Paper Citation Record · LEDGER

Symmetry protected topological orders and the group cohomology of their symmetry group

As of 6 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 28 inbound Pith citation observations for arXiv:1106.4772.

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

pith.paper-citation-record.v1
1106.4772 v6

Coverage vector

measured 0 of 0 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links

measured 28 of 28 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-06T06:34:29.942622+00:00

measured 28 of 28 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-05T00:05:51.470859Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-07-10T04:56:45.890887Z

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 5cf5b2de-4fd5-4347-8b71-1a8b871112ab · inbound

Generalized Global Symmetries cites this paper.

Generalized Global Symmetries Symmetry protected topological orders and the group cohomology of their symmetry group

Reference 27

Resolution: verified exact; arxiv_id, observed 2026-05-12T07:58:27.662273Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation bba38189-7e0e-4522-872a-c74ec9aaac41 · inbound

ICTP Lectures on (Non-)Invertible Generalized Symmetries cites this paper.

ICTP Lectures on (Non-)Invertible Generalized Symmetries Symmetry protected topological orders and the group cohomology of their symmetry group

Reference 101

Resolution: verified exact; local_arxiv, observed 2026-05-16T07:50:05.490455Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 42a0791c-65aa-45ce-9ed5-05cb41c71ffa · inbound

Lectures on Generalized Symmetries cites this paper.

Lectures on Generalized Symmetries Symmetry protected topological orders and the group cohomology of their symmetry group

Reference 40

Resolution: verified exact; local_arxiv, observed 2026-05-17T14:14:51.562344Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation bab435b3-ac35-4d38-9c0a-f96478436bf8 · inbound

Self-$G$-ality in 1+1 dimensions cites this paper.

Self-$G$-ality in 1+1 dimensions Symmetry protected topological orders and the group cohomology of their symmetry group

Reference 7

Resolution: verified exact; local_arxiv, observed 2026-05-24T00:35:56.218482Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 4dfdee6a-2dab-486f-aab5-4d89b804894e · inbound

Twisted quantum doubles are sign problem-free cites this paper.

Twisted quantum doubles are sign problem-free Symmetry protected topological orders and the group cohomology of their symmetry group

Reference 17

Resolution: verified exact; local_arxiv, observed 2026-05-18T18:51:45.496769Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 8cc73d88-9278-4b15-b0f5-f7951c35e50d · inbound

To Break or Not to Break: A Review of a No-Go Theorem on Chiral Symmetry Breaking in QCD-like Theories cites this paper.

To Break or Not to Break: A Review of a No-Go Theorem on Chiral Symmetry Breaking in QCD-like Theories Symmetry protected topological orders and the group cohomology of their symmetry group

Reference 120

Resolution: unresolved; no resolver link, observed 2026-08-05T00:05:51.470859Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a7bf748d-5629-4019-b381-2661e75df5e6 · inbound

Automorphism in Gauge Theories: Higher Symmetries and Transversal Non-Clifford Logical Gates cites this paper.

Automorphism in Gauge Theories: Higher Symmetries and Transversal Non-Clifford Logical Gates Symmetry protected topological orders and the group cohomology of their symmetry group

Reference 2

Resolution: verified exact; local_arxiv, observed 2026-05-17T20:20:11.617124Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation ff980587-5a7b-4feb-baac-b51482cf8a74 · inbound

Constant-Depth Clifford-Hierarchy Gates via Non-Abelian Surface Codes cites this paper.

Constant-Depth Clifford-Hierarchy Gates via Non-Abelian Surface Codes Symmetry protected topological orders and the group cohomology of their symmetry group

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-03T16:32:53.885270Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 72ec52ec-eb64-4d7a-bf28-82aa4565b3aa · inbound

Generalized Families of QFTs cites this paper.

Generalized Families of QFTs Symmetry protected topological orders and the group cohomology of their symmetry group

Reference 134

Resolution: verified exact; local_arxiv, observed 2026-05-16T05:10:40.652863Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 896fc0bc-fb0a-4da3-b51b-452bfa362b94 · inbound

Generalized Families of QFTs cites this paper.

