Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-14T13:53:05.260303Z
Paper Citation Record · LEDGER
Topological numbers of Happer model with "puzzling" degeneracy in periodic magnetic field
As of 20 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 0 inbound Pith citation observations for arXiv:1908.04726.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
35 of 35 outbound references displayed
- verified exact1
- verified fuzzy15
- unresolved19
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation fa400234-5d56-49d8-82a5-65fffbb63afc · outbound
This paper cites For 3 (a)S = 1, L = 1:Berry phase.
Topological numbers of Happer model with "puzzling" degeneracy in periodic magnetic field For 3 (a)S = 1, L = 1:Berry phase
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:53:05.840081Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation e2be17df-8549-48b8-a36b-1345bab5edce · outbound
This paper cites phase transition.
Topological numbers of Happer model with "puzzling" degeneracy in periodic magnetic field phase transition
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:53:05.815378Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation dad97523-b545-4a1d-8d25-90a4f123fbae · outbound
This paper cites 3, Ch(i) =−J(i) nB =−⟨ψi|JnB|ψi⟩.
Topological numbers of Happer model with "puzzling" degeneracy in periodic magnetic field 3, Ch(i) =−J(i) nB =−⟨ψi|JnB|ψi⟩
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:53:05.827628Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 419df028-173c-46f0-94ca-9c6fe3f95d2f · outbound
This paper cites an unresolved cited work.
Topological numbers of Happer model with "puzzling" degeneracy in periodic magnetic field Unresolved cited work
Reference 4
- Resolution
- unresolved
- no resolver link, observed 2026-08-14T13:53:05.151264Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b4e4ad25-2142-4c00-b859-b49f42233b26 · outbound
This paper cites The states labeled by n = 1, 2, 3, 4, 10, 11, 12, 13, 14, 15 are non-degenerate states, while the other statesn = 5, 6, 7, 8, 9 have degenerate energy level atx = 2 5.
Topological numbers of Happer model with "puzzling" degeneracy in periodic magnetic field The states labeled by n = 1, 2, 3, 4, 10, 11, 12, 13, 14, 15 are non-degenerate states, while the other statesn = 5, 6, 7, 8, 9 have degenerate energy level atx = 2 5
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:53:05.802765Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 6ff130db-a6f2-437a-96eb-b0388a41bb3e · outbound
This paper cites 7(a) shows the energy levels of our model for L = 2.
Topological numbers of Happer model with "puzzling" degeneracy in periodic magnetic field 7(a) shows the energy levels of our model for L = 2
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:53:05.790356Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 5a931fc6-7d3c-4a71-b1cf-8b77267402ba · outbound
This paper cites an unresolved cited work.
Topological numbers of Happer model with "puzzling" degeneracy in periodic magnetic field Unresolved cited work
Reference 7
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:53:05.775884Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 60122669-7659-4c47-ac3a-77b926f342d5 · outbound
This paper cites an unresolved cited work.
Topological numbers of Happer model with "puzzling" degeneracy in periodic magnetic field Unresolved cited work
Reference 8
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:53:05.759567Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 9d536412-df0e-47ca-94e7-a56d6862c771 · outbound
This paper cites an unresolved cited work.
Topological numbers of Happer model with "puzzling" degeneracy in periodic magnetic field Unresolved cited work
Reference 9
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:53:05.732498Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 466b922f-7f31-4346-90a1-73fbbf21df80 · outbound
This paper cites Weyl point.
Topological numbers of Happer model with "puzzling" degeneracy in periodic magnetic field Weyl point
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:53:05.718599Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation a7c64c41-0ba3-4b8b-8d40-31897c89e57a · outbound
This paper cites Weyl sphere.
Topological numbers of Happer model with "puzzling" degeneracy in periodic magnetic field Weyl sphere
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:53:05.704761Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation e89d2946-f361-41e4-8296-9697c7a207bb · outbound
This paper cites Zhu, Phys.
Topological numbers of Happer model with "puzzling" degeneracy in periodic magnetic field Zhu, Phys
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:53:05.691250Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 21e9a997-748a-407e-bac6-a629c789ae84 · outbound
This paper cites an unresolved cited work.
Topological numbers of Happer model with "puzzling" degeneracy in periodic magnetic field Unresolved cited work
Reference 13
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:53:05.678016Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 462f35b7-6579-43ba-b16e-88fd9ff1bbb9 · outbound
This paper cites an unresolved cited work.
Topological numbers of Happer model with "puzzling" degeneracy in periodic magnetic field Unresolved cited work
Reference 14
- Resolution
- unresolved
- no resolver link, observed 2026-08-14T13:53:05.146995Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 23f4fa71-68c2-47b4-8fd6-d406d78f8fe3 · outbound
This paper cites Qi and S.-C.
Topological numbers of Happer model with "puzzling" degeneracy in periodic magnetic field Qi and S.-C
Reference 15
- Resolution
- unresolved
- no resolver link, observed 2026-08-14T13:53:05.155240Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation df861873-801c-49b7-9dc0-b0404d700502 · outbound
This paper cites an unresolved cited work.
Topological numbers of Happer model with "puzzling" degeneracy in periodic magnetic field Unresolved cited work
Reference 16
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:53:05.631537Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 1b6231d9-9454-4d91-aad2-d75c9871b792 · outbound
This paper cites Armitage, E.
