Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-11T04:34:43.253986Z
Paper Citation Record · LEDGER
A Discrete Formulation of Second Stiefel-Whitney Class for Band Theory
As of 15 August 2026, this Paper Citation Record lists 33 of 33 outbound references and 1 inbound Pith citation observation for arXiv:2412.18796.
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 2026-08-15T06:32:42.880941+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-05-21T21:40:19.042178Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-05-21T21:40:40.344800Z
Reference resolution
33 of 33 outbound references displayed
- verified exact1
- verified fuzzy12
- unresolved20
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 2aa93bdf-fb98-44a1-921b-300d956b1bcd · outbound
This paper cites We show why the eigenvalues of qw can be assumed not to include −1 for our purpose.
A Discrete Formulation of Second Stiefel-Whitney Class for Band Theory We show why the eigenvalues of qw can be assumed not to include −1 for our purpose
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T04:34:43.627867Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation c46522ef-ce89-4cdc-b6ea-2517346c3551 · outbound
This paper cites However, it satisfies the following re- lation using the lift u(Vv) of the gauge transformation matrices: u(w′.
A Discrete Formulation of Second Stiefel-Whitney Class for Band Theory However, it satisfies the following re- lation using the lift u(Vv) of the gauge transformation matrices: u(w′
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T04:34:43.619468Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation a8b4fc89-ad38-41af-ba53-c6ce6b2a2aaf · outbound
This paper cites Thus, the trans- formation of the Z2-valued z012 under the gauge trans- formation can be written as z′ 012 := z012 + (δη)012 mod 2, (19) (δη)012 := η12 + η02 + η01 mod 2.
A Discrete Formulation of Second Stiefel-Whitney Class for Band Theory Thus, the trans- formation of the Z2-valued z012 under the gauge trans- formation can be written as z′ 012 := z012 + (δη)012 mod 2, (19) (δη)012 := η12 + η02 + η01 mod 2
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T04:34:43.610784Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 3202f7a3-a62d-43d4-a851-44c1f0eded00 · outbound
This paper cites an unresolved cited work.
A Discrete Formulation of Second Stiefel-Whitney Class for Band Theory Unresolved cited work
Reference 4
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T04:34:43.578481Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation fa5740ed-7f75-48a6-87d6-52102aacff16 · outbound
This paper cites an unresolved cited work.
A Discrete Formulation of Second Stiefel-Whitney Class for Band Theory Unresolved cited work
Reference 5
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T04:34:43.594285Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 9a1a1ce3-81b2-43d8-a846-2ff90798e7f9 · outbound
This paper cites an unresolved cited work.
A Discrete Formulation of Second Stiefel-Whitney Class for Band Theory Unresolved cited work
Reference 6
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T04:34:43.180224Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 219c392d-639c-4259-a88b-c67e3d0a0fd7 · outbound
This paper cites Qi and S.-C.
A Discrete Formulation of Second Stiefel-Whitney Class for Band Theory Qi and S.-C
Reference 7
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T04:34:43.182909Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 31019739-4b34-45d7-9743-5068c8cffbdc · outbound
This paper cites Wen and A.
A Discrete Formulation of Second Stiefel-Whitney Class for Band Theory Wen and A
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T04:34:43.558828Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 9d5604ec-fb39-443a-a193-5b5b771a6b35 · outbound
This paper cites an unresolved cited work.
A Discrete Formulation of Second Stiefel-Whitney Class for Band Theory Unresolved cited work
Reference 9
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T04:34:43.188586Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b3f42c86-ddc6-4dbe-ae33-54adf4e283dd · outbound
This paper cites an unresolved cited work.
A Discrete Formulation of Second Stiefel-Whitney Class for Band Theory Unresolved cited work
Reference 10
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T04:34:43.191425Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 883e36c7-0074-4a6a-98a8-dad563cee648 · outbound
This paper cites Fu and C.
A Discrete Formulation of Second Stiefel-Whitney Class for Band Theory Fu and C
Reference 11
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T04:34:43.194283Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ae9487b0-a174-404b-b8c9-750f25aa46a0 · outbound
This paper cites an unresolved cited work.
A Discrete Formulation of Second Stiefel-Whitney Class for Band Theory Unresolved cited work
Reference 12
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T04:34:43.539899Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 806ac99e-eeec-497a-bb53-7ecf09814cfc · outbound
This paper cites an unresolved cited work.
A Discrete Formulation of Second Stiefel-Whitney Class for Band Theory Unresolved cited work
Reference 13
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T04:34:43.199507Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e0845cfc-9435-44c7-8d54-61090dc36261 · outbound
This paper cites Fukui, Y.
A Discrete Formulation of Second Stiefel-Whitney Class for Band Theory Fukui, Y
Reference 14
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T04:34:43.202131Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 32038248-9465-40fd-a6ea-f3338d3fc02b · outbound
This paper cites an unresolved cited work.
A Discrete Formulation of Second Stiefel-Whitney Class for Band Theory Unresolved cited work
Reference 15
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T04:34:43.547396Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation f84d9736-fba7-44de-876e-a318853f94a6 · outbound
This paper cites Winding number on 3D lattice.
A Discrete Formulation of Second Stiefel-Whitney Class for Band Theory Winding number on 3D lattice
Reference 16
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T04:34:43.218657Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 93fbf8cd-be1a-442e-aabe-dc5140114b68 · outbound
This paper cites A discrete formulation for three-dimensional winding number.
