Paper Citation Record · LEDGER

Axion QED as a Lattice Gauge Theory and Non-Invertible Symmetry

As of 12 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 1 inbound Pith citation observation for arXiv:2412.08142.

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

pith.paper-citation-record.v1
2412.08142 v2

Coverage vector

measured 28 of 28 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T18:19:46.670166Z

measured 29 of 29 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-10T18:41:27.428791Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-11T00:05:52.292829Z

Reference resolution

28 of 28 outbound references displayed

verified exact1
verified fuzzy3
unresolved24
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation c102ec03-1325-493c-91a3-19be0bada822 · outbound

This paper cites Lattice realization of the axial $U(1)$ noninvertible symmetry.

Axion QED as a Lattice Gauge Theory and Non-Invertible Symmetry Lattice realization of the axial $U(1)$ noninvertible symmetry

Reference 1

Resolution: verified exact; local_arxiv, observed 2026-08-11T18:19:47.061643Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 2155f35f-27af-40c8-ada6-19cc75230368 · outbound

This paper cites ’t Hooft, Naturalness, chiral symmetry, and spontaneous chiral symm etry breaking , NATO Sci.Ser.B 59 (1980) 135.

Axion QED as a Lattice Gauge Theory and Non-Invertible Symmetry ’t Hooft, Naturalness, chiral symmetry, and spontaneous chiral symm etry breaking , NATO Sci.Ser.B 59 (1980) 135

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:19:47.141382Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 37f26702-a625-40fb-9b73-e848d53e9b25 · outbound

This paper cites an unresolved cited work.

Axion QED as a Lattice Gauge Theory and Non-Invertible Symmetry Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-11T18:19:47.125658Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation c8272ab0-e420-435e-bb4b-6e43595982f3 · outbound

This paper cites Bell and R.

Axion QED as a Lattice Gauge Theory and Non-Invertible Symmetry Bell and R

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:19:47.110358Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 92a15093-da34-45fc-877d-3f0611ad7211 · outbound

This paper cites Higher symmetry and gapped phases of gauge theories.

Axion QED as a Lattice Gauge Theory and Non-Invertible Symmetry Higher symmetry and gapped phases of gauge theories

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-11T18:19:46.553573Z

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Unavailable: canonical work link unavailable.

Observation 35809d3e-2fec-4f69-9f91-f7c399852b29 · outbound

This paper cites Coupling a QFT to a TQFT and Duality.

Axion QED as a Lattice Gauge Theory and Non-Invertible Symmetry Coupling a QFT to a TQFT and Duality

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-11T18:19:46.558779Z

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Unavailable: canonical work link unavailable.

Observation b019c004-e13c-4382-bbb8-731a6066cf80 · outbound

This paper cites Generalized Global Symmetries.

Axion QED as a Lattice Gauge Theory and Non-Invertible Symmetry Generalized Global Symmetries

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-11T18:19:46.564463Z

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Observation b8b32ad8-e560-48bd-8e26-747f018084d6 · outbound

This paper cites Non-invertible Global Symmetries in the Standard Model.

Axion QED as a Lattice Gauge Theory and Non-Invertible Symmetry Non-invertible Global Symmetries in the Standard Model

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-11T18:19:46.569169Z

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Unavailable: canonical work link unavailable.

Observation c40bcc63-eae8-4ebe-a181-919e5bf71873 · outbound

This paper cites Non-Invertible Chiral Symmetry and Exponential Hierarchies.

Axion QED as a Lattice Gauge Theory and Non-Invertible Symmetry Non-Invertible Chiral Symmetry and Exponential Hierarchies

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-11T18:19:46.574023Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 29f562f6-4a1b-4e33-b89b-c0b382c0c3be · outbound

This paper cites Non-invertible topological defects in 4-dimensional $\mathbb{Z}_2$ pure lattice gauge theory.

Axion QED as a Lattice Gauge Theory and Non-Invertible Symmetry Non-invertible topological defects in 4-dimensional $\mathbb{Z}_2$ pure lattice gauge theory

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-11T18:19:46.578952Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 67e24bee-278c-4018-8631-fc811daa18f9 · outbound

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

Axion QED as a Lattice Gauge Theory and Non-Invertible Symmetry Non-Invertible Duality Defects in 3+1 Dimensions

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-11T18:19:46.584467Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eaec718c-275b-470b-935e-dfb9b7008658 · outbound

This paper cites Kramers-Wannier-like duality defects in (3+1)d gauge theories.

Axion QED as a Lattice Gauge Theory and Non-Invertible Symmetry Kramers-Wannier-like duality defects in (3+1)d gauge theories

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-11T18:19:46.589343Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1b43c09e-d58a-4e9d-b03f-27e0fd31dc24 · outbound

This paper cites Non-Invertible Gauss Law and Axions.

Axion QED as a Lattice Gauge Theory and Non-Invertible Symmetry Non-Invertible Gauss Law and Axions

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-11T18:19:46.593779Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8e86044c-121a-4205-822e-fd62e3e09d21 · outbound

This paper cites Non-invertible symmetries in axion electrodynamics.

