Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-07T14:22:36.286671Z
Paper Citation Record · LEDGER
As of 19 August 2026, this Paper Citation Record lists 59 of 59 outbound references and 4 inbound Pith citation observations for arXiv:2505.19412.
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, observed 2026-08-07T14:22:36.286671Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-01T02:52:29.401514Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-07-03T16:48:40.160053Z
59 of 59 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation 1062675d-5645-4f57-8afd-24331054bece · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Strings, Monopoles and Gauge Fields,
Reference 1
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation f48e8362-52fd-437e-aba8-0c504763c9d3 · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Vortices and Quark Confinement in Nonabelian Gauge Theories,
Reference 2
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 3aa9aa37-f518-45e9-a59b-0131fcaddd96 · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Compact Gauge Fields and the Infrared Catastrophe,
Reference 3
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation bb2eedfe-d48b-44f7-b300-2629f0240c8e · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries On the Phase Transition Towards Permanent Quark Confinement,
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 57064482-559d-4b55-8314-fa491977270a · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries A Property of Electric and Magnetic Flux in Nonabelian Gauge Theories,
Reference 5
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 187587a3-88a4-45cc-a183-56e2b4b2148c · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Quark Confinement and Vortices in Massive Gauge Invariant QCD,
Reference 6
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 0645e1b7-7fbc-4f32-a540-18e51d7db46d · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries A Quantum Liquid Model for the QCD Vacuum: Gauge and Rotational Invariance of Domained and Quantized Homogeneous Color Fields,
Reference 7
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation c1c0fa7e-6375-4a9f-b0dc-046c7043c1b0 · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries A Color Magnetic Vortex Condensate in QCD,
Reference 8
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 5c4a5c8d-2eb5-4c6a-8077-b4f57247c65d · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Quantised singularities in the electromagnetic field,,
Reference 9
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation e3360637-bd80-4d8d-9b03-0fdcfd174648 · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Magnetic charge and quantum field theory,
Reference 10
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation bc103856-4b91-4028-a435-8241310ffb42 · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Quantum field theory of particles with both electric and magnetic charges,
Reference 11
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation b0db34da-0a83-4082-8717-3ed81678c16c · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Dyons of Charge e theta/2 pi,
Reference 12
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 993a140f-4dfc-4703-891a-498e3030c1c2 · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Topology of the Gauge Condition and New Confinement Phases in Nonabelian Gauge Theories,
Reference 13
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3b639e03-b889-485c-9503-4f18f0334342 · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Phase structure of Zp models in the presence of aθ parameter,
Reference 14
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 74245e76-05a3-4b33-a382-004ddc3bf08f · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Duality and theθ parameter in Abelian lattice models,
Reference 15
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation b961b889-6c0a-4d4e-aa1e-60a8e6e043cd · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Composite Particle Theory of Three-dimensional Gapped Fermionic Phases: Fractional Topological Insulators and Charge-Loop Excitation Symmetry
Reference 16
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation f5971516-0d9b-45e5-a913-1329ca174e1a · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Topological aspects of $4$D Abelian lattice gauge theories with the $\theta$ parameter
Reference 17
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 37fbc0b0-8ad4-4fa3-9729-105f45a9f0ab · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Non-invertible self-duality defects of Cardy-Rabinovici model and mixed gravitational anomaly
Reference 18
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 33b0edce-c3c2-4c9e-a046-7841dde001b0 · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Theory of oblique topological insulators
Reference 19
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 4049dcd1-e719-4730-a454-f2b86578fa62 · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Emergent higher-symmetry protected topological orders in the confined phase of $U(1)$ gauge theory
Reference 20
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 12433dff-e188-4f90-935b-6dbb8e600c4c · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Intertwined order of generalized global symmetries
Reference 21
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 378ff4b8-bccd-4d7f-9db4-ec062801fc2f · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Dual simulation of the 2d U(1) gauge Higgs model at topological angle $\theta = \pi\,$: Critical endpoint behavior
Reference 22
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d075bb09-9d00-4bc1-8114-249ead135bf6 · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Abelian gauge theories on the lattice: $\theta$-terms and compact gauge theory with(out) monopoles
Reference 23
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 423e84cd-bd0c-4ae3-b4c3-0039b92fc6e3 · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries First-principle simulations of 1+1d quantum field theories at $\theta=\pi$ and spin-chains
Reference 24
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c72a04b2-4c45-4f80-943b-e0703ec11233 · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Self-dual U(1) lattice field theory with a $\theta$-term
Reference 25
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4ec4a0bb-b28a-4699-8465-68686a1dea97 · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Phase structure of self-dual lattice gauge theories in 4d,
Reference 26
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 96a32d52-c03f-4fc8-9b6c-2d74fc0de0d0 · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Modified Villain formulation of abelian Chern-Simons theory
Reference 27
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8de0a689-e51e-4ee6-a707-3fefeb6d1cfc · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Theory of one-dimensional and two-dimensional magnets with an easy magnetization plane. 2. The Planar, classical, two-dimensional magnet,
Reference 28
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 173a336f-0ea0-4f75-b8b7-790ba0e3fa26 · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries A Modified Villain Formulation of Fractons and Other Exotic Theories
Reference 29
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e74ec79f-b321-467c-b8e2-3545171c74fc · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Non-Invertible Duality Defects in 3+1 Dimensions
Reference 30
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation bb393fb4-be2c-4f60-a200-f27d9fe2c538 · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Exact lattice chiral symmetry in 2d gauge theory
