Paper Citation Record · LEDGER

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole

As of 16 August 2026, this Paper Citation Record lists 59 of 59 outbound references and 1 inbound Pith citation observation for arXiv:2607.13053.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2607.13053 v1

Coverage vector

measured 59 of 59 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-02T09:03:14.272068Z

measured 60 of 60 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T04:26:33.293956Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

59 of 59 outbound references displayed

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External citation measurements

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Outbound references

Observation e809a4b4-5a32-46b4-af17-cd16d79383b7 · outbound

This paper cites Fork+p+reven, we can achieve such a normalization by dividing by the projecting factor k p r 0 0 0.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Fork+p+reven, we can achieve such a normalization by dividing by the projecting factor k p r 0 0 0

Reference 1

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Observation 50b677f9-0d7a-437c-86f5-c64f61497167 · outbound

This paper cites (28) are reproduced by choosing the following nor- malization constant: np = 1p (p+ 2)! ,(A3) which forp= 0,1 isn −1 0 = √ 2 andn −1 1 = √ 6.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole (28) are reproduced by choosing the following nor- malization constant: np = 1p (p+ 2)! ,(A3) which forp= 0,1 isn −1 0 = √ 2 andn −1 1 = √ 6

Reference 2

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Observation 2c8f22a7-5cf3-4806-a895-cd03b11d1db7 · outbound

This paper cites an unresolved cited work.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Unresolved cited work

Reference 3

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Observation c15b2023-af26-4364-b565-ccfcc9967e5d · outbound

This paper cites (A18) Using the Hermitian conjugate of the orbital and spin tensors given in eq.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole (A18) Using the Hermitian conjugate of the orbital and spin tensors given in eq

Reference 4

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Observation e11d4b0e-4243-4da7-813c-fea55c1bfa8a · outbound

This paper cites Orthogonality of the spherical orbital operators We determine the Hilbert-Schmidt inner product of the spherical tensor operator components as defined in eq.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Orthogonality of the spherical orbital operators We determine the Hilbert-Schmidt inner product of the spherical tensor operator components as defined in eq

Reference 5

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Observation addb9a64-e035-4c02-9d6a-51c9fde2ccfa · outbound

This paper cites As described in the appendix B, in particular with claim B.1, we determine the effect of the time-reversal operator by its action on the basis.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole As described in the appendix B, in particular with claim B.1, we determine the effect of the time-reversal operator by its action on the basis

Reference 6

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Observation f41a29e3-8ed1-4fb9-9882-bf76eeda3f7f · outbound

This paper cites its multipole moment, via upper- and lowercase letters.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole its multipole moment, via upper- and lowercase letters

Reference 7

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Observation b07a3ade-d624-468b-94d7-fc050aca62a0 · outbound

This paper cites WithUbeing a complex matrix, time-reversalτ(·) andUdo not com- mute.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole WithUbeing a complex matrix, time-reversalτ(·) andUdo not com- mute

Reference 8

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Observation 391646f6-f062-4da7-85fe-4f435c0f03d8 · outbound

This paper cites This relation can be leveraged to give insight into how different components of a density matrix of definite time-reversal symmetry relate to each other.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole This relation can be leveraged to give insight into how different components of a density matrix of definite time-reversal symmetry relate to each other

Reference 9

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Observation 4f9087e8-5f3c-463a-ba30-f2a0f51e379e · outbound

This paper cites Racah, Phys.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Racah, Phys

Reference 10

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Observation 2bcfdd7a-17c1-43eb-b8d2-700fc67ae90e · outbound

This paper cites an unresolved cited work.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Unresolved cited work

Reference 11

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Observation 594364ef-317b-4cc1-a6ec-1c4fce82e734 · outbound

This paper cites an unresolved cited work.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Unresolved cited work

Reference 12

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Observation fc53b371-6083-4e10-bea6-b89c98389723 · outbound

This paper cites an unresolved cited work.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Unresolved cited work

Reference 13

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Observation bccf0a62-b755-4d56-868a-9f0e302812c9 · outbound

This paper cites an unresolved cited work.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Unresolved cited work

Reference 14

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Observation 7d35e895-c8b5-45e3-ab12-08524cdae459 · outbound

This paper cites van der Laan and B.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole van der Laan and B

Reference 15

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Observation d0a3d11c-f90e-41ac-8857-bee82e449fcf · outbound

This paper cites Bultmark, F.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Bultmark, F

Reference 16

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Observation c46c082b-199a-4a7f-a239-2a6aa9eda72c · outbound

This paper cites Cricchio, F.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Cricchio, F

Reference 17

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Observation f4228272-d085-47d2-9cfb-41987e128a30 · outbound

This paper cites Ederer and N.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Ederer and N

Reference 18

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Observation fa415008-515c-472d-81d5-d6e3a3ca3b16 · outbound

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On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Unresolved cited work

Reference 19

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Observation 9d4c94bf-f27e-4795-b6cd-84fccd2efc37 · outbound

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On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Unresolved cited work

Reference 20

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Observation 66502213-0e8f-4646-9215-7794f4cc498c · outbound

This paper cites Fechner and N.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Fechner and N

Reference 21

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Observation a2b0ba07-f162-43bd-a62c-9158bed96804 · outbound

This paper cites Th¨ ole and N.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Th¨ ole and N

Reference 22

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Observation 2957c6db-e142-4db9-be56-ebd184f3701a · outbound

This paper cites Bhowal and N.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Bhowal and N

Reference 23

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Observation 90e8c958-ae95-4018-a17b-9b7e47607970 · outbound

This paper cites Urru and N.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Urru and N

Reference 24

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Observation bc1da96c-9b05-42c0-9b39-a86d48dfe82a · outbound

This paper cites Urru, J.-R.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Urru, J.-R

