Paper Citation Record · LEDGER

Non-invertible topological defects in 4-dimensional $\mathbb{Z}_2$ pure lattice gauge theory

As of 22 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 19 inbound Pith citation observations for arXiv:2109.05992.

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pith.paper-citation-record.v1
2109.05992 v3

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measured 0 of 0 reference resolution

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measured 19 of 19 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+00:00

measured 19 of 19 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-12T10:47:19.785271Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-06-30T23:25:07.787559Z

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Outbound references

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Pith citing papers

Observation 787e21c7-ffa3-433b-9a82-9e95f22e2179 · inbound

Non-Invertible Duality Defects in 3+1 Dimensions cites this paper.

Non-Invertible Duality Defects in 3+1 Dimensions Non-invertible topological defects in 4-dimensional $\mathbb{Z}_2$ pure lattice gauge theory

Reference 47

Resolution: verified exact; arxiv_id, observed 2026-05-24T08:56:32.415833Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 14610963-2070-4111-be28-d3e4eb38a193 · inbound

Higher Gauging and Non-invertible Condensation Defects cites this paper.

Higher Gauging and Non-invertible Condensation Defects Non-invertible topological defects in 4-dimensional $\mathbb{Z}_2$ pure lattice gauge theory

Reference 27

Resolution: verified exact; arxiv_id, observed 2026-05-24T09:58:23.005764Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation d6539bb6-2b35-4f81-9750-c1d43142cafc · inbound

Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond cites this paper.

Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond Non-invertible topological defects in 4-dimensional $\mathbb{Z}_2$ pure lattice gauge theory

Reference 108

Resolution: verified exact; arxiv_id, observed 2026-05-21T13:21:27.661460Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 004a38a4-6567-4181-86e7-6bf8786b321e · inbound

What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries cites this paper.

What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries Non-invertible topological defects in 4-dimensional $\mathbb{Z}_2$ pure lattice gauge theory

Reference 64

Resolution: verified exact; arxiv_id, observed 2026-05-24T07:34:08.211590Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5853d2f3-c200-4a83-96d2-f24df96f90cd · inbound

Lattice Models for Phases and Transitions with Non-Invertible Symmetries cites this paper.

Lattice Models for Phases and Transitions with Non-Invertible Symmetries Non-invertible topological defects in 4-dimensional $\mathbb{Z}_2$ pure lattice gauge theory

Reference 46

Resolution: verified exact; arxiv_id, observed 2026-05-24T01:18:42.530060Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5e8857d0-0c60-4bc2-ba6d-1390623ebc00 · inbound

Noninvertible Symmetry-Enriched Quantum Critical Point cites this paper.

Noninvertible Symmetry-Enriched Quantum Critical Point Non-invertible topological defects in 4-dimensional $\mathbb{Z}_2$ pure lattice gauge theory

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-12T10:47:19.785271Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 29f562f6-4a1b-4e33-b89b-c0b382c0c3be · inbound

Axion QED as a Lattice Gauge Theory and Non-Invertible Symmetry cites this paper.

Axion QED as a Lattice Gauge Theory and Non-Invertible Symmetry Non-invertible topological defects in 4-dimensional $\mathbb{Z}_2$ pure lattice gauge theory

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-11T18:19:46.578952Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 36a2864a-9f94-478a-b16d-f34c0c0d894f · inbound

2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries cites this paper.

2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Non-invertible topological defects in 4-dimensional $\mathbb{Z}_2$ pure lattice gauge theory

Reference 47

Resolution: unresolved; no resolver link, observed 2026-08-07T14:22:36.225267Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ae00f1df-3341-4185-a3f7-b5408a794cdd · inbound

Symmetry theta angles and topological Witten effects cites this paper.

Symmetry theta angles and topological Witten effects Non-invertible topological defects in 4-dimensional $\mathbb{Z}_2$ pure lattice gauge theory

Reference 51

Resolution: unresolved; no resolver link, observed 2026-08-06T21:32:23.397258Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 73a06ec6-3c77-47a6-ac06-769c1f479473 · inbound

Landau theory for lattice higher gauge theory and Kramers-Wannier duality cites this paper.

Landau theory for lattice higher gauge theory and Kramers-Wannier duality Non-invertible topological defects in 4-dimensional $\mathbb{Z}_2$ pure lattice gauge theory

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-06T19:14:34.374682Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ee8327f4-1e10-4afd-8d3e-ad4b1a9ef4cb · inbound

Non-Local Conserved Currents and Continuous Non-Invertible Symmetries cites this paper.

Non-Local Conserved Currents and Continuous Non-Invertible Symmetries Non-invertible topological defects in 4-dimensional $\mathbb{Z}_2$ pure lattice gauge theory

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-06T11:19:49.148796Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e577b0f4-586d-4d13-a31b-3e5912f069d4 · inbound

Symmetry Spans and Enforced Gaplessness cites this paper.

Symmetry Spans and Enforced Gaplessness Non-invertible topological defects in 4-dimensional $\mathbb{Z}_2$ pure lattice gauge theory

Reference 30

Resolution: metadata mismatch; arxiv_id, observed 2026-05-16T03:27:13.023086Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 71c42172-01fa-4274-ad24-d00b2817bfde · inbound

Half-Spacetime Gauging of 2-Group Symmetry in 3d cites this paper.

Half-Spacetime Gauging of 2-Group Symmetry in 3d Non-invertible topological defects in 4-dimensional $\mathbb{Z}_2$ pure lattice gauge theory

Reference 31

Resolution: verified exact; arxiv_id, observed 2026-05-11T20:51:13.832633Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation cb36f9bf-d2b6-4bf2-bd77-2712f649bf36 · inbound

Half-Spacetime Gauging of 2-Group Symmetry in 3d cites this paper.

Half-Spacetime Gauging of 2-Group Symmetry in 3d Non-invertible topological defects in 4-dimensional $\mathbb{Z}_2$ pure lattice gauge theory

Reference 36

Resolution: verified exact; arxiv_id, observed 2026-06-30T23:25:07.789094Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 3c98c39d-afc5-44c4-9a10-7ad2b2a1ac9f · inbound

Half dualization and non-invertible particle-vortex duality defect on lattice cites this paper.

Half dualization and non-invertible particle-vortex duality defect on lattice Non-invertible topological defects in 4-dimensional $\mathbb{Z}_2$ pure lattice gauge theory

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-02T06:13:34.436300Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 95a3cfcb-fe80-4569-aa4d-c74ee60ff157 · inbound

Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata cites this paper.

Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Non-invertible topological defects in 4-dimensional $\mathbb{Z}_2$ pure lattice gauge theory

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-01T07:04:48.958776Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2d075327-c3bc-4d19-96c3-498b599fc3c0 · inbound

Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata cites this paper.

Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Non-invertible topological defects in 4-dimensional $\mathbb{Z}_2$ pure lattice gauge theory

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-03T01:57:27.186464Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eb48c11a-a3d0-42be-a0bb-feac34efc21f · inbound

Quantum Cellular Automata from Kramers-Wannier Dualities and Modular Relations cites this paper.

Quantum Cellular Automata from Kramers-Wannier Dualities and Modular Relations Non-invertible topological defects in 4-dimensional $\mathbb{Z}_2$ pure lattice gauge theory

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-01T06:57:46.009573Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bd2a58e1-bb21-4697-ae45-30b5baa11cad · inbound

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation cites this paper.

$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation Non-invertible topological defects in 4-dimensional $\mathbb{Z}_2$ pure lattice gauge theory

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-01T02:52:32.408492Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.