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Paper Citation Record · LEDGER

Multifold degeneracy points of quantum systems and singularities of matrix varieties

As of 17 August 2026, this Paper Citation Record lists 64 of 64 outbound references and 0 inbound Pith citation observations for arXiv:2507.17485.

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pith.paper-citation-record.v1
2507.17485 v1

Coverage vector

measured 64 of 64 reference resolution

Typed states for the displayed outbound observations.

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measured 64 of 64 standing notices

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measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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Source: cited_works

Reference resolution

64 of 64 outbound references displayed

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External citation measurements

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Outbound references

Observation cdd4b9f4-1243-4de8-91b2-b84f016cdc47 · outbound

This paper cites Fundamental laws of chiral band crossings: Local constraints, global con- straints, and topological phase diagrams.

Multifold degeneracy points of quantum systems and singularities of matrix varieties Fundamental laws of chiral band crossings: Local constraints, global con- straints, and topological phase diagrams

Reference 1

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This paper cites Weyl and Dirac semimetals in three- dimensional solids.

Multifold degeneracy points of quantum systems and singularities of matrix varieties Weyl and Dirac semimetals in three- dimensional solids

Reference 2

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This paper cites Remarks on Eigenvalues and Eigenvectors of Hermitian Matrices, Berry Phase, Adiabatic Connections and Quantum Hall Effect.

Multifold degeneracy points of quantum systems and singularities of matrix varieties Remarks on Eigenvalues and Eigenvectors of Hermitian Matrices, Berry Phase, Adiabatic Connections and Quantum Hall Effect

Reference 3

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This paper cites “Singularities of differentiable maps, Volume.

Multifold degeneracy points of quantum systems and singularities of matrix varieties “Singularities of differentiable maps, Volume

Reference 4

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Multifold degeneracy points of quantum systems and singularities of matrix varieties Unresolved cited work

Reference 5

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Reference 6

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This paper cites Solid state physics.

Multifold degeneracy points of quantum systems and singularities of matrix varieties Solid state physics

Reference 7

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This paper cites Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals.

Multifold degeneracy points of quantum systems and singularities of matrix varieties Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals

Reference 8

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This paper cites Schrieffer–Wolff transformation for quantum many-body systems.

Multifold degeneracy points of quantum systems and singularities of matrix varieties Schrieffer–Wolff transformation for quantum many-body systems

Reference 9

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This paper cites On the Geometry of the Set of Sym- metric Matrices with Repeated Eigenvalues.

Multifold degeneracy points of quantum systems and singularities of matrix varieties On the Geometry of the Set of Sym- metric Matrices with Repeated Eigenvalues

Reference 10

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This paper cites Berry phase, topology, and degeneracies in quantum nanomagnets.

Multifold degeneracy points of quantum systems and singularities of matrix varieties Berry phase, topology, and degeneracies in quantum nanomagnets

Reference 11

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Observation 5e9a1f15-af02-44c9-a8af-ed7ab85bfaa9 · outbound

This paper cites Determinantal Rings.

Multifold degeneracy points of quantum systems and singularities of matrix varieties Determinantal Rings

Reference 12

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This paper cites Complex symmetric matrices.

Multifold degeneracy points of quantum systems and singularities of matrix varieties Complex symmetric matrices

Reference 13

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Multifold degeneracy points of quantum systems and singularities of matrix varieties Codebase release 2.1 for Pymablock

Reference 14

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Multifold degeneracy points of quantum systems and singularities of matrix varieties Pymablock: An algorithm and a package for quasi-degenerate pertur- bation theory

Reference 15

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This paper cites Hermitian matrices with a bounded number of eigenvalues.

Multifold degeneracy points of quantum systems and singularities of matrix varieties Hermitian matrices with a bounded number of eigenvalues

Reference 16

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Observation 8658be34-065f-42e8-9fa4-b374d30989bd · outbound

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Multifold degeneracy points of quantum systems and singularities of matrix varieties Local analytic geometry: Basic theory and applications

Reference 17

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Observation 7419da49-b8bf-4e95-b71f-80af6a2cfba4 · outbound

This paper cites Discriminant of symmetric matrices as a sum of squares and the orthogonal group.