Topological numbers of Happer model with "puzzling" degeneracy in periodic magnetic field Armitage, E
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:53:05.617308Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation f0ffcb95-eca8-4d73-a57f-63a9dd188d32 · outbound
This paper cites Bradlyn, J.
Topological numbers of Happer model with "puzzling" degeneracy in periodic magnetic field Bradlyn, J
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:53:05.604623Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 912a6ce6-fc21-48d6-9e80-a51e584b5362 · outbound
This paper cites an unresolved cited work.
Topological numbers of Happer model with "puzzling" degeneracy in periodic magnetic field Unresolved cited work
Reference 19
- Resolution
- unresolved
- no resolver link, observed 2026-08-14T13:53:05.172643Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 46b60aee-5b70-43be-8e5f-7d518f0ca4bd · outbound
This paper cites Lv, Z.-L.
Topological numbers of Happer model with "puzzling" degeneracy in periodic magnetic field Lv, Z.-L
Reference 20
- Resolution
- unresolved
- no resolver link, observed 2026-08-14T13:53:05.179045Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 1dfed606-579b-41a8-ac01-e39eb2b7ba16 · outbound
This paper cites an unresolved cited work.
Topological numbers of Happer model with "puzzling" degeneracy in periodic magnetic field Unresolved cited work
Reference 21
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:53:05.576109Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 8c7f96ea-96ad-4cc8-a852-e6ecb92ffc87 · outbound
This paper cites Erickson, D.
Topological numbers of Happer model with "puzzling" degeneracy in periodic magnetic field Erickson, D
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:53:05.561852Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 886e2eb3-dc92-48d3-91de-d0691db8ba64 · outbound
This paper cites Breit and I.
Topological numbers of Happer model with "puzzling" degeneracy in periodic magnetic field Breit and I
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:53:05.546624Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation f7f825ab-d22e-451b-8bab-016ffad79a25 · outbound
This paper cites Bai, M.-L.
Topological numbers of Happer model with "puzzling" degeneracy in periodic magnetic field Bai, M.-L
Reference 24
- Resolution
- verified exact
- raw_fallback, observed 2026-08-14T13:53:05.382973Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation e4b52dbf-303a-4a1f-8a25-776b928dc0fc · outbound
This paper cites an unresolved cited work.
Topological numbers of Happer model with "puzzling" degeneracy in periodic magnetic field Unresolved cited work
Reference 25
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:53:05.531226Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation f901bd52-cf87-4549-9b19-1ea9d0ae9c86 · outbound
This paper cites an unresolved cited work.
Topological numbers of Happer model with "puzzling" degeneracy in periodic magnetic field Unresolved cited work
Reference 26
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:53:05.515857Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 335192ae-6bee-4015-b4d0-b091292e3a9e · outbound
This paper cites an unresolved cited work.
Topological numbers of Happer model with "puzzling" degeneracy in periodic magnetic field Unresolved cited work
Reference 27
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:53:05.501082Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 708b3466-2fb5-46c8-8069-829475eddfe1 · outbound
This paper cites Wilczek and A.
Topological numbers of Happer model with "puzzling" degeneracy in periodic magnetic field Wilczek and A
Reference 28
- Resolution
- unresolved
- no resolver link, observed 2026-08-14T13:53:05.217317Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 776b62a5-8853-4c4f-8afe-6103ca20bc6d · outbound
This paper cites an unresolved cited work.
Topological numbers of Happer model with "puzzling" degeneracy in periodic magnetic field Unresolved cited work
Reference 29
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:53:05.480876Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 139abe59-1c4f-4d7a-b270-c28d64d54fc3 · outbound
This paper cites Zener, Proc.
Topological numbers of Happer model with "puzzling" degeneracy in periodic magnetic field Zener, Proc
Reference 30
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:53:05.466894Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation fec6422a-916a-4628-9cad-af8907fe217c · outbound
This paper cites In topological semimetal, the bases are usually{a† k, ak}, where a† k(ak) rep- resents the fermionic operator in momentum space.
Topological numbers of Happer model with "puzzling" degeneracy in periodic magnetic field In topological semimetal, the bases are usually{a† k, ak}, where a† k(ak) rep- resents the fermionic operator in momentum space
Reference 31
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:53:05.452900Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation b44f8dac-1349-4468-9e8a-92d5c3984fbe · outbound
This paper cites an unresolved cited work.
Topological numbers of Happer model with "puzzling" degeneracy in periodic magnetic field Unresolved cited work
Reference 32
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:53:05.438855Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 35784e78-c178-4d66-9d84-73c47d470145 · outbound
This paper cites an unresolved cited work.
Topological numbers of Happer model with "puzzling" degeneracy in periodic magnetic field Unresolved cited work
Reference 33
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:53:05.425469Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation b40f2e92-aa30-4be4-bcf5-c26a0b33b6fd · outbound
This paper cites an unresolved cited work.
Topological numbers of Happer model with "puzzling" degeneracy in periodic magnetic field Unresolved cited work
Reference 34
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:53:05.413192Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 1ec972c2-13f1-4d0d-a508-bd25087c4ee0 · outbound
This paper cites (C11) These are the bases in the 5-dimension degenerate state space and they are smooth in the parameter space.
Topological numbers of Happer model with "puzzling" degeneracy in periodic magnetic field (C11) These are the bases in the 5-dimension degenerate state space and they are smooth in the parameter space
Reference 35
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:53:05.397565Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Pith citing papers
No inbound Pith citation observations are available.