Paper Citation Record · LEDGER

A Modified Villain Formulation of Fractons and Other Exotic Theories

As of 22 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 26 inbound Pith citation observations for arXiv:2103.01257.

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pith.paper-citation-record.v1
2103.01257 v4

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measured 26 of 26 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+00:00

measured 26 of 26 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T15:16:13.186178Z

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Source: arxiv_reference, observed 2026-07-03T13:48:21.054705Z

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Outbound references

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Pith citing papers

Observation 9d267a4e-bd6d-43f4-87b8-4047bb5c0e4d · inbound

Non-Invertible Duality Defects in 3+1 Dimensions cites this paper.

Non-Invertible Duality Defects in 3+1 Dimensions A Modified Villain Formulation of Fractons and Other Exotic Theories

Reference 57

Resolution: verified exact; arxiv_id, observed 2026-05-24T08:56:32.457705Z

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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 28aee967-0f36-43cf-8d63-dc78738f655c · inbound

Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond cites this paper.

Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond A Modified Villain Formulation of Fractons and Other Exotic Theories

Reference 147

Resolution: verified exact; arxiv_id, observed 2026-05-21T13:21:27.764830Z

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Observation 621d3f9b-2282-427c-b24f-befa138c34c9 · inbound

What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries cites this paper.

What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries A Modified Villain Formulation of Fractons and Other Exotic Theories

Reference 259

Resolution: verified exact; arxiv_id, observed 2026-05-24T07:34:07.874074Z

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Observation d88fc316-05b1-40ca-8059-6a5eb464c206 · 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 A Modified Villain Formulation of Fractons and Other Exotic Theories

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-11T18:19:46.670166Z

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Observation 9114a879-a3f0-4ed6-86b3-ad219971b2d4 · inbound

Anomalous Continuous Translations cites this paper.

Anomalous Continuous Translations A Modified Villain Formulation of Fractons and Other Exotic Theories

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-11T12:21:40.681921Z

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Observation 6cf868b1-4d8e-4664-874e-92bdc942f0bd · inbound

Fractionalization of flux tubes in 3d and screening by emergent electric charges in 2d cites this paper.

Fractionalization of flux tubes in 3d and screening by emergent electric charges in 2d A Modified Villain Formulation of Fractons and Other Exotic Theories

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-11T12:18:30.191725Z

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Observation 768cea28-8a68-4d7b-9e73-50f53f1a2c27 · inbound

U(1)-gauged 2-flavor spin system in 3-D cites this paper.

U(1)-gauged 2-flavor spin system in 3-D A Modified Villain Formulation of Fractons and Other Exotic Theories

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-09T05:04:57.919259Z

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Observation 173a336f-0ea0-4f75-b8b7-790ba0e3fa26 · 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 A Modified Villain Formulation of Fractons and Other Exotic Theories

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-07T14:22:36.123982Z

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Observation 5d7df8b8-04ee-4d29-9662-040b45f077f5 · inbound

Discrete $p$-Form Symmetry and Higher Coulomb Phases cites this paper.

Discrete $p$-Form Symmetry and Higher Coulomb Phases A Modified Villain Formulation of Fractons and Other Exotic Theories

Reference 59

Resolution: malformed identifier; arxiv_id, observed 2026-05-19T04:52:59.582016Z

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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation da8f651c-c111-4833-9f14-68c9c5b9c165 · inbound

Exactly Solvable 1+1d Chiral Lattice Gauge Theories cites this paper.

Exactly Solvable 1+1d Chiral Lattice Gauge Theories A Modified Villain Formulation of Fractons and Other Exotic Theories

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-03T09:26:54.464936Z

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Observation 89240045-3c4f-4cfe-b1ba-8bbecae31428 · inbound

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

Lattice chiral symmetry from bosons in 3+1d A Modified Villain Formulation of Fractons and Other Exotic Theories

Reference 11

Resolution: verified exact; arxiv_id, observed 2026-05-11T00:10:49.608828Z

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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation ae22e5bd-0efd-4c11-aa84-9ae1c98367b9 · inbound

Exotic theta terms in 2+1d fractonic field theory cites this paper.

Exotic theta terms in 2+1d fractonic field theory A Modified Villain Formulation of Fractons and Other Exotic Theories

Reference 33

Resolution: verified exact; arxiv_id, observed 2026-05-11T00:50:50.266068Z

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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5d837edc-6e62-4576-9ac5-539ec75ce835 · 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 A Modified Villain Formulation of Fractons and Other Exotic Theories

Reference 17

Resolution: verified exact; arxiv_id, observed 2026-05-11T07:51:01.713781Z

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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation a6887e3d-3817-4885-9167-8c5feea6b063 · inbound

Lattice Realizations of Flat Gauging and T-duality Defects at Any Radius cites this paper.

