d T ( µ Ω · K - 1 ) 0 5 10 15 20 0 .0 1 .0 2 .0 TN 1 TN 2 0 50 100 150 200 250 300 1.0 2.0 3.0 T(K) 0 5 10 15 20 25 30 35 7.0 7.5 8.0 8.5 9.0 9.5 B ( T) −7 0 7 −0.006 0 .000 0.006 M ( e m u ) Temp=2K (g) R ( μ Ω ） R ( μ Ω ） E(k, σ⊥ ) = E(-k, -σ⊥ ) FIG. 1. Basic properties and transport measurements. (a) Spin-polarized Fermi surfaces of a p-wave magnet with the dispersion satisfying E(k, σ⊥ ) = E(−k, −σ⊥ ) . (b) Tetrago- nal crystal structure of CeNiAsO showing alternating stacked layers. (c) Incommensurate SDW below TN 1: a magnetic cycloid approximately treated as a longitudinal spin-density wave. (d) Commensurate coplanar order below TN 2: a copla- nar helical spin structure. (e) Resistivity R(T ) of CeNiAsO; inset shows dR/dT to resolve the two-step transitions, where TN 1= 8.66K, TN 2= 6.23K. (f) Susceptibility χ(T ) measured at B = 1 T along the c axis; inset magnifies the low-T region. (g) Magnetoresistance R(B) up to 35 T at 2 K temperature; inset shows M (B) from -7 T to 7 T. In this Letter, we address this issue by tracking the low-energy electronic structure of single-crystal CeNiAsO using high-resolution angle-resolved photoemission spec- troscopy (ARPES). Across the magnetic transitions into the coplanar NCL AFM state, our momentum-resolved spectra reveal strict, unlifted electronic degeneracy with no detectable p-wave band splitting at zero magnetic field. Furthermore, resonant ARPES (rARPES) mea- surements detect no spectral signatures of coherent Ce 4f hybridization with the conduction bands near the Fermi level (EF ) within the magnetically ordered state. This strongly suppressed hybridization confirms that the f electrons remain nearly fully localized, thereby isolating the conduction electrons from the expected odd-parity magnetic background such that there is no spin split- ting. Our results demonstrate that while SSG provides a necessary framework for identifying the symmetry of al- termagnets and odd-parity magnets, it is not a sufficient condition for the expected spin splitting in the systems with strong electronic correlations. Details of our experiments and ab − initio calculations can be found in Section 1 of the Supplemental Material (SM). CeNiAsO crystallizes in a tetragonal ZrCuSiAs- type structure with space group P 4/nmm (No. 129) [Fig. 1(b)] [55–57]. Prior neutron scattering and trans- port studies resolve two successive magnetic transitions upon cooling from the paramagnetic state: a spin- density-wave (SDW) phase below TN 1 ≈ 9 K [Fig. 1(c)], and then a coplanar NCL AFM state below TN 2 ≈ 6 K [Fig. 1(d)] [52, 53]. Governed by the non-trivial SSG op- eration [C2 ⊥| t], where t is a fractional spatial translation, this state was predicted to exhibit an asymmetric p-wave spin splitting [E(k, σ⊥ ) = E(−k, −σ⊥ ) ] with nonzero spin textures along the C2 ⊥ rotation axis [Fig. 1(a)]. To benchmark our samples against established struc- tural and magnetic properties, single-crystal X-ray diffraction (XRD) was performed [Fig. S1, TABLE I and II in SM], revealing sharp Bragg reflections with no de- tectable impurity phases. The temperature-dependent resistivity R(T ) [Fig. 1(e)] exhibits clear anomalies, with the derivative dR/dT resolving magnetic transitions at 8.66 K and 6.23 K, respectively, in good agreement with literature [52, 53]. The magnetic susceptibility χ(T ) [Fig. 1(f)], measured under B = 1 T along the c-axis, displays a pronounced peak at TN 1 and a subtle shoul- der around TN 2 under both zero-field/field cooling con- ditions, substantiating the two-step magnetic ordering. Moreover, high-field magnetotransport measurements re- veal a hysteretic magnetoresistance between 15 and 25 T [Fig. 1(g)], indicative of magnetic frustration within the ordered Ce layers. As shown in the inset of Fig. 1(g), the magnetization increases monotonically up to 7 T, while the negative magnetoresistance emerging beyond B > 25 T indicates that the system approaches a field- induced polarized magnetic state. The bulk Brillouin zone (BZ) of CeNiAsO and its pro- jection onto the (001) surface BZ are schematically illus- trated in Fig. 2(a). Because CeNiAsO naturally cleaves along polar planes to yield either [CeO]+ - or [NiAs]− - terminated surfaces, we characterized these cleavage pro- files using micro-focused ARPES. Figure 2(b) displays representative As 3d core-level spectra from two distinct domains. Specifically, domain 1 exhibits a pronounced satellite splitting within the As 3d3 /2 and 3d5 /2 spin- orbit doublets, whereas this feature is substantially sup- pressed in domain 2. This distinct line-shape disparity allows us to assign domain 1 to the [NiAs]− -terminated surface layer. Paramagnetic state ARPES cuts along Γ-X [Fig. 2(c), with second-order derivatives on the right halves] confirm that both domains possess highly similar bulk bands. However, because domain 2 hosts additional folding replicas driven by cleavage-induced surface recon-

