The DOI matches its Crossref record; 33 of the 33 references it cites were found in a registry or an index; none of the 24 sources its claims cite is checked for support yet.
Observation of topological order in a superconducting doped topological insulator
Open accessAbstract
When doped with copper, the topological insulator Bi2Se3 becomes superconducting. But for new physics and applications the search is not for just any superconductor; the material must retain its topological character. And indeed that is the case with doped Bi2Se3.
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21 Own result · 16 Not checked yet · 14 Own interpretation · 5 No basis given · 1 Own method
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“an unusual doping mechanism causes the spin-polarized topological surface states to remain well preserved at the Fermi level of the superconductor where Cooper pairing takes place.”
§ Observation of topological order in a superconducting doped topological insulator > Abstract
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In the paper
“Our data show that superconductivity occurs in a bulk relativistic quasiparticle regime”
§ Observation of topological order in a superconducting doped topological insulator > Abstract
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In the paper
“The slope of the surface-state band represents particle velocity, and is globally reduced in amplitude by 30% above the Dirac point when copper doping of x = 0.05 is added to the stoichiometric compound (see Fig. 2c).”
§ Observation of topological order in a superconducting doped topological insulator > Abstract
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In the paper
“Our results, summarized in Fig. 1, suggest that copper atoms can add holes or electrons depending on their net preference for occupying different kinds of site in the Bi 2 Se 3 lattice.”
§ Observation of topological order in a superconducting doped topological insulator > Abstract
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In the paper
“Here we present measurements of the bulk and surface electron dynamics in Bi 2 Se 3 doped with copper with a transition temperature T c up to 3.8 K”
- Also stated in: § Methods · plain
“Samples exhibit a superconducting transition at 3.8 K at optimal copper doping (x = 0.12).”
§ Observation of topological order in a superconducting doped topological insulator > Abstract
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- Also stated in: § Methods · plain
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In the paper
“Bulk and surface electrons are non-degenerate at the Fermi level.”
§ Observation of topological order in a superconducting doped topological insulator > Abstract
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In the paper
“Bulk and surface bands remain separate at intermediate k z values.”
§ Observation of topological order in a superconducting doped topological insulator > Methods
plain- Asserted: passes — The authors put it forward as true.
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In the paper
“The addition of copper causes the surface-state kinetics to become strongly hexagonally anisotropic (Fig. 2b)”
§ Observation of topological order in a superconducting doped topological insulator > Abstract
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In the paper
“On doping into the superconducting regime (x = 0.12), the Fermi energy is found to be raised to 0.25 eV above the bulk conduction-band minimum, placing the Fermi level in the linear (relativistic) regime of bulk band dispersion.”
§ Observation of topological order in a superconducting doped topological insulator > Abstract
plain- Asserted: passes — The authors put it forward as true.
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In the paper
“The superconducting coherence length can be estimated from the average Fermi velocity we observe here to be about 2,000 Å”
§ Observation of topological order in a superconducting doped topological insulator > Abstract
hedged- Asserted: passes — The authors put it forward as true.
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- The authors state this as an assumption: Scattering is minimal, and the superconducting gap follows the BCS relation to Tc.
- It may state two separate claims as one. 19
- The quote only partly states this claim. 1
- Probably not a substantial claim. 3
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In the paper
“The qualitative result of copper addition is a gradual enlargement of the Fermi surface from electron doping and, further surprisingly, a strong reduction in surface electron velocities through reshaping of the surface conduction band.”
§ Observation of topological order in a superconducting doped topological insulator > Abstract
boosteddirect- Asserted: passes — The authors put it forward as true.
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In the paper
“The phase-ordering temperature scale, also estimated from our data, is approximately T θ = 60,000 K, four orders of magnitude larger than the superconducting critical temperature of 3.8 K”
§ Observation of topological order in a superconducting doped topological insulator > Abstract
hedged- Asserted: passes — The authors put it forward as true.
