Paper Citation Record · LEDGER

Equivalence between the Axion Invariant and the $S_4$ Symmetry Indicator

As of 14 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 2 inbound Pith citation observations for arXiv:2607.05719.

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

pith.paper-citation-record.v1
2607.05719 v2

Coverage vector

measured 22 of 22 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-14T16:11:29.071531Z

measured 24 of 24 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-14T16:11:29.071531Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-07-11T03:17:52.276543Z

Reference resolution

22 of 22 outbound references displayed

verified exact0
verified fuzzy0
unresolved21
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation dc037da1-56d2-4eb5-9b41-23044408661c · outbound

This paper cites Equivalence between the Axion Invariant and the $S_4$ Symmetry Indicator.

Equivalence between the Axion Invariant and the $S_4$ Symmetry Indicator Equivalence between the Axion Invariant and the $S_4$ Symmetry Indicator

Reference 1

Resolution: unresolved; no resolver link, observed 2026-07-14T16:11:29.071531Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 65eb4515-81cd-4055-aeb5-fa76dd9df4b8 · outbound

This paper cites After projecting onto the spinful sector relevant to theZ 4 ×Z 2 ×Z 2 indicator group, a symmetry-data vector is B= m(¯Γ5),.

Equivalence between the Axion Invariant and the $S_4$ Symmetry Indicator After projecting onto the spinful sector relevant to theZ 4 ×Z 2 ×Z 2 indicator group, a symmetry-data vector is B= m(¯Γ5),

Reference 2

Resolution: unresolved; no resolver link, observed 2026-07-14T16:11:29.071531Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 262f12a2-e7ef-4b19-9d64-5483503eed56 · outbound

This paper cites (B6) from an infinite family to a finite check based on Gordan’s lemma [18].

Equivalence between the Axion Invariant and the $S_4$ Symmetry Indicator (B6) from an infinite family to a finite check based on Gordan’s lemma [18]

Reference 3

Resolution: unresolved; no resolver link, observed 2026-07-14T16:11:29.071531Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ebd772d5-54e4-47a4-95b9-d75585ef1145 · outbound

This paper cites B2 guarantee that this content propagates consistently across the Brillouin zone.

Equivalence between the Axion Invariant and the $S_4$ Symmetry Indicator B2 guarantee that this content propagates consistently across the Brillouin zone

Reference 4

Resolution: unresolved; no resolver link, observed 2026-07-14T16:11:29.071531Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 36279f6b-5444-4673-8691-2a4366fd2806 · outbound

This paper cites Fu and C.

Equivalence between the Axion Invariant and the $S_4$ Symmetry Indicator Fu and C

Reference 5

Resolution: unresolved; no resolver link, observed 2026-07-14T16:11:29.071531Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 62f2dc26-1c4b-40f9-8912-13e26e2ef9af · outbound

This paper cites an unresolved cited work.

Equivalence between the Axion Invariant and the $S_4$ Symmetry Indicator Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-07-14T16:11:29.071531Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8cfb3d7a-3fab-4178-8549-7dc5249a3241 · outbound

This paper cites an unresolved cited work.

Equivalence between the Axion Invariant and the $S_4$ Symmetry Indicator Unresolved cited work

Reference 7

Resolution: unresolved; no resolver link, observed 2026-07-14T16:11:29.071531Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 071dca6b-b219-484f-9a84-d83ebbbb8a28 · outbound

This paper cites Qi and S.-C.

Equivalence between the Axion Invariant and the $S_4$ Symmetry Indicator Qi and S.-C

Reference 8

Resolution: unresolved; no resolver link, observed 2026-07-14T16:11:29.071531Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a08710b9-deb6-46b5-9e96-d55520d5e8bb · outbound

This paper cites Wang, X.-L.

Equivalence between the Axion Invariant and the $S_4$ Symmetry Indicator Wang, X.-L

Reference 9

Resolution: unresolved; no resolver link, observed 2026-07-14T16:11:29.071531Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3dd67b70-ae81-401d-8a84-ba57723d4088 · outbound

This paper cites an unresolved cited work.