3

Γ X M E - E F ( e V ) SS -1.0 -0.5 0 E - E F ( e V ) -1.0 0 1.0 k/ / (Å- 1 ) Γ X X Domain 1 SS kz ky kx Γ Z M X Γ M X -1.0 0 1.0 k/ / (Å- 1 ) Γ X X Domain 2 -1.0 -0.5 0 E - E F ( e V ) (a) (e) I n t e n s i t y ( a r b . u n i t s ) -42 -41 -40 E - EF (eV) As 3d3 /2 Domain1 As 3d5 /2 Domain2 (b) (c) MAX MIN (d) k z ( 2 π / c ) 5 6 7 Γ M M FIG. 2. Paramagnetic-state ARPES results. (a) 3D Bril- louin zone of CeNiAsO and its projection onto the (001) sur- face Brillouin zone. (b) Cleaved CeNiAsO surface with pos- sible terminations; spatially resolved As 3d core-level spectra for two surface domains (gray curves: Lorentzian fits). (c) ARPES intensity and second-derivative images along Γ-X for the two domains; arrow: an extra surface-related band in do- main 1. (d) Photon-energy-dependent ARPES intensity along M -Γ-M as a function of kz ; dashed line guides the eye for pe- riodic kz dispersion, the inner potential is 10 eV . (e) 3D ARPES intensity on the Γ-X-M plane, including the Fermi- surface map and band dispersions; white curves: renormal- ized bulk-band calculations; black arrows: additional surface states. structions, we focus our subsequent systematic analysis on the domain 1 (datasets of domain 2 are compiled in Fig. S3). By mapping the kz -k∥ photoemission intensity disper- sion on domain 1 [Fig. 2(d)], we resolved a clear periodic modulation along the kz axis that matches density func- tional theory (DFT) bulk band calculations (dashed lines and Fig. S7 and S8), establishing hν = 90 eV as the bulk Γ-X-M plane. Figure 2(e) summarizes the paramagnetic electronic structure mapped within the high-symmetry plane, displaying the Fermi surface alongside the cor- responding dispersions. The overlaid DFT calculations, treating the Ce 4f electrons as localized core states, re- produce the primary experimental bulk dispersions ex- ceptionally well under a modest renormalization factor of ∼ 0.7, while a few mismatched spectral features (marked by black arrows) can be assigned to surface states. Having established the paramagnetic state, we next tracked the low-energy bands across the successive mag- netic phase transitions of CeNiAsO. As illustrated in Figs. 3(a1)–(a3) and (b1)–(b2), DFT calculations with- out considering the strong electron correlations of Ce- 4f electrons, i.e., in the itinerant limit, predict two distinct electronic signatures upon entering the ordered states [49, 50]. Firstly, the approximate 2 × 1 collinear SDW phase below TN 1 doubles the magnetic unit cell, re- constructing the BZ and folding the Fermi surface along the Γ-X direction [Fig. 3(a2)]. Second, the onset of the coplanar NCL AFM order below TN 2 is predicted to ex- hibit sizeable p-wave spin splitting, in particular, along the Γ-X direction [Figs. 3(a3) and (b2)]. As shown in Figs. 3(b1) and (b2), the calculated 4f bands near EF are highly dispersive and strongly hybridized with the Ni-3d orbitals. Consequently, the predicted spin split- tings are jointly sustained by both the itinerant Ce-4f and Ni-3d electrons. This itinerant picture is consistent with previous theoretical reports [33, 49–51]. Remarkably, our experimental observations stand in sharp contrast to these theoretical predictions. Fig- ures 3(c)–(e) display the Fermi surfaces systematically mapped across the three distinct magnetic regimes at 13.5 K, 7 K, and 5.9 K, respectively. The global Fermi surface topography remains entirely invariant, exhibiting no signatures of folded replicas or split bands. This per- sistent rigidity is further verified by the high-resolution Γ-X energy-momentum dispersions [Fig. 3(f)–(h)], in which the primary electron pocket evolves smoothly across both TN 1 and TN 2 without any detectable back- folding or symmetry-breaking reconstruction. Most im- portantly, the low-temperature bands below TN 2 retain strict spin degeneracy, displaying no evidence of the predicted p-wave nonrelativistic splitting as illustrated in Fig. 3(b2). This complete quenching of the ex- pected spin splitting is further substantiated by ultra- low-temperature laser-ARPES scans down to 2.9 K (Fig. S4) and systematic temperature-dependent surveys extending across multiple distinct kz planes (Fig. S2, S5 and S6), both of which consistently resolve a single band feature devoid of any energy or momentum splitting. This unexpected decoupling between the magnetic or- der in real space and the spin splitting in momentum space points to a deeply localized regime where the c-f coupling is strongly suppressed, effectively screen- ing the conduction electrons from the underlying mag- netic background. To elucidate its microscopic origin, we performed rARPES measurements across the Ce 4d-4f threshold (hν = 118–122 eV) to systematically enhance the 4f spectral weight along Γ-X [Figs. 4(a1) and (a2)]. This allows us to discern whether the missing spin split- ting stems from a fundamental lack of phase-coherent