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In the paper
“Carefully tracing the band (Fig. 3e,f) reveals a Fermi velocity of 3.5±2 eV Å along -M and 4.1±2 eV Å along -K, estimated within 50 meV of the Fermi level.”
§ Observation of topological order in a superconducting doped topological insulator > Abstract
hedged- Asserted: passes — The authors put it forward as true.
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In the paper
“A dispersion anomaly that we have noted in the inset to Fig. 3f also affects low-energy electron kinetics, making the bands more linear locally at the Fermi level.”
§ Observation of topological order in a superconducting doped topological insulator > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“In Cu x Bi 2 Se 3 , calculations predict that band inversion occurs at the -point (k x = k y = k z = 0) in the centre of the bulk conduction band, leading to a spin-orbit-induced Dirac-like bulk band, in qualitative agreement with our experiments.”
§ Observation of topological order in a superconducting doped topological insulator > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“In an ideal Dirac band structure, the rest mass will be equal to half the band gap, or 150 meV (giving M * = 0.15 eV, µ = 0.15 eV + 0.25 eV, and M * /µ ∼ 1/3).”
§ Observation of topological order in a superconducting doped topological insulator > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
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- Rests on an assumption: For the relativistic Hamiltonian, the chemical potential is the rest mass plus the valence-band minimum binding energy.
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In the paper
“Bulk Fermi momenta of 0.110±3 Å -1 and 0.106 ± 3 Å -1 are observed along the -M and -K directions respectively.”
§ Observation of topological order in a superconducting doped topological insulator > Abstract
plain- Asserted: passes — The authors put it forward as true.
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In the paper
“We also observed that attempting to force the creation of Cu Bi replacement defects by adding less bismuth results in very weak hole doping for Cu 0.1 Bi 1.9 Se 3 (Fig. 1c), raising the bulk conduction band entirely above the Fermi level.”
§ Observation of topological order in a superconducting doped topological insulator > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“Owing to asymmetries between conduction-and valence-band dispersion in the real experimental system, a larger effective rest mass is used to fit the curvature of the bottom of the conduction band in Fig. 3f, consistent with a ratio of M * /µ = 3/4.”
§ Observation of topological order in a superconducting doped topological insulator > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
- Rests on an assumption: For the relativistic Hamiltonian, the chemical potential is the rest mass plus the valence-band minimum binding energy.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“establishing that bulk superconducting pairing occurs in the presence of a non-degenerate, spin-polarized two-dimensional topological surface state”
§ Observation of topological order in a superconducting doped topological insulator > Abstract
boostedcorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“probing near the Fermi level, our data show that the spin-textured surface and doubly degenerate bulk bands are well separated by 0.04 Å -1 in momentum and by an energy spacing of about ∆ E = 130 meV”
§ Observation of topological order in a superconducting doped topological insulator > Abstract
boosted- Asserted: passes — The authors put it forward as true.
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In the paper
“Copper atoms intercalated between van der Waals-like bonded selenium planes (Cu int ) in the crystal are known to be single electron donors, whereas substitutional defects in which copper replaces bismuth in the lattice (Cu Bi ) contribute two holes to the system, which is similar to the behaviour reported in the impurity-atom study on the Bi 2 Se 3 matrix 25 .”
§ Observation of topological order in a superconducting doped topological insulator > Abstract
What the sources say
- Not checked yetcites [25] Vasko, A. Amphoteric nature of copper in Bi2Se3 crystals. Appl. Phys. 5, 217–221 (1974). source
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None of the sources cited for this claim have been checked yet.
In the paper
“Theoretically, superconducting pairing induced on a two-dimensional topological surface state through proximity to a bulk superconductor is believed to be inherently unconventional, with the potential to host non-Abelian (non-commutative) particles such as Majorana fermions in their vortices 12,13,20 .”
