Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links
Paper Citation Record · LEDGER
As of 17 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 48 inbound Pith citation observations for arXiv:1912.13492.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-16T10:20:21.542331Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-07-10T18:07:31.532771Z
0 of 0 outbound references displayed
External citation measurements
No source-named external measurement is stored.
No outbound reference observations are available for this paper version.
Observation 49f2635b-ca3a-419a-9f01-8ad7f9eaf4f5 · inbound
Non-Invertible Duality Defects in 3+1 Dimensions Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 50
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 91f5d4ce-df1c-47b4-9846-ca4c51caab21 · inbound
Higher Gauging and Non-invertible Condensation Defects Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d91fcff8-5820-456d-90b9-7b4ab0e4f853 · inbound
Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 129
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 006ea34d-b5cd-451e-9faa-878980e1ce19 · inbound
ICTP Lectures on (Non-)Invertible Generalized Symmetries Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 116
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 247dd2a3-c007-4d25-a7bf-0d4c05d05d58 · inbound
What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 204
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 24ccc8d8-5f83-48f0-a047-06fe66bd3c8e · inbound
Lattice Models for Phases and Transitions with Non-Invertible Symmetries Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 36
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d76777cd-5d44-4f08-98d6-c88c7074c2fb · inbound
Self-$G$-ality in 1+1 dimensions Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 30
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 0bc02945-65c3-4535-a88e-f767649aa763 · inbound
SymTFTs for $U(1)$ symmetries from descent Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 2
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation daa2712c-5782-42cf-96c9-2c8509b986d1 · inbound
Noninvertible Symmetry-Enriched Quantum Critical Point Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 13
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 82994cb7-fcd2-41e9-88bb-4c1bac19ac47 · inbound
Quantum Cellular Automata on Symmetric Subalgebras Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 49
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3e43383a-7e0e-4888-9ef1-facaadf13bc8 · inbound
Tube Category, Tensor Renormalization and Topological Holography Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 17
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation cff32083-7ce0-4fba-a978-9c3aeb67bc49 · inbound
SymTFTs and Non-Invertible Symmetries of 6d (2,0) SCFTs of Type $D$ from M-theory Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 31
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b4a78d4a-3267-4f72-b847-5eaf156864e3 · inbound
QG from SymQRG: AdS$_3$/CFT$_2$ Correspondence as Topological Symmetry-Preserving Quantum RG Flow Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 7
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 1c6a07a6-e4d5-499f-8c61-bde590ea1371 · inbound
Gauging or extending bulk and boundary conformal field theories: Application to bulk and domain wall problem in topological matter and their descriptions by (mock) modular covariant Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 23
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9490aaa9-6757-464d-913a-7271c6afa758 · inbound
Relative Quantum Gravity: Localized Gravity and the Swampland Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 105
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation fd719ac3-dac4-4a4b-8692-91f6d7dfd5da · inbound
SymSETs and self-dualities under gauging non-invertible symmetries Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 48
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 323ac577-8d87-44f2-9f2f-55fe15341ee1 · inbound
SymTFT construction of gapless exotic-foliated dual models Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 9
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation b9a0a6f8-265c-4921-bfa3-9b4f963c29d2 · inbound
SymTFT, Protected Gaplessness, and Spontaneous Breaking of Non-invertible Symmetries Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 87
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 61d7a4da-caa1-481d-9bfc-522fd0337867 · inbound
Strange correlator and string order parameter for non-invertible symmetry protected topological phases in 1+1d Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 53
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9274a7af-76d5-4b03-b7fe-ffceda93bdfb · inbound
Twisted Partition Functions as Order Parameters Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 10
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 1325aa0e-abf3-4791-9eb1-501d6ba30575 · inbound
A 2D-CFT Factory: Critical Lattice Models from Competing Anyon Condensation Processes in SymTO/SymTFT Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 10
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation bb709b9b-6e9f-4d33-a924-fe56da22659e · inbound
SymTFT Approach for Mixed States with Non-Invertible Symmetries Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 16
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5a8bad75-ce30-4403-98be-6b32be763762 · inbound
Symmetry, Symmetry Topological Field Theory and von Neumann Algebra Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 123
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3a0dc295-df04-4b41-8853-e5a61f34f39a · inbound