Multifold degeneracy points of quantum systems and singularities of matrix varieties Discriminant of symmetric matrices as a sum of squares and the orthogonal group

Reference 18

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Observation 246c24a9-b919-47a1-9cbf-6df73239e20a · outbound

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Multifold degeneracy points of quantum systems and singularities of matrix varieties Invariant theoretic characterization of subdiscriminants of matrices

Reference 19

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Observation 2c5ce5c9-4d6b-4167-b828-07f6857464fa · outbound

This paper cites An Algebraic Approach to the Topological Degree of a Smooth Map.

Multifold degeneracy points of quantum systems and singularities of matrix varieties An Algebraic Approach to the Topological Degree of a Smooth Map

Reference 20

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Multifold degeneracy points of quantum systems and singularities of matrix varieties Unresolved cited work

Reference 21

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This paper cites An Algebraic Formula for the Degree of a C ∞ Map Germ / Sur une in´ egalit´ e ` a la Minkowski pour les Multiplicit´ es.

Multifold degeneracy points of quantum systems and singularities of matrix varieties An Algebraic Formula for the Degree of a C ∞ Map Germ / Sur une in´ egalit´ e ` a la Minkowski pour les Multiplicit´ es

Reference 22

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Multifold degeneracy points of quantum systems and singularities of matrix varieties Commutative Algebra with a View Toward Algebraic Geometry

Reference 23

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Observation f116972e-f68e-4f1b-bcc4-e82d55f08f39 · outbound

This paper cites Magnetic degeneracy points in interacting two-spin systems: Geometrical patterns, topological charge distributions, and their stability.

Multifold degeneracy points of quantum systems and singularities of matrix varieties Magnetic degeneracy points in interacting two-spin systems: Geometrical patterns, topological charge distributions, and their stability

Reference 24

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Observation 9d075b0e-385d-463d-a57a-af2315c171f1 · outbound

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Multifold degeneracy points of quantum systems and singularities of matrix varieties Singularity theory of Weyl-point creation and annihilation

Reference 25

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Observation 9c33f6cf-6ead-48f3-9185-61c191d7e88c · outbound

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Multifold degeneracy points of quantum systems and singularities of matrix varieties Weyl-point teleportation

Reference 26

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Observation 16178b39-6e9e-40c4-be88-149f607dc3f4 · outbound

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Multifold degeneracy points of quantum systems and singularities of matrix varieties Topological charge distributions of an interacting two-spin system

Reference 27

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Multifold degeneracy points of quantum systems and singularities of matrix varieties Fulton and R

Reference 28

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Observation 38ac142b-a557-40e3-8469-786ad0135d9e · outbound

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Multifold degeneracy points of quantum systems and singularities of matrix varieties Fulton and J

Reference 29

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Observation 9a3b4853-980d-41ba-b83f-17a855a088a6 · outbound

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Multifold degeneracy points of quantum systems and singularities of matrix varieties Tjurina and Milnor numbers of matrix singularities

Reference 30

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Observation c0b35f8c-de88-48ea-8856-3002a0efe673 · outbound

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Multifold degeneracy points of quantum systems and singularities of matrix varieties Teoriya Matrits

Reference 31

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Observation 530e6976-de9b-40e4-9c10-97b303bff2eb · outbound

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Multifold degeneracy points of quantum systems and singularities of matrix varieties Principles of Algebraic Geometry

Reference 32

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Observation 130126f2-c75d-41d4-95c6-b5cf417149f0 · outbound

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Multifold degeneracy points of quantum systems and singularities of matrix varieties Griffiths and Darrell F

Reference 33

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Observation 70e44900-1492-44cf-b590-707ba0e5279d · outbound

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Multifold degeneracy points of quantum systems and singularities of matrix varieties Un complexe resolvant pour certain id´ eaux d´ et` erminentiels

Reference 34

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Observation 4516c312-5f0b-4638-8d1a-fb05218998c5 · outbound

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Multifold degeneracy points of quantum systems and singularities of matrix varieties Weyl points in ball-and-spring mechanical systems

Reference 35

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Observation 1bb3876c-bc8c-42aa-a777-12a040378e2d · outbound

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Multifold degeneracy points of quantum systems and singularities of matrix varieties Algebraic Geometry

Reference 36

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Observation cb45587d-068e-44da-bbdc-088c250725f0 · outbound

This paper cites On symmetric and skew-symmetric determinantal varieties.