A Discrete Formulation of Second Stiefel-Whitney Class for Band Theory A discrete formulation for three-dimensional winding number
Reference 17
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T04:34:43.210241Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 67c21c7f-9db7-4dff-b56c-f09acb094eaf · outbound
This paper cites Alexandradinata and B.
A Discrete Formulation of Second Stiefel-Whitney Class for Band Theory Alexandradinata and B
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T04:34:43.532786Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 3b098322-9e03-4f84-b073-9fbd2e29e8e1 · outbound
This paper cites Lattice gradient flows (de-)stabilizing topological sectors.
A Discrete Formulation of Second Stiefel-Whitney Class for Band Theory Lattice gradient flows (de-)stabilizing topological sectors
Reference 19
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T04:34:43.215772Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2deb2a1d-f778-438b-8c02-a5dabb14d9c7 · outbound
This paper cites the most probable interpolation.
A Discrete Formulation of Second Stiefel-Whitney Class for Band Theory the most probable interpolation
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T04:34:43.602168Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation d49ecfb9-a6ac-4312-b991-2d94ef7d9db7 · outbound
This paper cites Towards complete characterization of topological insulators and superconductors: A systematic construction of topological invariants based on Atiyah-Hirzebruch spectral sequence.
A Discrete Formulation of Second Stiefel-Whitney Class for Band Theory Towards complete characterization of topological insulators and superconductors: A systematic construction of topological invariants based on Atiyah-Hirzebruch spectral sequence
Reference 21
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T04:34:43.221452Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 7f4f1e98-11e8-4caa-957d-2f5fbf00ca5c · outbound
This paper cites an unresolved cited work.
A Discrete Formulation of Second Stiefel-Whitney Class for Band Theory Unresolved cited work
Reference 22
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T04:34:43.524562Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 00656ce4-c378-4761-90c6-785bd92e6669 · outbound
This paper cites an unresolved cited work.
A Discrete Formulation of Second Stiefel-Whitney Class for Band Theory Unresolved cited work
Reference 23
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T04:34:43.516507Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 7d489276-3254-4895-b435-398a83a3f418 · outbound
This paper cites Davoyan, W.
A Discrete Formulation of Second Stiefel-Whitney Class for Band Theory Davoyan, W
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T04:34:43.508102Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 1c7022bb-b7db-4942-9d35-d7ee6fbf4fec · outbound
This paper cites an unresolved cited work.
A Discrete Formulation of Second Stiefel-Whitney Class for Band Theory Unresolved cited work
Reference 25
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T04:34:43.500102Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation e9318ace-4710-428d-af88-f0c66a8fae08 · outbound
This paper cites Chen, Instanton Density Operator in Lattice QCD from Higher Category Theory (2024), arXiv:2406.06673 [hep-lat].
A Discrete Formulation of Second Stiefel-Whitney Class for Band Theory Chen, Instanton Density Operator in Lattice QCD from Higher Category Theory (2024), arXiv:2406.06673 [hep-lat]
Reference 26
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T04:34:43.234886Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3cb0ecdd-653f-410d-975b-70f836d92011 · outbound
This paper cites Sachdev and R.
A Discrete Formulation of Second Stiefel-Whitney Class for Band Theory Sachdev and R
Reference 27
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T04:34:43.491825Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 6b143e74-c54d-48af-b805-ce07ccbedd3a · outbound
This paper cites Rabinovici and S.
A Discrete Formulation of Second Stiefel-Whitney Class for Band Theory Rabinovici and S
Reference 28
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T04:34:43.483302Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 74fcd4e0-a5f5-49c2-8860-7087dd4245c4 · outbound
This paper cites Di Vecchia, A.
A Discrete Formulation of Second Stiefel-Whitney Class for Band Theory Di Vecchia, A
Reference 29
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T04:34:43.475498Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 01aad093-ed13-4095-8134-71a079bce5d0 · outbound
This paper cites an unresolved cited work.
A Discrete Formulation of Second Stiefel-Whitney Class for Band Theory Unresolved cited work
Reference 30
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T04:34:43.467620Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 2217d9fc-2bed-47d1-9cbc-229b06929b89 · outbound
This paper cites Berg and M.
A Discrete Formulation of Second Stiefel-Whitney Class for Band Theory Berg and M
Reference 31
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T04:34:43.458634Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 65fc1d9d-2bd7-4f42-844b-48ad84ba8553 · outbound
This paper cites A Comment On Berry Connections.
A Discrete Formulation of Second Stiefel-Whitney Class for Band Theory A Comment On Berry Connections
Reference 32
- Resolution
- verified exact
- local_arxiv, observed 2026-08-11T04:34:43.284651Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 80c525a3-a71c-468e-87d9-84bdd37406c6 · outbound
This paper cites Mack and V.
A Discrete Formulation of Second Stiefel-Whitney Class for Band Theory Mack and V
Reference 33
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T04:34:43.449989Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Pith citing papers
Observation cb23c153-3be0-411d-8b2e-68e3c4402693 · inbound
$\mathbb{Z}_2$ topological invariant in three-dimensional PT- and PC-symmetric class CI band structures cites this paper.
$\mathbb{Z}_2$ topological invariant in three-dimensional PT- and PC-symmetric class CI band structures A Discrete Formulation of Second Stiefel-Whitney Class for Band Theory
Reference 13
- Resolution
- verified exact
- arxiv_id, observed 2026-05-21T21:40:40.347081Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.