§ Observation of topological order in a superconducting doped topological insulator > Abstract
What the sources say
- Not checked yetcites [12] Fu, L. & Kane, C. L. Superconducting proximity effect and Majorana fermions at the surface of a topological insulator. Phys. Rev. Lett. 100, 096407 (2008). source
- Not checked yetcites [13] Wilczek, F. Majorana returns. Nature Phys. 5, 614–618 (2009). source
- Not checked yetcites [20] Fu, L. & Berg, E. Odd-parity topological superconductors: theory and application to CuxBi2Se3. Preprint at http://arxiv.org/abs/0912.3294 (2009).
hedgedconditional- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. It may state two separate claims as one.
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In the paper
“Therefore, our experimental results, in contrast to first-principle calculations, suggest that the crystal surface of Cu x Bi 2 Se 3 can, in fact, host two-dimensional vortices, which is critical for observing the non-Abelian statistics of the vortex Majorana fermions on the topological surface.”
§ Observation of topological order in a superconducting doped topological insulator > Abstract
hedgeddirect- Asserted: passes — The authors put it forward as true.
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What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“ARPES measurements were carried out at the Advanced Light Source beamlines 10 and 12 using 35.5-48 eV photons and at the Stanford Synchrotron Radiation Lightsource (7-22 eV photons) with better than 15 meV energy resolution and overall angular resolution better than 1% of the Brillouin zone.”
§ Observation of topological order in a superconducting doped topological insulator > Methods
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
In the paper
“A three-dimensional massive Dirac-like dispersion in topological spin-orbit materials is expected as a direct result of the band-inversion mechanism that causes the topological insulator state, and has also been experimentally observed in other topological insulator Bi 1-x Sb x alloys 4 .”
§ Observation of topological order in a superconducting doped topological insulator > Abstract
What the sources say
- Not checked yetcites [4] Hsieh, D. et al. A topological Dirac insulator in a quantum spin Hall phase. Nature 452, 970–974 (2008). source
plaindirect- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
In the paper
“Of the two remaining possibilities, even parity will result in a fully gapped band structure, and odd parity will generate new surface states resembling those shown in Fig. 4d (ref.20).”
§ Observation of topological order in a superconducting doped topological insulator > Abstract
What the sources say
- Not checked yetcites [20] Fu, L. & Berg, E. Odd-parity topological superconductors: theory and application to CuxBi2Se3. Preprint at http://arxiv.org/abs/0912.3294 (2009).
plaindirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The specific band structure and strong spin-orbit coupling of Cu x Bi 2 Se 3 suggest that the topological invariant 'n' may be non-zero, allowing the possibility of topological superconductivity in Cu x Bi 2 Se 3 .”
§ Observation of topological order in a superconducting doped topological insulator > Abstract
hedgedconditional- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The fact that superconductivity occurs in the relativistically linear bulk bands in Cu x Bi 2 Se 3 as seen in our data allows unusual combinations of spin and orbital mixing in the bulk superconducting state, making pairing take an unusual form”
§ Observation of topological order in a superconducting doped topological insulator > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
The authors state this as an assumption.
The Dirac point of the surface state has a fixed energy relative to the bulk bands.
“Assuming that the surface-state Dirac point energy is fixed relative to bulk bands”
The authors state this as an assumption.
The velocity v_C of the three-dimensional Dirac band is isotropic.
“For this discussion, we assume that v C is isotropic to illustrate the essential points”
The authors state this as an assumption.
Scattering is minimal, and the superconducting gap follows the BCS relation to Tc.
“assuming minimal scattering and a superconducting gap related to T C by the Bardeen-Cooper-Schrieffer formula.”
The paper relies on this without support.
For the relativistic Hamiltonian, the chemical potential is the rest mass plus the valence-band minimum binding energy.
“The chemical potential of this Hamiltonian is equal to the sum of the rest mass and the binding energy of the valence-band minimum”
The paper relies on this without support.
Bi2Se3 is a centrosymmetric crystal.