Multifold degeneracy points of quantum systems and singularities of matrix varieties On symmetric and skew-symmetric determinantal varieties

Reference 37

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Observation 3dcec769-ea0c-49a2-807d-63ca4c223510 · outbound

This paper cites Geometry of symmetric determinantal loci.

Multifold degeneracy points of quantum systems and singularities of matrix varieties Geometry of symmetric determinantal loci

Reference 38

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Observation daa5adcc-3b13-4df8-bd7b-cab35db56488 · outbound

This paper cites Gr¨ obner bases and multiplicity of determinantal and pfaffian ideals.

Multifold degeneracy points of quantum systems and singularities of matrix varieties Gr¨ obner bases and multiplicity of determinantal and pfaffian ideals

Reference 39

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Observation ec8941b1-d6b3-4e39-a364-4c410960df31 · outbound

This paper cites Weyl semimetals, Fermi arcs and chiral anomalies.

Multifold degeneracy points of quantum systems and singularities of matrix varieties Weyl semimetals, Fermi arcs and chiral anomalies

Reference 40

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Observation e95f13a9-b692-4bd8-96df-5e6c269c392e · outbound

This paper cites A Weyl Fermion semimetal with surface Fermi arcs in the transition metal monopnictide TaAs class.

Multifold degeneracy points of quantum systems and singularities of matrix varieties A Weyl Fermion semimetal with surface Fermi arcs in the transition metal monopnictide TaAs class

Reference 41

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Observation f9401e98-80c5-48bf-ab30-e11f595f59d1 · outbound

This paper cites Perturbation theory for linear operators.

Multifold degeneracy points of quantum systems and singularities of matrix varieties Perturbation theory for linear operators

Reference 42

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source=pdf_text observed=2026-08-06T14:56:54.973073Z digest=sha256:b9742239949b29b971f961295e65170a5275b9436e14f4cdde4370b6cca9003d

Observation 5fecdc11-bb46-4af4-a8cd-f27d98e24db6 · outbound

This paper cites Ideals generated by minors of a symmetric matrix.

Multifold degeneracy points of quantum systems and singularities of matrix varieties Ideals generated by minors of a symmetric matrix

Reference 43

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Observation 05400135-ae37-4d21-b618-4c2398992270 · outbound

This paper cites Characteristic classes.

Multifold degeneracy points of quantum systems and singularities of matrix varieties Characteristic classes

Reference 44

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source=pdf_text observed=2026-08-06T14:56:54.981795Z digest=sha256:09e2fdc4d9ab8871b7bbcdaea383e051812e19ae87b9ffc3e50a1cda8bb065b1

Observation 742657d0-8cde-4eac-981e-7a4ef02c2b31 · outbound

This paper cites On minimality of determinantal varieties.

Multifold degeneracy points of quantum systems and singularities of matrix varieties On minimality of determinantal varieties

Reference 45

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Observation b3a62421-b3de-4168-8bdf-8a960087b06d · outbound

This paper cites On contact between submanifolds.

Multifold degeneracy points of quantum systems and singularities of matrix varieties On contact between submanifolds

Reference 46

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source=pdf_text observed=2026-08-06T14:56:54.991039Z digest=sha256:4c7802bd9736d4c13c6684aa6389bd3c6d99d1fadb7bdf47092cc74849b93c71

Observation e4f5e334-5ffc-41f0-bda6-430e6ead0f22 · outbound

This paper cites Singularities of mappings: The local behaviour of smooth and complex analytic mappings.