Reference 31
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 520a745c-421f-4ce6-a081-30945ad5af79 · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Instanton Density Operator in Lattice QCD from Higher Category Theory,
Reference 32
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c243725a-152c-4e89-883d-c572b953f0d7 · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries An Explicit Categorical Construction of Instanton Density in Lattice Yang-Mills Theory
Reference 33
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation de0cf1eb-e80a-4312-9a06-1f9cf888386e · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Magnetic operators in 2D compact scalar field theories on the lattice
Reference 34
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 87d960f9-4e4c-4e97-977b-b25b92a7c485 · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Geometrically Interpreting Higher Cup Products, and Application to Combinatorial Pin Structures
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 9cc93670-bf8e-47d1-9199-7ec03a5cbcd7 · outbound
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
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2d071534-1927-4370-9f9d-99aa2731ee9d · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Noncommutative differential calculus and lattice gauge theory,
Reference 37
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 31a6da8b-3e02-44b3-985a-b23a6dd6e2a2 · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries An introduction to non-commutative differential geometry on quantum groups
Reference 38
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 73dcd46a-5557-4e21-8e1d-96ff783a7114 · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Theta, Time Reversal, and Temperature
Reference 39
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f7488872-8336-401c-9b2c-eb4df589529b · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Vacuum structure of bifundamental gauge theories at finite topological angles
Reference 40
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 68b939c3-3394-4a8c-91e9-4f7f56db906f · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Global inconsistency, 't Hooft anomaly, and level crossing in quantum mechanics
Reference 41
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b523d7c7-06fd-4e82-8733-093a4c127acb · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Comments on Abelian Higgs Models and Persistent Order
Reference 42
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 1084d5a9-c286-4cb1-a389-c4f42611b03b · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Anomaly and global inconsistency matching: $\theta$-angles, $SU(3)/U(1)^2$ nonlinear sigma model, $SU(3)$ chains and its generalizations
Reference 43
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3bcb3327-d0cb-4f35-a8ae-d7c7500b4969 · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Anomalies in the Space of Coupling Constants and Their Dynamical Applications I
Reference 44
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d21f1db6-612d-4039-a4ac-6c00067a757b · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Topological Defects on the Lattice I: The Ising model
Reference 45
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 18892ead-c66b-4945-ad5f-aef809dec7f8 · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Topological Defects on the Lattice: Dualities and Degeneracies
Reference 46
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 36a2864a-9f94-478a-b16d-f34c0c0d894f · outbound
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
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 34503d6e-88de-42df-8d17-ab04b9100694 · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Kramers-Wannier-like duality defects in (3+1)d gauge theories
Reference 48
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 806fa1fb-adc5-4070-a5bd-c7a0d50b158b · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Preroughening transitions in crystal surfaces and valence-bond phases in quantum spin chains,
Reference 49
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation f5c38090-ad01-495c-9898-a22d40e064d2 · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Hidden symmetry breaking and the Haldane phase inS=1 quantum spin chains,
Reference 50
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation a0eebefd-5a6e-4bf8-831f-461a649ea409 · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Non-Invertible Duality Transformation Between SPT and SSB Phases
Reference 51
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 16e929f3-39e7-407c-9e2c-2d5f38822991 · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Twisted Partition Functions as Order Parameters
Reference 52
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8e5c9135-0225-4545-85d9-93a5e89bb96d · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Study of gapped phases of 4d gauge theories using temporal gauging of the $\mathbb{Z}_N$ 1-form symmetry
Reference 53
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation fd788072-407d-4873-bebc-ff0a8314c92d · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Lattice Quantum Villain Hamiltonians: Compact scalars, $U(1)$ gauge theories, fracton models and Quantum Ising model dualities
Reference 54
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 34299817-7f6b-4a92-a834-26eab8367d9d · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Lieb-Schultz-Mattis, Luttinger, and 't Hooft -- anomaly matching in lattice systems
Reference 55
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ad0d25ed-f6a5-4a01-b0a8-fe74a3476c7d · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Lieb-Schultz-Mattis anomalies as obstructions to gauging (non-on-site) symmetries
Reference 56
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c54decb7-00cf-4af8-bc5b-d853854d5c24 · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Spin and Statistics Connection for Charge-Monopole Composites,
Reference 57
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation c0196949-7154-4fe6-9756-183090c83f0c · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Spin from Isospin in a Gauge Theory,
Reference 58
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 0df340d8-2ca8-4498-a5a9-2e5b5a255e2b · outbound
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries Spin TQFTs and fermionic phases of matter
Reference 59
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 21b5f0f4-d707-451b-811f-637d827c0278 · inbound
Exotic theta terms in 2+1d fractonic field theory 2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries
Reference 47
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 79e7e698-4b82-44a3-901d-a16f71d27d9a · inbound
Exact SL(2,Z)-Structure of Lattice Maxwell Theory with $\theta$-term in Modified Villain Formulation 2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries
Reference 13
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 8757e497-f510-4468-9e3b-d3b6656c82dc · inbound
Numerical Hints for Dyon Condensation at $\theta=2\pi$ via Wilson-'t Hooft Loops in $SU(2)$ Yang-Mills Theory 2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries
Reference 64
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 802dff50-9e6e-4629-89e4-95f870c1c752 · inbound
$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation 2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries
Reference 11
Source-reported events for the cited work
Unavailable: canonical work link unavailable.