4 (a2) T < T N1 T > T N1

Y M (c) 1.0 (a3) T < T N2 Y M M

0.3 Γ Γ X Γ X X 0 0 -0.5

-0.3

-1.0

(g) kx (Å- 1 ) -1 .0 -0.5 0 0.5 1.0 -1.0 -0.5 0 0.5 1.0 (f) x -1.0 -1.0 -0.5 0 0.5 1.0 -1.0 -0.8 -0.6 -0.4 -0.2 0 k (Å- 1 ) E - E F ( e V ) -1.0 -0.5 0 0.5 1.0 -1 .0 -0.5 0 0.5 1.0 (h) kx (Å- 1 ) -1.0 -0.5 0 0.5 1.0 0 -0.1 -0.2 E - E F ( e V ) Γ 0 0.3 -0.3 <Sz > -X (b1) 0.1 0.2 X Γ -X X T < TN 2 T < TN 2 (b2)

T = 7K (d) T = 13.5K T = 5.9K (e)

FIG. 3. Evolution of electronic structures as decreasing temperatures. (a1)-(a3) The DFT calculated Fermi surfaces for the nonmagnetic phase, SDW phase below TN 1, and p-wave magnetic phase below TN 2, respectively. The magnetic order doubles the unit-cell and folds the bands along Γ-X direction, and shows a p-wave spin splitting with nonzero sz (k). The incommensurate SDW phase below TN 1 is approximated as a 2 × 1 collinear AFM order in calculation. (b1) The bands are projected onto Ce-f (pink) and Ni-d (blue) orbitals. (b2) Spin projections of sz (k). (c)-(e) ARPES Fermi-surface maps at 13.5 K, 7 K, and 5.9 K; red dots: high-symmetry points; red squares: appended Brillouin zone. (f)-(h) ARPES spectra along Γ–X at the same temperatures corresponding to (c)-(e). c-f hybridization, or merely from a suppressed photoe- mission cross-section. Despite the massive resonance- induced enhancement of 4f sensitivity, particularly at the 122 eV maximum, the spectra resolve two sharply localized 4f flat bands traversing the pre-existing non- magnetic bands, with no discernible signatures of coher- ent c-f hybridization or f band splitting near EF . These rARPES results unambiguously establish that the ab- sence of nonrelativistic spin splitting is not an artifact of insufficient photoemission intensity. Instead, the low- energy physics remains dominated by deeply localized 4f moments that fail to form phase-coherent itinerant quasi- particle bands within the magnetically ordered ground state. To provide a microscopic basis for this localized ground state, we then performed systematic DFT plus dynami- cal mean-field theory (DFT+DMFT) calculations in the paramagnetic phase to track the evolution of the Ce 4f states as a function of the local Coulomb repulsion U . As increasing U from 6 eV to 8 eV, the Ce-4f bands significantly deviate from the itinerant limit [Figs. 4(c)- (d), DFT calculation with Ce-4f as valence