“Bi 2 Se 3 is a centrosymmetric crystal.”
The paper relies on this without support.
A topological superconductor naturally supports a Majorana surface state.
“Topological superconductors spontaneously realize a Majorana surface state.”
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“Such magnetic and superconducting orders on the surface states in Pb 1 À x Sn x Te can be different from those recently observed in the Z 2 TIs 37,38 because of its very distinct topology of surface electronic structure.”
From Observation of a topological crystalline insulator phase and topological phase transition in Pb1−xSnxTe (2012) · cites this paper as [37]
In the citing paper
“Unlike the bulk electronic states of Bi 2 Se 3 (ref.22), these features have no z-axis momentum dependence, confirming that they are largely two dimensional in nature (Fig. 1e).”
From A topological insulator surface under strong Coulomb, magnetic and disorder perturbations (2011) · cites this paper as [22]
In the citing paper
“Momentum along the ẑ axis is determined using an inner potential of 9.5 eV, consistent with previous photoemission investigations of undoped Bi 2 Se 3 (refs 7,22).”
From A topological insulator surface under strong Coulomb, magnetic and disorder perturbations (2011) · cites this paper as [22]
Citations
Cites
Colloquium : Topological insulators
Hasan, M. Z., & Kane, C. L. (2010) · Reviews of Modern Physics · doi:10.1103/revmodphys.82.3045 · Cited by 19,930
Self-citationSuperconducting Proximity Effect and Majorana Fermions at the Surface of a Topological Insulator
Fu, L., & Kane, C. L. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.096407 · Cited by 4,868
Topological insulators with inversion symmetry
Fu, L., & Kane, C. L. (2007) · Physical Review B · doi:10.1103/physrevb.76.045302 · Cited by 4,252
Observation of a large-gap topological-insulator class with a single Dirac cone on the surface
Xia, Y., Qian, D., Hsieh, D., Wray, L., Pal, A., Lin, H., Bansil, A., Grauer, D., Hor, Y. S., Cava, R. J., et al. (2009) · Nature Physics · doi:10.1038/nphys1274 · Cited by 3,765
Self-citationExperimental Realization of a Three-Dimensional Topological Insulator, Bi 2 Te 3
Chen, Y. L., Analytis, J. G., Chu, J.-H., Liu, Z. K., Mo, S.-K., Qi, X. L., Zhang, H. J., Lu, D. H., Dai, X., Fang, Z., et al. (2009) · Science · doi:10.1126/science.1173034 · Cited by 3,585
A topological Dirac insulator in a quantum spin Hall phase
Hsieh, D., Qian, D., Wray, L., Xia, Y., Hor, Y. S., Cava, R. J., & Hasan, M. Z. (2008) · Nature · doi:10.1038/nature06843 · Cited by 3,523
Self-citationClassification of topological insulators and superconductors in three spatial dimensions
Schnyder, A. P., Ryu, S., Furusaki, A., & Ludwig, A. W. W. (2008) · Physical Review B · doi:10.1103/physrevb.78.195125 · Cited by 3,322
The Universe in a Helium Droplet
Volovik, G. E. (2009) · doi:10.1093/acprof:oso/9780199564842.001.0001 · Cited by 2,632
A tunable topological insulator in the spin helical Dirac transport regime
Hsieh, D., Xia, Y., Qian, D., Wray, L., Dil, J. H., Meier, F., Osterwalder, J., Patthey, L., Checkelsky, J. G., Ong, N. P., et al. (2009) · Nature · doi:10.1038/nature08234 · Cited by 1,979
Self-citationObservation of Unconventional Quantum Spin Textures in Topological Insulators
Hsieh, D., Xia, Y., Wray, L., Qian, D., Pal, A., Dil, J. H., Osterwalder, J., Meier, F., Bihlmayer, G., Kane, C. L., et al. (2009) · Science · doi:10.1126/science.1167733 · Cited by 1,239
Self-citation
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- Hasan, M. Z. & Kane, C. L. Topological insulators. Preprint at http://arxiv.org/abs/1002.3895 (2010). · arXiv
- Kitaev, A. Proc. of the L.D. Landau Memorial Conf. ‘Advances in Theoretical Physics’, June 22–26 (2008).