Fusion Rules of Mobility Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 26
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation a7dd3d2a-8fd8-462a-bf90-21d6f314a670 · inbound
Disjoint additivity and local quantum physics Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 58
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 6c33fffc-702b-4164-9bf0-e5ef065bdf2d · inbound
Symmetry TFTs for Continuous Spacetime Symmetries Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 8
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8a888498-997f-4ac6-b5e3-aa3a9170cd11 · inbound
Sandwich Construction of Symmetry TFTs for the Centre Symmetries of Chern-Simons, Yang-Mills, and Einstein Gravity Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 28
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5f93eab5-8aa6-4824-88c3-61dcb93f3f3a · inbound
SymTFT for Continuous Symmetries: Non-linear Realizations and Spontaneous Breaking Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 14
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e275dbb8-8b42-41c5-872e-270128245a30 · inbound
Information Loss in Generalized Symmetry Breaking Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 12
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ad4edf83-c6be-4fb4-b8c2-5ae5dce17154 · inbound
The Line, the Strip and the Duality Defect Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 9
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 62bd3c6d-037b-42cc-8afe-7fcc0ad2296a · inbound
The Line, the Strip and the Duality Defect Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 9
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5707509c-7e10-45bb-85a0-ff5b9d13971e · inbound
Symmetry Spans and Enforced Gaplessness Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 38
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 00f7f610-2221-4922-9485-a94f6d31fb86 · inbound
Categorical Symmetries via Operator Algebras Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 8fdb913c-f628-4b53-a063-b95c93ea8593 · inbound
Characterizing gapped phases by smeared boundary conformal field theories: Duality in unusual ordering with spontaneously broken generalized symmetries Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 86
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 044a8c9b-587e-4f8c-9dc3-ee922e5cb715 · inbound
Characterizing gapped phases by smeared boundary conformal field theories: Duality in unusual ordering with spontaneously broken generalized symmetries Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 86
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d0c65d97-fbc8-42eb-8611-3d09a1b0e434 · inbound
Characterizing gapped phases by smeared boundary conformal field theories: Duality in unusual ordering with spontaneously broken generalized symmetries Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 79
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 49ef0c72-3559-402d-8558-de55e79beb35 · inbound
Characterizing gapped phases by smeared boundary conformal field theories: Duality in unusual ordering with spontaneously broken generalized symmetries Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 78
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 40022b26-3143-4f1e-9612-0cb6e7a3b9c9 · inbound
Hilbert Space and Defect Hilbert Spaces Associated with Categorical Symmetries Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 11
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 20c76692-910d-4713-b5bc-b9e18451c011 · inbound
Twin Phases: Intrinsic Deconfined Quantum Criticality Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 23
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation ac238322-30bc-435e-a0d1-72409500bd14 · inbound
Twin Algebras: Condensable Algebras beyond Anyons Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 24
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation c677a878-bd56-4f17-9928-c60c1ad423ad · inbound
Fracton Topological Holography Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 47
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation fd1ca501-a359-4cf1-a08b-1618c1255552 · inbound
Chiral Tube Algebras I: Topological Defect Lines, Twisted Modules, and Finite Gauging Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 26
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 1dc41975-d044-4081-8a9a-13929fcef031 · inbound
Holographic Theory of Mixed-Dimensional Statistics and Conservation-Encoding Hopping-Operator Algebras Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 52
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation abbe0bf6-59c9-4baf-92d8-3d1cf28537c2 · inbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 31
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ed23af3c-734d-4ad6-87bd-9a59d7880e7e · inbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 31
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 622f0b8d-6316-4c45-be79-54289b992e47 · inbound
Distinct finite-temperature phase diagrams of non-invertible Kennedy--Tasaki duals Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 4
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f0dae9ea-4390-45ae-8907-dba0ec0837e2 · inbound
Understanding Non-Split 2-Group Symmetry: (3+1)D SymTFT, Anomaly and Bordism Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 124
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 68567e66-725c-4979-9f5f-873a33fd7bd0 · inbound
Proliferation Transitions for Non-Abelian Anyons Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 51
Source-reported events for the cited work
Unavailable: canonical work link unavailable.