Reference 25

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Observation 3663afc2-1a84-417f-b2c9-f28cff71885a · outbound

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On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Unresolved cited work

Reference 26

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Observation 2f355e91-0cba-46b6-b6ee-f9f990e50580 · outbound

This paper cites Winkler and U.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Winkler and U

Reference 27

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Observation a79cf5cf-69b8-4213-86a8-b617fd32a69f · outbound

This paper cites Hayami and H.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Hayami and H

Reference 28

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Observation d5aef00b-7100-40bb-8193-443d3b3613cd · outbound

This paper cites Hayami, M.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Hayami, M

Reference 29

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Observation 33cd205c-33df-4929-9113-c0830eb8cc5a · outbound

This paper cites Kusunose, R.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Kusunose, R

Reference 30

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Observation 6102de8e-c473-41d4-a328-0bb78ea85f29 · outbound

This paper cites Yatsushiro, H.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Yatsushiro, H

Reference 31

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Observation 8d54b9d0-01f7-414d-9852-973dc1b89587 · outbound

This paper cites Hayami and H.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Hayami and H

Reference 32

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Observation da5e8fde-8452-4b93-ac19-5164da8b4d7a · outbound

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On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Unresolved cited work

Reference 33

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Observation 803011b7-0ef8-468a-b92f-3dcfb75a833d · outbound

This paper cites Kusunose, J.-i.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Kusunose, J.-i

Reference 34

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Observation 036f2e8b-077b-4c58-9ee1-065d24e0ac52 · outbound

This paper cites Oiwa and H.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Oiwa and H

Reference 35

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Observation 320d9ebc-99b5-4832-bea6-0575a9e0af7f · outbound

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On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Unresolved cited work

Reference 36

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Observation 45413a5f-aad6-4df8-9cce-c5acc618db79 · outbound

This paper cites Furukawa, Y.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Furukawa, Y

Reference 37

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Observation a6608a82-0121-4a2a-945e-3e52d43510d3 · outbound

This paper cites Sakano, M.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Sakano, M

Reference 38

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Observation f70c2798-af34-43c6-90d1-bfe3ff434cfb · outbound

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On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Unresolved cited work

Reference 39

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Observation 96c8c2ac-fe9b-4c24-99ba-af6f31950c7d · outbound

This paper cites Gatti, D.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Gatti, D

Reference 40

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Observation 63535712-9a6c-4714-be5a-6b8aa71f9233 · outbound

This paper cites Calavalle, M.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Calavalle, M

Reference 41

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Observation a1c32886-12e0-4b7c-b5bf-b62934ed8a0f · outbound

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On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Unresolved cited work

Reference 42

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Observation 9fc08dc8-1955-4fd0-bc78-acba11753e36 · outbound

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On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Unresolved cited work

Reference 43

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Observation c3e6ef87-bc5b-4577-ad2e-47cd41cdb842 · outbound

This paper cites Kresse and D.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Kresse and D

Reference 44

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Observation 7245250d-3150-4d51-83ee-1690e0c7fe9e · outbound

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On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Unresolved cited work

Reference 45

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Observation fdbaaf3c-db75-4d46-a98f-774ca8c6c28e · outbound

This paper cites Duros, A.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Duros, A

Reference 46

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Observation 16f4e761-c4ba-4ac9-ba74-acf64f18b2c5 · outbound

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On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Unresolved cited work

Reference 47

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Observation 1eae2660-5cea-4c2c-92bc-190c9ee9b3dc · outbound

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On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Unresolved cited work

Reference 48

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Observation 27aa6dff-48cb-4244-aea8-b8fb580ea2f7 · outbound

This paper cites Oiwa and H.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Oiwa and H

Reference 49

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Observation 11071f4f-66b1-48fe-963e-af17950f747b · outbound

This paper cites Kresse and J.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Kresse and J

Reference 50

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Observation 169e8329-6aa3-4a31-9dde-f3e7141a5ffd · outbound

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On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Unresolved cited work

Reference 51

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Observation a04cd028-3c1c-4ac4-ba24-27de6f73076b · outbound

This paper cites Buˇ cko, S.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Buˇ cko, S

Reference 52

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Observation 10a88231-13d7-4f23-a226-a2211b882a96 · outbound

This paper cites Buˇ cko, S.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Buˇ cko, S

Reference 53

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Observation e05437db-b00b-4b4d-8660-7f30857c3250 · outbound

This paper cites Keller, W.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Keller, W

Reference 54

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Observation 6a20e84e-0dd8-43cd-8af5-36214f0f1e88 · outbound

This paper cites Momma and F.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Momma and F

Reference 55

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Observation db9c8722-7e2a-4cc4-8707-00cef4aa8bb4 · outbound

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On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Unresolved cited work

Reference 56

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Observation 7f00b382-b7ca-47d3-a31e-c89e11d4b2ec · outbound

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On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Unresolved cited work

Reference 57

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Observation d8ec1e30-fe2a-43a5-8cf4-d4a60f919251 · outbound

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On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Unresolved cited work

Reference 58

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Observation 2516f6fd-d5f9-488b-8fa9-e3bfd9412733 · outbound

This paper cites Shapiro, Notes on topological aspects of condensed matter physics (2016), based on notes by Prof.

On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole Shapiro, Notes on topological aspects of condensed matter physics (2016), based on notes by Prof

Reference 59

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Pith citing papers

Observation 1f367318-dc78-47eb-b1dc-0a76472692c0 · inbound

Hidden chiral signatures in ferroaxial K2Zr(PO4)2 cites this paper.

Hidden chiral signatures in ferroaxial K2Zr(PO4)2 On multipoles, their decomposition by time-reversal symmetry, and the electric toroidal monopole

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-03T04:26:33.293956Z

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