Paper Citation Record · LEDGER

A deep neural network approach to solve the Dirac equation

As of 12 August 2026, this Paper Citation Record lists 46 of 46 outbound references and 1 inbound Pith citation observation for arXiv:2412.03090.

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

pith.paper-citation-record.v1
2412.03090 v2

Coverage vector

measured 46 of 46 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T22:53:53.083602Z

measured 47 of 47 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 2026-08-10T14:01:09.004267Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-10T14:01:09.330033Z

Reference resolution

46 of 46 outbound references displayed

verified exact0
verified fuzzy14
unresolved32
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 6471909e-dde0-41f3-b1b8-587e7510e73f · outbound

This paper cites 11, whereFnκ and Gnκ are gener- ated by two output units, respectively.

A deep neural network approach to solve the Dirac equation 11, whereFnκ and Gnκ are gener- ated by two output units, respectively

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:53:53.710109Z

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 83bf653e-aeb5-45f7-81ce-6e016d50fe4f · outbound

This paper cites IIIA, a trial wave functionfnκ is used as the DNN output to calculateFnκ and Gnκ.

A deep neural network approach to solve the Dirac equation IIIA, a trial wave functionfnκ is used as the DNN output to calculateFnκ and Gnκ

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:53:53.699060Z

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 22d1b3fc-9854-42be-86f1-6dc8cf785a92 · outbound

This paper cites an unresolved cited work.

A deep neural network approach to solve the Dirac equation Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-11T22:53:53.686461Z

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 4d1a7a86-1096-4cda-a4bc-3c0f418ed535 · outbound

This paper cites Carleo, I.

A deep neural network approach to solve the Dirac equation Carleo, I

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-11T22:53:52.931588Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d95f3b8c-c6f0-4d3e-9fba-716a02ebd4af · outbound

This paper cites Carleo and M.

A deep neural network approach to solve the Dirac equation Carleo and M

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:53:53.668426Z

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 c9f00d2c-1bf2-4895-bb5d-244341f3cf29 · outbound

This paper cites Nomura, A.

A deep neural network approach to solve the Dirac equation Nomura, A

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-11T22:53:52.939394Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 554dc165-2404-4997-9bca-ba535b186740 · outbound

This paper cites Carleo, Y.

A deep neural network approach to solve the Dirac equation Carleo, Y

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-11T22:53:52.943171Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation def97745-951e-4ee4-b106-0fdeac59dc3f · outbound

This paper cites an unresolved cited work.

A deep neural network approach to solve the Dirac equation Unresolved cited work

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-11T22:53:52.947102Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2a6c8e53-2978-4279-883c-a6cd43f108a2 · outbound

This paper cites Nomura, Machine Learning Quantum States - Exten- sions to Fermion-Boson Coupled Systems and Excited- State Calculations, J.

A deep neural network approach to solve the Dirac equation Nomura, Machine Learning Quantum States - Exten- sions to Fermion-Boson Coupled Systems and Excited- State Calculations, J

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:53:53.633933Z

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 b3beaec3-5127-4b2a-8440-265789f468c3 · outbound

This paper cites Stokes, J.

A deep neural network approach to solve the Dirac equation Stokes, J

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-11T22:53:52.955094Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f325e4e5-a473-4a89-9b5c-bc4e1102da82 · outbound

This paper cites an unresolved cited work.

A deep neural network approach to solve the Dirac equation Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-11T22:53:53.615132Z

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 9b128a21-f8e0-4152-9853-08829922a309 · outbound

This paper cites Yoshino, Spatially heterogeneous learning by a deep student machine, Phys.

A deep neural network approach to solve the Dirac equation Yoshino, Spatially heterogeneous learning by a deep student machine, Phys

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:53:53.602231Z

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 ed6f2b4c-f9bb-437c-9a12-449995618606 · outbound

This paper cites Saito, Method to Solve Quantum Few-Body Problems with Artificial Neural Networks, J.

A deep neural network approach to solve the Dirac equation Saito, Method to Solve Quantum Few-Body Problems with Artificial Neural Networks, J

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-11T22:53:52.965828Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 940a82dd-c153-4fd3-b612-5e270cb1b99f · outbound

This paper cites Pescia, J.