Multifold degeneracy points of quantum systems and singularities of matrix varieties Singularities of mappings: The local behaviour of smooth and complex analytic mappings

Reference 47

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source=pdf_text observed=2026-08-06T14:56:54.986825Z digest=sha256:452a9d807944510fc2f120d7259ccda4f69d6b2cc1c6b74f1e02d4211ce8827e

Observation e93e5528-8891-48f2-95f7-a6ffb14ba74c · outbound

This paper cites Stability of Weyl Node Merging Processes under Symmetry Con- straints.

Multifold degeneracy points of quantum systems and singularities of matrix varieties Stability of Weyl Node Merging Processes under Symmetry Con- straints

Reference 48

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source=pdf_text observed=2026-08-06T14:56:54.999336Z digest=sha256:79140e2838674b5c6cf04f03f1efe31afe42b1d7790aec13f67ee48fc0c63d20

Observation 4cd35674-cedf-470c-8470-eeb403d038dc · outbound

This paper cites Geometry, Topology and Physics.

Multifold degeneracy points of quantum systems and singularities of matrix varieties Geometry, Topology and Physics

Reference 49

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Observation 89afe1da-6fc9-4c64-8d88-93abd427eb96 · outbound

This paper cites an unresolved cited work.

Multifold degeneracy points of quantum systems and singularities of matrix varieties Unresolved cited work

Reference 50

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source=pdf_text observed=2026-08-06T14:56:54.846833Z digest=sha256:ece9d0b19467422aeaf750cea24e4ecc97fdb37e813efc08ad3696c74fef50c4

Observation 8bf9f355-32bb-47bb-b591-86b004557f08 · outbound

This paper cites ¨Uber das Verhalten von Eigenwerten bei adiabatischen Prozessen.

Multifold degeneracy points of quantum systems and singularities of matrix varieties ¨Uber das Verhalten von Eigenwerten bei adiabatischen Prozessen

Reference 51

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source=pdf_text observed=2026-08-06T14:56:55.003768Z digest=sha256:b46091029c018114aff40db9552c8085544a1a2ebfb9268a8bf83698825947be

Observation e2088415-5b26-42e8-9100-894d9e252942 · outbound

This paper cites The geometry of the Hermitian matrix space and the Schrieffer–Wolff trans- formation.

Multifold degeneracy points of quantum systems and singularities of matrix varieties The geometry of the Hermitian matrix space and the Schrieffer–Wolff trans- formation

Reference 52

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Observation 1f7d9157-9548-490c-8109-09e2bfe889d7 · outbound

This paper cites Upper bound on the number of Weyl points born from a nongeneric degeneracy point.

Multifold degeneracy points of quantum systems and singularities of matrix varieties Upper bound on the number of Weyl points born from a nongeneric degeneracy point

Reference 53

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source=pdf_text observed=2026-08-06T14:56:55.012748Z digest=sha256:e3c9a4b041c1c30894f6c368b0c49b19f49de0984526bb309a9847c3ab9c670e

Observation e3a3a321-d327-42f5-bce9-633728864cdb · outbound

This paper cites Multifold topological semimetals.

Multifold degeneracy points of quantum systems and singularities of matrix varieties Multifold topological semimetals

Reference 54

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Observation 584cd210-bf1a-4a7f-bdec-d452107156e2 · outbound

This paper cites Sakurai and Jim Napolitano.

Multifold degeneracy points of quantum systems and singularities of matrix varieties Sakurai and Jim Napolitano

Reference 55

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source=pdf_text observed=2026-08-06T14:56:55.021697Z digest=sha256:0df4c6150b6c0c556e526c0b20e6a5b5f5d07208b1ae3947ed1a09840dce5b07

Observation 98cb30be-0d1c-491a-b81c-248bbe64ca33 · outbound

This paper cites Observation of spin–orbit coupling induced Weyl points in a two- electron double quantum dot.

Multifold degeneracy points of quantum systems and singularities of matrix varieties Observation of spin–orbit coupling induced Weyl points in a two- electron double quantum dot

Reference 56

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source=pdf_text observed=2026-08-06T14:56:55.025891Z digest=sha256:af409b768ea272db52be0e0d0cee8a503dc8469b85fc0278b1a39784401e6c6d

Observation 891aee5a-791f-4e8d-90cb-1c3b8f71d431 · outbound

This paper cites Relation between the Anderson and Kondo Hamiltonians.