Generalized Families of QFTs Symmetry protected topological orders and the group cohomology of their symmetry group

Reference 134

Resolution: unresolved; no resolver link, observed 2026-08-03T03:21:15.174127Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ca04053f-64e9-46a5-a464-1d7395eda654 · inbound

Symmetry Spans and Enforced Gaplessness cites this paper.

Symmetry Spans and Enforced Gaplessness Symmetry protected topological orders and the group cohomology of their symmetry group

Reference 96

Resolution: verified exact; local_arxiv, observed 2026-05-16T03:27:13.249683Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation ce0f3846-a07e-4621-be5e-4b8bcbf9a168 · inbound

On Lagrangians of Non-abelian Dijkgraaf-Witten Theories cites this paper.

On Lagrangians of Non-abelian Dijkgraaf-Witten Theories Symmetry protected topological orders and the group cohomology of their symmetry group

Reference 38

Resolution: verified exact; arxiv_id, observed 2026-05-13T21:08:17.230039Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 08e5dac3-a5b4-4496-81ee-0cb58b7857e0 · inbound

On Lagrangians of Non-abelian Dijkgraaf-Witten Theories cites this paper.

On Lagrangians of Non-abelian Dijkgraaf-Witten Theories Symmetry protected topological orders and the group cohomology of their symmetry group

Reference 38

Resolution: unresolved; no resolver link, observed 2026-07-13T13:50:27.597426Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7a0352f0-405b-4dd3-ac4a-afb24a3306c2 · inbound

Type-IV 't Hooft Anomalies on the Lattice: Emergent Higher-Categorical Symmetries and Applications to LSM Systems cites this paper.

Type-IV 't Hooft Anomalies on the Lattice: Emergent Higher-Categorical Symmetries and Applications to LSM Systems Symmetry protected topological orders and the group cohomology of their symmetry group

Reference 1

Resolution: verified exact; arxiv_id, observed 2026-05-13T18:18:06.288866Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 79ed715d-399c-47b4-91e5-c28300227f24 · inbound

Exploring Entropic Orders: High Temperature Continuous Symmetry Breaking, Chiral Topological States and Local Commuting Projector Models cites this paper.

Exploring Entropic Orders: High Temperature Continuous Symmetry Breaking, Chiral Topological States and Local Commuting Projector Models Symmetry protected topological orders and the group cohomology of their symmetry group

Reference 51

Resolution: verified exact; arxiv_id, observed 2026-05-11T12:41:04.012733Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 6d805089-f563-4ae3-bda0-a871c6583e24 · inbound

Exploring Entropic Orders: High Temperature Continuous Symmetry Breaking, Chiral Topological States and Local Commuting Projector Models cites this paper.

Reference 51

Resolution: unresolved; no resolver link, observed 2026-08-02T15:57:24.809186Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5b0bcf56-69a5-4232-b3db-32f761cbe9d5 · inbound

Gauging Time Reversal Symmetry in Quantum Gravity: Arrow of Time from a Confinement--Deconfinement Transition cites this paper.

Gauging Time Reversal Symmetry in Quantum Gravity: Arrow of Time from a Confinement--Deconfinement Transition Symmetry protected topological orders and the group cohomology of their symmetry group

Reference 47

Resolution: verified exact; local_arxiv, observed 2026-05-21T01:13:53.776744Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation ef639d8f-fe9b-41aa-b094-467b4e2c49fb · inbound

When Symmetries Twist: Anomaly Inflow on Monodromy Defects cites this paper.

When Symmetries Twist: Anomaly Inflow on Monodromy Defects Symmetry protected topological orders and the group cohomology of their symmetry group

Reference 45

Resolution: verified exact; local_arxiv, observed 2026-05-20T16:38:39.899134Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 02084f91-7914-4bf7-966c-f5ae55a0b23a · inbound

When Symmetries Twist: Anomaly Inflow on Monodromy Defects cites this paper.

