Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links
Paper Citation Record · LEDGER
Non-invertible topological defects in 4-dimensional $\mathbb{Z}_2$ pure lattice gauge theory
As of 7 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 17 inbound Pith citation observations for arXiv:2109.05992.
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 2026-08-07T06:34:17.273281+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-07T14:22:36.225267Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-06-30T23:25:07.787559Z
Reference resolution
0 of 0 outbound references displayed
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External citation measurements
No source-named external measurement is stored.
Outbound references
No outbound reference observations are available for this paper version.
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 2026-08-07T06:34:17.273281+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 2026-08-07T06:34:17.273281+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 2026-08-07T06:34:17.273281+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 2026-08-07T06:34:17.273281+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 2026-08-07T06:34:17.273281+00:00.
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 2026-08-07T06:34:17.273281+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 2026-08-07T06:34:17.273281+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 2026-08-07T06:34:17.273281+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.