- Fu, L. & Berg, E. Odd-parity topological superconductors: theory and application to CuxBi2Se3. Preprint at http://arxiv.org/abs/0912.3294 (2009). · arXiv
- Carlson, E. W. et al. in The Physics of Conventional and Unconventional Superconductors (eds Bennemann, K. H. & Ketterson, J. B.) (Springer-Verlag,2002).
- Blaha, P. et al. Computer Code WIEN2K (Vienna Universityof Technology, 2001).
Cited by
Sorted by citations
Topological insulators and superconductors
Qi, X.-L., & Zhang, S.-C. (2011) · Reviews of Modern Physics · doi:10.1103/revmodphys.83.1057 · Cited by 14,394
New directions in the pursuit of Majorana fermions in solid state systems
Alicea, J. (2012) · Reports on Progress in Physics · doi:10.1088/0034-4885/75/7/076501 · Cited by 3,066
Classification of topological quantum matter with symmetries
Chiu, C.-K., Teo, J. C. Y., Schnyder, A. P., & Ryu, S. (2016) · Reviews of Modern Physics · doi:10.1103/revmodphys.88.035005 · Cited by 2,736
Topological Insulator Materials
Ando, Y. (2013) · Journal of the Physical Society of Japan · doi:10.7566/jpsj.82.102001 · Cited by 1,789
Topological superconductors: a review
Sato, M., & Ando, Y. (2017) · Reports on Progress in Physics · doi:10.1088/1361-6633/aa6ac7 · Cited by 1,733
Metadata
- Authors
- Wray, L. A., Xu, S.-Y., Xia, Y., Hor, Y. S., Qian, D., Fedorov, A. V., Lin, H., Bansil, A., Cava, R. J., & Hasan, M. Z.
- Affiliations
- Lawrence Berkeley National Laboratory (US)
- Princeton University (US)
- Northeastern University (US)
- Corresponding author
- Hasan, M. Zahid
- ORCID
- Venue
- Nature Physics
- Published
- 2010-09-19
- Volume
- 6
- Issue
- 11
- Pages
- 855-859
- ISSN
- 1745-2473 (ISSN-L)
- 1745-2481
- OpenAlex
- W1767686761
- Semantic Scholar
- 28e8bd9546e82f3fc6ddec020df5f72266a60f44
- Cited by
- 464
- References
- 33
- Citations by year
- 2026: 3 · 2025: 11 · 2024: 24 · 2023: 28 · 2022: 30 · 2021: 25 · 2020: 33 · 2019: 34 · 2018: 29 · 2017: 35 · 2016: 34 · 2015: 36 · 2014: 31 · 2013: 38 · 2012: 37
- FWCI
- 19.04
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Nature Physics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation (0819860)
- U.S. Department of Energy (DEFG0207ER46352, AC03-76SF00098, DE‐FG02‐, DEFG0205ER46200, FG02-07ER46352)
- Alfred P. Sloan Foundation
- Division of Materials Research (DMR-0819860)
- Basic Energy Sciences (DE-FG-02-07ER46352, AC03-76SF00098, DE-FG-02-05ER46200, DE-FG02)
- Topics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Topological Materials and Phenomena
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Physics of Superconductivity and Magnetism
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Advanced Condensed Matter Physics
- Keywords
- topological superconductivity, doped topological insulators, Bi2Se3, copper doping, Majorana fermions, topological surface states, spin-polarized surface states, Cooper pairing, topological order, electron dynamics
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
A language model drew the claims from the paper on 2026-10-06, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-10-06 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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