Paper Citation Record · LEDGER

A Discrete Formulation of Second Stiefel-Whitney Class for Band Theory

As of 13 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.

pith.paper-citation-record.v1
2412.18796 v1

Coverage vector

measured 33 of 33 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T04:34:43.253986Z

measured 34 of 34 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-21T21:40:19.042178Z

measured 0 of 1 external citation measurements

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
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External citation measurements

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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 2026-08-13T06:32:02.005865+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

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+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

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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

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+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

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+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

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+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

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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

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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

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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

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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

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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

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+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

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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 2026-08-13T06:32:02.005865+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

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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

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+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

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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

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+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

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+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

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+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 2026-08-13T06:32:02.005865+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

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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

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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

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+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

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+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

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+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

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+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

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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

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+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

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.