Paper Citation Record · LEDGER

Higher cup products on hypercubic lattices: application to lattice models of topological phases

As of 9 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 12 inbound Pith citation observations for arXiv:2106.05274.

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

pith.paper-citation-record.v1
2106.05274 v2

Coverage vector

measured 0 of 0 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links

measured 12 of 12 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 12 of 12 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T14:22:36.162653Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-21T19:15:31.092328Z

Reference resolution

0 of 0 outbound references displayed

verified exact0
verified fuzzy0
unresolved0
parse uncertain0
malformed identifier0
metadata mismatch0

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 9cc93670-bf8e-47d1-9199-7ec03a5cbcd7 · 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 Higher cup products on hypercubic lattices: application to lattice models of topological phases

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-07T14:22:36.162653Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dd1f77dc-ca78-40f0-9af7-45e00a9604cb · inbound

Bulk Excitations of Invertible Phases cites this paper.

Bulk Excitations of Invertible Phases Higher cup products on hypercubic lattices: application to lattice models of topological phases

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:34.827885Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 18a69de0-d0e4-468c-9a58-c1a7a54a80df · inbound

Symmetry theta angles and topological Witten effects cites this paper.

Symmetry theta angles and topological Witten effects Higher cup products on hypercubic lattices: application to lattice models of topological phases

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-06T21:32:23.315524Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e74918ed-61ee-4ca5-bc30-cf1a0134c693 · inbound

Clifford Hierarchy Stabilizer Codes: Transversal Non-Clifford Gates and Magic cites this paper.

Clifford Hierarchy Stabilizer Codes: Transversal Non-Clifford Gates and Magic Higher cup products on hypercubic lattices: application to lattice models of topological phases

Reference 50

Resolution: verified exact; arxiv_id, observed 2026-05-21T19:15:31.094709Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 715ef2b1-5ad1-4ca5-a77e-4ceaebed2880 · inbound

Lattice chiral symmetry from bosons in 3+1d cites this paper.

Lattice chiral symmetry from bosons in 3+1d Higher cup products on hypercubic lattices: application to lattice models of topological phases

Reference 106

Resolution: verified exact; arxiv_id, observed 2026-05-11T00:05:52.259287Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 8f77a391-0fe8-471d-9734-49bedb685b0c · inbound

Exact SL(2,Z)-Structure of Lattice Maxwell Theory with $\theta$-term in Modified Villain Formulation cites this paper.

Exact SL(2,Z)-Structure of Lattice Maxwell Theory with $\theta$-term in Modified Villain Formulation Higher cup products on hypercubic lattices: application to lattice models of topological phases

Reference 30

Resolution: verified exact; arxiv_id, observed 2026-05-11T07:51:01.577568Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 9ff6009d-a652-4ee8-9d7a-648cb4787eed · inbound

Constructing Bulk Topological Orders via Layered Gauging cites this paper.

Constructing Bulk Topological Orders via Layered Gauging Higher cup products on hypercubic lattices: application to lattice models of topological phases

Reference 52

Resolution: verified exact; arxiv_id, observed 2026-05-12T09:36:26.666994Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 0781e4a1-e7d9-4f03-b629-ffe40d629084 · inbound

Stringy T-duality on the lattice and the twisted Villain model cites this paper.

Stringy T-duality on the lattice and the twisted Villain model Higher cup products on hypercubic lattices: application to lattice models of topological phases

Reference 52

Resolution: verified exact; arxiv_id, observed 2026-05-20T04:03:04.322490Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 09cfd722-a9dc-4ef1-bd0c-9c63abcc1209 · 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 Higher cup products on hypercubic lattices: application to lattice models of topological phases

Reference 61

Resolution: unresolved; no resolver link, observed 2026-08-01T07:04:53.035680Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3963a8b5-af36-4d9c-b699-ab174fc2c809 · 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 Higher cup products on hypercubic lattices: application to lattice models of topological phases

Reference 61

Resolution: unresolved; no resolver link, observed 2026-08-03T01:57:30.960442Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2710b1a8-2f85-4329-bf6b-6b38504d005a · inbound

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

Quantum Cellular Automata from Kramers-Wannier Dualities and Modular Relations Higher cup products on hypercubic lattices: application to lattice models of topological phases

Reference 73

Resolution: unresolved; no resolver link, observed 2026-08-01T06:57:49.236779Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 66cb34e5-b3df-4df6-9589-bb4cf2217b01 · 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 Higher cup products on hypercubic lattices: application to lattice models of topological phases

Reference 45

Resolution: unresolved; no resolver link, observed 2026-08-01T02:52:33.761192Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.