Multifold degeneracy points of quantum systems and singularities of matrix varieties Relation between the Anderson and Kondo Hamiltonians

Reference 57

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source=pdf_text observed=2026-08-06T14:56:55.029927Z digest=sha256:5aa53649ddb3b7305e4108bbf1a6de8225144aaf862479f28e943e353e190b92

Observation ca632abb-6cb3-4f28-8daf-213844cd2bd7 · outbound

This paper cites G´ eom´ etrie alg´ ebrique et g´ eom´ etrie analytique.

Multifold degeneracy points of quantum systems and singularities of matrix varieties G´ eom´ etrie alg´ ebrique et g´ eom´ etrie analytique

Reference 58

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source=pdf_text observed=2026-08-06T14:56:55.034248Z digest=sha256:b8fabf480d408b55e1117782eaad83a484a9eb7f2862e25905dd8d7e15b9a5fd

Observation 1a8251cb-b851-4b66-a871-324fb99e3eb8 · outbound

This paper cites Shafarevich.

Multifold degeneracy points of quantum systems and singularities of matrix varieties Shafarevich

Reference 59

Resolution
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source=pdf_text observed=2026-08-06T14:56:55.038723Z digest=sha256:c679adfa497bee9729251304eeb283ef848bbbaa7e4c17e96f46e26a6970990f

Observation 0f690551-ecf3-468a-9734-dd7789a43062 · outbound

This paper cites Application of singularity theory to bifurcation of band structures in crystals.

Multifold degeneracy points of quantum systems and singularities of matrix varieties Application of singularity theory to bifurcation of band structures in crystals

Reference 60

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source=pdf_text observed=2026-08-06T14:56:55.043077Z digest=sha256:e8336ee433af43a18d421a547811eb6dca2b0b9c0bec6a0c761125a8cffddd1c

Observation 91fd09c2-93c4-4ab4-8403-6dfdd0b8580e · outbound

This paper cites Classification of Hamiltonians in neighborhoods of band crossings in terms of the theory of singularities.

Multifold degeneracy points of quantum systems and singularities of matrix varieties Classification of Hamiltonians in neighborhoods of band crossings in terms of the theory of singularities

Reference 61

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source=pdf_text observed=2026-08-06T14:56:55.047269Z digest=sha256:3bfd65e97a193acc7b256bb87c40292f4b941bd6136cdd873082f0fd954695c4

Observation ece0039b-73f8-4dd7-894b-e14692aa6155 · outbound

This paper cites Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differ- entialgleichungen (mit einer Anwendung auf die Theorie der Hohlraumstrahlung).

Multifold degeneracy points of quantum systems and singularities of matrix varieties Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differ- entialgleichungen (mit einer Anwendung auf die Theorie der Hohlraumstrahlung)

Reference 62

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source=pdf_text observed=2026-08-06T14:56:55.051507Z digest=sha256:86453f5d3cb53f43b34226963ffb5a6b413fe6212f4edb0be1b5a6837c93c98d

Observation dcac1aaf-9ca8-4178-89fe-e2b1d279c2fe · outbound

This paper cites Discovery of a Weyl fermion semimetal and topological Fermi arcs.

Multifold degeneracy points of quantum systems and singularities of matrix varieties Discovery of a Weyl fermion semimetal and topological Fermi arcs

Reference 63

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source=pdf_text observed=2026-08-06T14:56:55.055714Z digest=sha256:dd0759ee0aa7f9511ab60db5b65b283705bd226a2291f083508a94908686be4a

Observation 2b3b6b32-18ba-4bdd-9401-0229d03ed793 · outbound

This paper cites Encyclopedia of emergent particles in three-dimensional crystals.

Multifold degeneracy points of quantum systems and singularities of matrix varieties Encyclopedia of emergent particles in three-dimensional crystals

Reference 64

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source=pdf_text observed=2026-08-06T14:56:55.060058Z digest=sha256:d706a9ba0c583f860d3222eb080bd2588b096292e4550452b526a224a9116470

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