Axion QED as a Lattice Gauge Theory and Non-Invertible Symmetry Non-invertible symmetries in axion electrodynamics

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-11T18:19:46.598915Z

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Unavailable: canonical work link unavailable.

Observation b00a709c-86cf-4366-a5ca-e148def7f274 · outbound

This paper cites Abelian gauge theories on the lattice: $\theta$-terms and compact gauge theory with(out) monopoles.

Axion QED as a Lattice Gauge Theory and Non-Invertible Symmetry Abelian gauge theories on the lattice: $\theta$-terms and compact gauge theory with(out) monopoles

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-11T18:19:46.603778Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 37c247e3-a7b8-4fa9-b359-a723d52b2121 · outbound

This paper cites Gauging C on the Lattice.

Axion QED as a Lattice Gauge Theory and Non-Invertible Symmetry Gauging C on the Lattice

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-11T18:19:46.608490Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3057ec47-08e8-47e8-85b9-3061c7fa3d9b · outbound

This paper cites an unresolved cited work.

Axion QED as a Lattice Gauge Theory and Non-Invertible Symmetry Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-11T18:19:47.094094Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 35330f0e-5c3b-434b-8a86-a8d55e3f40c6 · outbound

This paper cites Anomalies in the Space of Coupling Constants and Their Dynamical Applications I.

Axion QED as a Lattice Gauge Theory and Non-Invertible Symmetry Anomalies in the Space of Coupling Constants and Their Dynamical Applications I

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-11T18:19:46.617599Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3c85668f-d927-43bf-829d-9aa20a6724e4 · outbound

This paper cites Witten effect, anomaly inflow, and charge teleportation.

Axion QED as a Lattice Gauge Theory and Non-Invertible Symmetry Witten effect, anomaly inflow, and charge teleportation

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-11T18:19:46.622545Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f3315441-32ef-432b-9328-8bbe9f76b410 · outbound

This paper cites Axion Mass from Magnetic Monopole Loops.

Axion QED as a Lattice Gauge Theory and Non-Invertible Symmetry Axion Mass from Magnetic Monopole Loops

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-11T18:19:46.628386Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ca277180-13d4-4f9e-9523-dabff4c87165 · outbound

This paper cites The Weak Gravity Conjecture and Axion Strings.

Axion QED as a Lattice Gauge Theory and Non-Invertible Symmetry The Weak Gravity Conjecture and Axion Strings

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-11T18:19:46.634058Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c79e94a4-3980-45e3-8bcd-c089bbc1f17c · outbound

This paper cites Non-standard axion electrodynamics and the dual Witten effect.

Axion QED as a Lattice Gauge Theory and Non-Invertible Symmetry Non-standard axion electrodynamics and the dual Witten effect

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-11T18:19:46.638970Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c83f8743-65ba-4709-aeee-bb9d5ff98549 · outbound

This paper cites Higher cup products on hypercubic lattices: application to lattice models of topological phases.

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 53e52358-3e14-4923-987d-3327b2bbe193 · outbound

This paper cites Modified Villain formulation of abelian Chern-Simons theory.

Axion QED as a Lattice Gauge Theory and Non-Invertible Symmetry Modified Villain formulation of abelian Chern-Simons theory

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-11T18:19:46.649475Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7bb0e8fd-392f-4f54-b05f-e44b88a97ec2 · outbound

This paper cites Dimakis, F.

Axion QED as a Lattice Gauge Theory and Non-Invertible Symmetry Dimakis, F

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:19:47.078011Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 0ccfcbf3-fae8-4a0d-91f1-d332f313b7fc · outbound

This paper cites Action of the axial $U(1)$ non-invertible symmetry on the 't~Hooft line operator: A lattice gauge theory study.

Axion QED as a Lattice Gauge Theory and Non-Invertible Symmetry Action of the axial $U(1)$ non-invertible symmetry on the 't~Hooft line operator: A lattice gauge theory study

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-11T18:19:46.659714Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e4d8d9c3-0414-4572-a84b-551984bb3477 · outbound

This paper cites Action of the axial $U(1)$ non-invertible symmetry on the 't~Hooft line operator: A simple argument.

Axion QED as a Lattice Gauge Theory and Non-Invertible Symmetry Action of the axial $U(1)$ non-invertible symmetry on the 't~Hooft line operator: A simple argument

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-11T18:19:46.665375Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d88fc316-05b1-40ca-8059-6a5eb464c206 · outbound

This paper cites A Modified Villain Formulation of Fractons and Other Exotic Theories.

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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Pith citing papers

Observation ed92b822-7408-43ea-b41a-73eda6a00c3c · inbound

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

Lattice chiral symmetry from bosons in 3+1d Axion QED as a Lattice Gauge Theory and Non-Invertible Symmetry

Reference 47

Resolution: verified exact; arxiv_id, observed 2026-05-11T00:05:52.295536Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.