Equivalence between the Axion Invariant and the $S_4$ Symmetry Indicator Unresolved cited work

Reference 10

Resolution: unresolved; no resolver link, observed 2026-07-14T16:11:29.071531Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 37368265-bef7-4446-bbc7-cee3eafbc3f7 · outbound

This paper cites Li and K.

Equivalence between the Axion Invariant and the $S_4$ Symmetry Indicator Li and K

Reference 11

Resolution: unresolved; no resolver link, observed 2026-07-14T16:11:29.071531Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4cafb3ab-6749-4676-b6ca-01f44510bf63 · outbound

This paper cites an unresolved cited work.

Equivalence between the Axion Invariant and the $S_4$ Symmetry Indicator Unresolved cited work

Reference 12

Resolution: unresolved; no resolver link, observed 2026-07-14T16:11:29.071531Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 67e7684a-ba47-482d-99dc-6110790e5a9f · outbound

This paper cites Kruthoff, J.

Equivalence between the Axion Invariant and the $S_4$ Symmetry Indicator Kruthoff, J

Reference 13

Resolution: unresolved; no resolver link, observed 2026-07-14T16:11:29.071531Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6f2fddca-196a-4ba0-8e83-ed45c115ccfb · outbound

This paper cites an unresolved cited work.

Equivalence between the Axion Invariant and the $S_4$ Symmetry Indicator Unresolved cited work

Reference 14

Resolution: unresolved; no resolver link, observed 2026-07-14T16:11:29.071531Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation abbde6ab-96ff-4cc4-9354-69e5d92a3818 · outbound

This paper cites Bradlyn, L.

Equivalence between the Axion Invariant and the $S_4$ Symmetry Indicator Bradlyn, L

Reference 15

Resolution: unresolved; no resolver link, observed 2026-07-14T16:11:29.071531Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c11b5318-dee6-4f49-9206-f0580b0c2490 · outbound

This paper cites Khalaf, H.

Equivalence between the Axion Invariant and the $S_4$ Symmetry Indicator Khalaf, H

Reference 16

Resolution: unresolved; no resolver link, observed 2026-07-14T16:11:29.071531Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cf9a1024-5222-46b1-b2ff-c47dabdaaca0 · outbound

This paper cites an unresolved cited work.

Equivalence between the Axion Invariant and the $S_4$ Symmetry Indicator Unresolved cited work

Reference 17

Resolution: unresolved; no resolver link, observed 2026-07-14T16:11:29.071531Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 343ed97b-a2d5-4698-89e2-9d2ca314d1bc · outbound

This paper cites Elcoro, B.

Equivalence between the Axion Invariant and the $S_4$ Symmetry Indicator Elcoro, B

Reference 18

Resolution: unresolved; no resolver link, observed 2026-07-14T16:11:29.071531Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4837f88b-742c-42d4-a096-ef440f508dae · outbound

This paper cites an unresolved cited work.

Equivalence between the Axion Invariant and the $S_4$ Symmetry Indicator Unresolved cited work

Reference 19

Resolution: unresolved; no resolver link, observed 2026-07-14T16:11:29.071531Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6f5469fe-941f-4a57-86d2-612041701d8f · outbound

This paper cites Chen, Intrinsic Axion Statistical Topological In- sulator, Physical Review Letters134, 10.1103/Phys- RevLett.134.226601 (2025).

Equivalence between the Axion Invariant and the $S_4$ Symmetry Indicator Chen, Intrinsic Axion Statistical Topological In- sulator, Physical Review Letters134, 10.1103/Phys- RevLett.134.226601 (2025)

Reference 20

Resolution: malformed identifier; no resolver link, observed 2026-07-14T16:11:29.071531Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0459a660-7a5b-4ebc-8c3b-0bcdf3f1d894 · outbound

This paper cites an unresolved cited work.

Equivalence between the Axion Invariant and the $S_4$ Symmetry Indicator Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-07-14T16:11:29.071531Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8af3c8d8-533d-4b9f-b343-b0c0263db7d7 · outbound

This paper cites Bruns and J.

Equivalence between the Axion Invariant and the $S_4$ Symmetry Indicator Bruns and J

Reference 22

Resolution: unresolved; no resolver link, observed 2026-07-14T16:11:29.071531Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation b3aec7d4-1d45-4d8c-8e38-8f459be55854 · inbound