states] and become highly incoherent atomic-like levels pinned near EF , and the c-f hybridization is significantly suppressed [Figs. 4(e)-(j)], which asymptotically converges toward the fully localized limit where the 4f electrons are frozen as core states in DFT calculations [Figs. 4(k)-(l)]. This evolution directly substantiates a comprehensive c-f or- bital decoupling. We note that the calculated Fermi sur- face at U = 7.3 eV in the paramagnetic state [Fig. 4(h)] exhibits an exceptional match with our experimental data in the magnetically ordered state [Fig. 4(b)]. While a trace of residual c-f hybridization remains, as shown in the inset of Fig. 4(g), its dynamic scattering ampli- tude is heavily suppressed. This confirms that the Ce-4f electrons reside deep within the localized-moment limit. This underscores a correlation-enforced boundary where the localized 4f electrons fail to transfer their magnetism to the conduction electrons to induce a spin splitting of the Fermi surface. The failure of the conduction electrons to inherit the magnetism directly reflects a deep positioning of CeNiAsO within the classic Doniach phase diagram, which scales the microscopic balance between intersite RKKY interactions (TR KKY ∝ J 2 c -f ) and intrasite Kondo screening (T ∗ ∝ exp(−1/ρJc -f )) [58]. In the predic- tions of the p-wave magnets based on SSG symmetries and DFT calculations, it was implicitly assumed that the candidate materials reside on the right side of the Doniach framework, developing a heavy-fermion coher- ence temperature (T ∗ ) well above the magnetic order- ing temperature (TN ) [34, 49–51, 58–61]. In that sce- nario, pre-established coherent c-f hybridization would integrate the Ce 4f electrons into the Fermi sea, allow- ing the low-temperature odd-parity exchange field to eas- ily transfer to the itinerant heavy quasiparticles and lift the Kramers degeneracy. However, CeNiAsO actually occupies the opposite, localized extreme of the Doniach

5 DFT , f as valence states 118eV 6.5K 122eV 6.5K 0 (a1) (a2) 0.5 (c) 4f 5/2 -0.2

Γ M X Γ M X Γ M X Γ X Γ M DFT , f as core states DFT+DMFT , U=6 eV Γ X Γ M DFT , f as valence states .5 0 .5 .0 Γ X Γ M low high Γ M X DFT+DMFT , U=7.3 eV Γ X Γ M X DFT+DMFT , U=8 eV Γ Γ M .5 (h) Γ M X (c) (d) (e) (f) (g) (h) (i) (j) (k) (l)

-1.0

_ _ _ _ _ X Γ X Γ X

90eV 5.9K _ -1.5 X _ M _ _ min X max (h) (d) (b)