When Symmetries Twist: Anomaly Inflow on Monodromy Defects Symmetry protected topological orders and the group cohomology of their symmetry group

Reference 45

Resolution: verified exact; local_arxiv, observed 2026-07-01T14:55:47.823470Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 29afbb64-5b90-4329-b7fb-8ae9995ec297 · inbound

Hilbert Space and Defect Hilbert Spaces Associated with Categorical Symmetries cites this paper.

Hilbert Space and Defect Hilbert Spaces Associated with Categorical Symmetries Symmetry protected topological orders and the group cohomology of their symmetry group

Reference 6

Resolution: verified exact; local_arxiv, observed 2026-06-29T13:13:27.893103Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 6aa83e66-2569-4698-a9c8-3c72ee626e47 · inbound

A local description of strong symmetries and strong-to-weak symmetry breaking in quantum many-body systems cites this paper.

A local description of strong symmetries and strong-to-weak symmetry breaking in quantum many-body systems Symmetry protected topological orders and the group cohomology of their symmetry group

Reference 15

Resolution: verified exact; local_arxiv, observed 2026-06-29T11:43:23.204588Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 7952ab81-8ab0-4787-95dc-5cd14480e166 · inbound

On Quantum Aspects of 1-Form Symmetries II: Bordism, Invertible Phases, and Anomalies cites this paper.

On Quantum Aspects of 1-Form Symmetries II: Bordism, Invertible Phases, and Anomalies Symmetry protected topological orders and the group cohomology of their symmetry group

Reference 15

Resolution: verified exact; local_arxiv, observed 2026-07-02T19:17:18.775832Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation e0f6f0bf-8518-4847-9d90-ead5521c5bd0 · inbound

On Quantum Aspects of 1-Form Symmetries II: Bordism, Invertible Phases, and Anomalies cites this paper.

On Quantum Aspects of 1-Form Symmetries II: Bordism, Invertible Phases, and Anomalies Symmetry protected topological orders and the group cohomology of their symmetry group

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-02T12:28:22.537851Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 21b85214-fb65-433f-a2cd-b20877da5824 · inbound

Invariants of Sequential Circuits and Generalized Non-Abelian Statistics cites this paper.

Invariants of Sequential Circuits and Generalized Non-Abelian Statistics Symmetry protected topological orders and the group cohomology of their symmetry group

Reference 19

Resolution: verified exact; local_arxiv, observed 2026-07-03T12:58:08.410913Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation d92a8a80-1ce3-43ff-8ba6-85b2959f6ada · inbound

Sixteen-Fold Way for Fermionic Topological Orders cites this paper.

Sixteen-Fold Way for Fermionic Topological Orders Symmetry protected topological orders and the group cohomology of their symmetry group

Reference 1

Resolution: verified exact; local_arxiv, observed 2026-06-30T12:54:40.171354Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 68c75fc3-6140-40e9-a1de-da702b009152 · inbound

Holographic Theory of Mixed-Dimensional Statistics and Conservation-Encoding Hopping-Operator Algebras cites this paper.

Holographic Theory of Mixed-Dimensional Statistics and Conservation-Encoding Hopping-Operator Algebras Symmetry protected topological orders and the group cohomology of their symmetry group

Reference 92

Resolution: verified exact; local_arxiv, observed 2026-07-10T04:56:45.892343Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 43d7f5b2-dc63-4c39-9c59-0a31d24ea2fc · inbound

Bosonic SPT and invertible phases and its relation to Steenrod's problem cites this paper.

Bosonic SPT and invertible phases and its relation to Steenrod's problem Symmetry protected topological orders and the group cohomology of their symmetry group

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-02T01:41:18.394414Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 08974deb-a3fb-41c9-bd4b-2313e076c649 · inbound

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

Quantum Cellular Automata from Kramers-Wannier Dualities and Modular Relations Symmetry protected topological orders and the group cohomology of their symmetry group

Reference 75

Resolution: unresolved; no resolver link, observed 2026-08-01T06:57:49.246464Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.