A deep neural network approach to solve the Dirac equation Pescia, J

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-11T22:53:52.969450Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2d2eb6ba-031c-4e0e-addd-146f7580dc0f · outbound

This paper cites an unresolved cited work.

A deep neural network approach to solve the Dirac equation Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-11T22:53:53.576969Z

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 f2fe3ba4-b1b7-4790-abd4-fe22678de523 · outbound

This paper cites Cassella, H.

A deep neural network approach to solve the Dirac equation Cassella, H

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:53:53.565848Z

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 2cc901af-db2e-4c2f-9367-4eb164d00ef7 · outbound

This paper cites an unresolved cited work.

A deep neural network approach to solve the Dirac equation Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-11T22:53:53.554160Z

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 2046102c-9d44-4627-8d1d-f5d7f5ebf675 · outbound

This paper cites an unresolved cited work.

A deep neural network approach to solve the Dirac equation Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-11T22:53:53.541428Z

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 f56459d4-ec86-4e74-8a14-2d750906eeab · outbound

This paper cites Hermann, Z.

A deep neural network approach to solve the Dirac equation Hermann, Z

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-11T22:53:52.987352Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 05d6fd22-771a-440a-a6ff-f86ee1b0a11b · outbound

This paper cites an unresolved cited work.

A deep neural network approach to solve the Dirac equation Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-11T22:53:53.519663Z

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 69620537-77fb-4ffd-9a54-69362d133ecc · outbound

This paper cites Adams, G.

A deep neural network approach to solve the Dirac equation Adams, G

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-11T22:53:52.995102Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a4f8d050-2ef5-4141-8a74-5361b05d81cb · outbound

This paper cites Gnech, C.

A deep neural network approach to solve the Dirac equation Gnech, C

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:53:53.499522Z

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 24a05b2d-967c-4e51-a409-7ba844d2bc88 · outbound

This paper cites an unresolved cited work.

A deep neural network approach to solve the Dirac equation Unresolved cited work

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-11T22:53:53.002454Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7c332df1-a02a-42e5-9297-eb2b75254aff · outbound

This paper cites an unresolved cited work.

A deep neural network approach to solve the Dirac equation Unresolved cited work

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-11T22:53:53.005700Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 18045f40-b39a-4b6c-b7f2-bc847365bf79 · outbound

This paper cites an unresolved cited work.

A deep neural network approach to solve the Dirac equation Unresolved cited work

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-11T22:53:53.008772Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3f39dfe3-d246-46c7-a89a-c842e8429e82 · outbound

This paper cites Investigating the crust of neutron stars with neural-network quantum states.

A deep neural network approach to solve the Dirac equation Investigating the crust of neutron stars with neural-network quantum states

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-11T22:53:53.011885Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b930ca6e-8f04-4e5a-88d0-85b0fade8e4c · outbound

This paper cites Lovato, C.

A deep neural network approach to solve the Dirac equation Lovato, C

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-11T22:53:53.015405Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 163d1943-8343-445c-8f87-f910b0830ff9 · outbound

This paper cites Wilson, S.

A deep neural network approach to solve the Dirac equation Wilson, S

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-11T22:53:53.019103Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 291b4477-48dd-46db-b37f-2882ce82bbcf · outbound

This paper cites Hermann, J.

A deep neural network approach to solve the Dirac equation Hermann, J

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-11T22:53:53.022070Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b9a90a53-c5ac-4aa3-97bd-fe2bbd17e580 · outbound

This paper cites an unresolved cited work.

A deep neural network approach to solve the Dirac equation Unresolved cited work

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-11T22:53:53.025025Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 25825cd6-c68e-4896-af46-a0209ac2bf06 · outbound

This paper cites Naito, H.

A deep neural network approach to solve the Dirac equation Naito, H

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:53:53.302267Z

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 6571bb33-d2f8-4f9e-840b-6533ae0e660c · outbound

This paper cites A neural network approach for two-body systems with spin and isospin degrees of freedom.

A deep neural network approach to solve the Dirac equation A neural network approach for two-body systems with spin and isospin degrees of freedom

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-11T22:53:53.031761Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2101f230-9957-46d6-9807-1c3e73f16e33 · outbound

This paper cites Lorin and X.