Lattice Realizations of Flat Gauging and T-duality Defects at Any Radius A Modified Villain Formulation of Fractons and Other Exotic Theories

Reference 33

Resolution: verified exact; arxiv_id, observed 2026-05-11T05:30:58.772860Z

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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 254a693e-a48e-4768-9175-00c0fd5895b2 · inbound

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

When Symmetries Twist: Anomaly Inflow on Monodromy Defects A Modified Villain Formulation of Fractons and Other Exotic Theories

Reference 105

Resolution: metadata mismatch; arxiv_id, observed 2026-05-20T16:38:39.759148Z

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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 192fde6e-9596-43e6-a35a-4993d316f451 · inbound

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

When Symmetries Twist: Anomaly Inflow on Monodromy Defects A Modified Villain Formulation of Fractons and Other Exotic Theories

Reference 105

Resolution: metadata mismatch; arxiv_id, observed 2026-07-01T14:55:47.589914Z

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Observation 01612eb6-c219-482b-9f20-99dfc9631be3 · 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 A Modified Villain Formulation of Fractons and Other Exotic Theories

Reference 8

Resolution: verified exact; arxiv_id, observed 2026-05-20T04:03:04.506188Z

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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation f08cf80e-2c62-4b05-af87-4455617faf61 · inbound

Lattice chiral non-Abelian gauge symmetry via bosonization cites this paper.

Lattice chiral non-Abelian gauge symmetry via bosonization A Modified Villain Formulation of Fractons and Other Exotic Theories

Reference 45

Resolution: verified exact; arxiv_id, observed 2026-07-03T13:48:21.056117Z

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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 1ba8dffe-7691-4919-a988-165167b297bc · inbound

Infinite-Order Lattice Chiral Anomalies and CPT cites this paper.

Infinite-Order Lattice Chiral Anomalies and CPT A Modified Villain Formulation of Fractons and Other Exotic Theories

Reference 40

Resolution: metadata mismatch; arxiv_id, observed 2026-07-03T12:08:06.515054Z

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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation c1f4d516-c390-44a1-9369-0cbba671a9a2 · inbound

Axions on de Sitter space cites this paper.

Axions on de Sitter space A Modified Villain Formulation of Fractons and Other Exotic Theories

Reference 59

Resolution: verified exact; arxiv_id, observed 2026-06-30T09:04:32.791711Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5068f164-a86f-4c0a-b135-e51d813402e0 · inbound

Toward Hamiltonian simulations of Maxwell-Chern-Simons theory: constant modes and gauge field truncation cites this paper.

Toward Hamiltonian simulations of Maxwell-Chern-Simons theory: constant modes and gauge field truncation A Modified Villain Formulation of Fractons and Other Exotic Theories

Reference 27

Resolution: verified exact; arxiv_id, observed 2026-07-02T18:37:16.302142Z

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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation df8ba7fd-69d9-49b7-b9b3-b6f96b086bdc · inbound

Bosonization versus the Nielsen-Ninomiya theorem cites this paper.

Bosonization versus the Nielsen-Ninomiya theorem A Modified Villain Formulation of Fractons and Other Exotic Theories

Reference 45

Resolution: unresolved; no resolver link, observed 2026-07-14T14:29:24.660809Z

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Observation af7ef792-32eb-43b6-b704-6c37fcc5e5be · inbound

Bosonization versus the Nielsen-Ninomiya theorem cites this paper.

Bosonization versus the Nielsen-Ninomiya theorem A Modified Villain Formulation of Fractons and Other Exotic Theories

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-02T07:43:50.193819Z

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Observation 0ef30445-9267-49f6-8132-70753a6670b2 · inbound

1+1d Lattice Dirac Fermions from Non-Onsite Vector and Axial Symmetries cites this paper.

1+1d Lattice Dirac Fermions from Non-Onsite Vector and Axial Symmetries A Modified Villain Formulation of Fractons and Other Exotic Theories

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-15T15:16:13.186178Z

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Observation 1d8046ce-bf99-463c-82a7-9146d3e6bdb4 · inbound

Fermionic Villain model with exact lattice chiral symmetries cites this paper.

Fermionic Villain model with exact lattice chiral symmetries A Modified Villain Formulation of Fractons and Other Exotic Theories

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-15T15:10:42.523777Z

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Observation 6f151a67-787f-436d-be51-15f10052e60e · inbound

Classical fractons with cosmological fixed points cites this paper.

Classical fractons with cosmological fixed points A Modified Villain Formulation of Fractons and Other Exotic Theories

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-11T00:32:19.428988Z

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Unavailable: canonical work link unavailable.