Paper Citation Record · LEDGER

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

As of 24 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 16 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 16 of 16 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+00:00

measured 16 of 16 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T23:16:14.782310Z

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

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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 604f86be-8f3e-47b9-8468-a902da3b5566 · inbound

Classifying Logical Gates in Quantum Codes via Cohomology Operations and Symmetry cites this paper.

Classifying Logical Gates in Quantum Codes via Cohomology Operations and Symmetry Higher cup products on hypercubic lattices: application to lattice models of topological phases

Reference 83

Resolution: unresolved; no resolver link, observed 2026-08-12T13:57:59.365998Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c83f8743-65ba-4709-aeee-bb9d5ff98549 · 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 Higher cup products on hypercubic lattices: application to lattice models of topological phases

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-11T18:19:46.644842Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bb9c3357-487a-4ff9-8ebf-95e34297403e · inbound

Planar fault-tolerant circuits for non-Clifford gates on the 2D color code cites this paper.

Planar fault-tolerant circuits for non-Clifford gates on the 2D color code Higher cup products on hypercubic lattices: application to lattice models of topological phases

Reference 60

Resolution: unresolved; no resolver link, observed 2026-08-15T23:16:14.782310Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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 2026-08-23T06:30:58.430688+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 2026-08-23T06:30:58.430688+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 2026-08-23T06:30:58.430688+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 2026-08-23T06:30:58.430688+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 2026-08-23T06:30:58.430688+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.

Observation 4cb268de-4131-48ae-a25c-131eea811904 · inbound

Coupled-Layer Codes: Beyond Quantum Product Constructions cites this paper.

Coupled-Layer Codes: Beyond Quantum Product Constructions Higher cup products on hypercubic lattices: application to lattice models of topological phases

Reference 74

Resolution: unresolved; no resolver link, observed 2026-08-14T04:20:47.262071Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.