A deep neural network approach to solve the Dirac equation Lorin and X

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:53:53.289877Z

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 cf665e03-39e7-417a-8f12-6bc21a763621 · outbound

This paper cites Armstrong, Lloyd, Relativistic Effects in Atomic Fine Structure, J.

A deep neural network approach to solve the Dirac equation Armstrong, Lloyd, Relativistic Effects in Atomic Fine Structure, J

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:53:53.276945Z

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 657e850a-3bf3-4ebf-a764-f50098bd0884 · outbound

This paper cites Ernzerhof and F.

A deep neural network approach to solve the Dirac equation Ernzerhof and F

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:53:53.264433Z

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 befc6fa0-89ba-4405-9c17-d67b419711c4 · outbound

This paper cites an unresolved cited work.

A deep neural network approach to solve the Dirac equation Unresolved cited work

Reference 36

Resolution: unresolved; raw_fallback, observed 2026-08-11T22:53:53.251783Z

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 77055d33-4a2f-4cf6-bc62-a3a0232475ab · outbound

This paper cites Hagino and Y.

A deep neural network approach to solve the Dirac equation Hagino and Y

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:53:53.240435Z

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 abb28501-8942-46da-82d6-bd2459370396 · outbound

This paper cites an unresolved cited work.

A deep neural network approach to solve the Dirac equation Unresolved cited work

Reference 38

Resolution: unresolved; raw_fallback, observed 2026-08-11T22:53:53.229639Z

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 f103e40b-62e0-4563-a570-b1c60f8b8ec7 · outbound

This paper cites an unresolved cited work.

A deep neural network approach to solve the Dirac equation Unresolved cited work

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-11T22:53:53.056999Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 38c6b6db-bbf6-4b86-afc5-5c867a9696e1 · outbound

This paper cites Adam: A Method for Stochastic Optimization.

A deep neural network approach to solve the Dirac equation Adam: A Method for Stochastic Optimization

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-11T22:53:53.060779Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0f08f0a5-f975-4b38-b426-5fb81629871f · outbound

This paper cites an unresolved cited work.

A deep neural network approach to solve the Dirac equation Unresolved cited work

Reference 41

Resolution: unresolved; raw_fallback, observed 2026-08-11T22:53:53.210906Z

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 24a60fed-cc22-40f4-888f-3d6b11799f2f · outbound

This paper cites Koepf and P.

A deep neural network approach to solve the Dirac equation Koepf and P

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:53:53.199516Z

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 1fc3a722-282a-4abd-8f58-471e032b4d38 · outbound

This paper cites Yao and S.-I.

A deep neural network approach to solve the Dirac equation Yao and S.-I

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:53:53.187323Z

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 12326272-6089-48a3-b39d-9a570885edee · outbound

This paper cites an unresolved cited work.

A deep neural network approach to solve the Dirac equation Unresolved cited work

Reference 44

Resolution: unresolved; raw_fallback, observed 2026-08-11T22:53:53.175240Z

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 2ce8f461-43b4-4add-9147-9cf5875123a5 · outbound

This paper cites an unresolved cited work.

A deep neural network approach to solve the Dirac equation Unresolved cited work

Reference 45

Resolution: unresolved; raw_fallback, observed 2026-08-11T22:53:53.162117Z

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 81174690-0c99-424b-8d4f-214c388979cd · outbound

This paper cites Two-Body Dirac Equations for Relativistic Bound States of Quantum Field Theory.

A deep neural network approach to solve the Dirac equation Two-Body Dirac Equations for Relativistic Bound States of Quantum Field Theory

Reference 46

Resolution: unresolved; no resolver link, observed 2026-08-11T22:53:53.083602Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 7ded3147-a9e6-4c0b-8bbc-58dd0712b58f · inbound

Towards constraining QCD phase transitions in neutron star interiors: Bayesian Inference with TOV linear response analysis cites this paper.

Towards constraining QCD phase transitions in neutron star interiors: Bayesian Inference with TOV linear response analysis A deep neural network approach to solve the Dirac equation

Reference 100

Resolution: verified exact; local_arxiv, observed 2026-08-10T14:01:09.335117Z

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.