Γ

FIG. 4. Reduced c–f coupling due to localized f electrons. (a1),(a2) ARPES intensity along Γ–X at 6.5 K with near-resonant photon energies 118 eV and 122 eV, respectively. Dashed lines: first Brillouin-zone boundaries; solid line: EF . In (a2), horizontal dashed lines mark resonant 4f levels, 4f 5/2 and 4f 7/2 . (b) ARPES Fermi surface at 5.9 K; black arrow indicates the surface state (SS). (c),(d) DFT band structure and Fermi surface in nonmagnetic state with Ce-f as valence states. (e)-(j) DFT+DMFT results in paramagnetic state for three values of Hubbard U . (k),(l) DFT results in nonmagnetic state with Ce-f as core states. SOC is included in calculations. continuum, in which weak c-f coupling locks the system into an RKKY-dominated regime (TR KKY ≫ T ∗ ) [58– 68]. Our spectroscopic and theoretical results confirm that these Ce 4f states remain entirely confined to a highly incoherent atomic-like levels, leaving the conduc- tion bands completely detached from the magnetic skele- ton in terms of low-energy quantum coherence. This creates a severe paradox: while the conduction electrons act as virtual high-energy intermediaries to me- diate the RKKY exchange and stabilize the long-range magnetic ordering, they remain dynamically decoupled from the ordered 4f moments near EF due to the lack of phase-coherent c-f entanglement. Consequently, the low-energy exchange potential experienced by conduction bands remains symmetric, suppressing the nonrelativis- tic spin splitting and preserving full degeneracy. This c-f decoupling reveals a critical boundary when applying the SSG-based symmetry classifications to the strongly cor- related materials. While the real space magnetic ordering provides the structural symmetry required by theory, it is not a sufficient condition to realize the desired spin split- ting of electronic bands in the momentum space. Our findings suggest that future materials searching for al- termagnets or odd-parity magnets in f -electron systems need to evaluate the competition between TR KKY and T ∗ alongside the structural and magnetic ordering clas- sifications, preferentially targeting systems with intrinsic carrier itineracy or robust Kondo lattices with higher co- herence temperatures. In summary, our detailed ARPES investigation of single-crystal CeNiAsO provides a definitive arbitration on the physical realization of odd-parity nonrelativistic spin splittings. Across the consecutive magnetic transi- tions, the conduction bands retain full Kramers degener- acy, exhibiting neither the expected p-wave spin splitting nor SDW-induced unidirectional band folding, which di- rectly challenges the symmetry-based predictions. This absence of spin splitting stems from the full localiza- tion of Ce 4f electrons and the lack of coherent c-f hy- bridization, thereby quenching the exchange potential of the conduction electrons. Our findings demonstrate that symmetry classifications constitute a necessary frame- work but not a sufficient condition for nonrelativistic spin splittings, highlighting a rigid many-body constraint. Acknowledgment-This work is supported by National Key R&D Program of China (Grants No. 2023YFA1406304, 2023YFA1406100 and 2024YFA1408103), National Natural Science Foundation of China (Grant No. 12494593), HFNL Self-Deployed Project (Grant No. ZB2602000302), Anhui Provincial Natural Science Foundation (Grant No. 2408085J003), and the New Cornerstone Science Foundation. Y. F. Guo acknowledges the Analytical Instrumentation Center (SPST-AIC10112914) and the Double First- Class Initiative Fund of ShanghaiTech University. Y.L. Wang was supported by Quantum Science and Technology-National Science and Technology Major Project (No. 2021ZD0302803). Z.C.J. acknowledges the China National Postdoctoral Program for Innovative Talents (BX20240348) and Xiaomi Young Talents Pro- gram. We thank the Shanghai Synchrotron Radiation Facility (SSRF) of BL03U (31124.02.SSRF.BL03U) for assistance on the ARPES measurements. Data availability-The data that support the findings of this article are not publicly available. The data are available from the authors upon reasonable request.

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