Paper Citation Record · LEDGER

Integrating Neural Networks and Tensor Networks for Computing Free Energy

As of 18 August 2026, this Paper Citation Record lists 33 of 33 outbound references and 0 inbound Pith citation observations for arXiv:2504.12037.

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

pith.paper-citation-record.v1
2504.12037 v1

Coverage vector

measured 33 of 33 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-16T12:40:28.978742Z

measured 33 of 33 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

33 of 33 outbound references displayed

verified exact0
verified fuzzy11
unresolved22
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation e4d7227a-0d58-473e-a368-343c0f0aea83 · outbound

This paper cites an unresolved cited work.

Integrating Neural Networks and Tensor Networks for Computing Free Energy Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-16T12:40:29.524180Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 4adf6400-53eb-43ce-b56c-db3a02230d51 · outbound

This paper cites for 0≤i< Epoch do (a) Draw samples from the nerual network based on Eq.8.

Integrating Neural Networks and Tensor Networks for Computing Free Energy for 0≤i< Epoch do (a) Draw samples from the nerual network based on Eq.8

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:40:29.506846Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 3546fb68-86fc-42c1-9da8-d25c7f4ce4f8 · outbound

This paper cites We calculated the free energy at different temperatures using different variational methods and CATN with different hyper-parameters.

Integrating Neural Networks and Tensor Networks for Computing Free Energy We calculated the free energy at different temperatures using different variational methods and CATN with different hyper-parameters

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:40:29.489241Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation bd71ac74-4e38-4977-ad20-9d5726d73cdb · outbound

This paper cites Landau and E.

Integrating Neural Networks and Tensor Networks for Computing Free Energy Landau and E

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:40:29.471651Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation ab5243a9-832c-4bad-bf39-312e88bd3f24 · outbound

This paper cites an unresolved cited work.

Integrating Neural Networks and Tensor Networks for Computing Free Energy Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-16T12:40:29.454430Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 72d3959c-ba68-4607-ac61-57e91e3f19c9 · outbound

This paper cites an unresolved cited work.

Integrating Neural Networks and Tensor Networks for Computing Free Energy Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-16T12:40:29.435730Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation feb1f33c-e29d-42e3-92a6-96a38dfe7e7f · outbound

This paper cites an unresolved cited work.

Integrating Neural Networks and Tensor Networks for Computing Free Energy Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-16T12:40:29.418634Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 614aa629-a6d1-4a43-b0b7-7ea26c41ab4e · outbound

This paper cites Kikuchi, A theory of cooperative phenomena, Phys.

Integrating Neural Networks and Tensor Networks for Computing Free Energy Kikuchi, A theory of cooperative phenomena, Phys

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-16T12:40:28.841269Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c5e41cdf-5248-4a35-a281-cc0a1db4b0f4 · outbound

This paper cites an unresolved cited work.

Integrating Neural Networks and Tensor Networks for Computing Free Energy Unresolved cited work

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-16T12:40:28.847011Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3dc8c8fd-35c7-4226-8cb8-d54cd1e80d56 · outbound

This paper cites Levin and C.

Integrating Neural Networks and Tensor Networks for Computing Free Energy Levin and C

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:40:29.380505Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation d4dfef23-56f6-4555-8c12-45c9ecc7536b · outbound

This paper cites an unresolved cited work.

Integrating Neural Networks and Tensor Networks for Computing Free Energy Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-16T12:40:29.362683Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation d0a61d95-8cbb-484c-9ef1-d55f4c735fa0 · outbound

This paper cites an unresolved cited work.

Integrating Neural Networks and Tensor Networks for Computing Free Energy Unresolved cited work

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-16T12:40:28.862585Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fadde6d0-5137-47a4-b480-e78606a401bd · outbound

This paper cites MADE: Masked Autoencoder for Distribution Estimation.

Integrating Neural Networks and Tensor Networks for Computing Free Energy MADE: Masked Autoencoder for Distribution Estimation

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-16T12:40:28.868819Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4ecd2d05-2a91-4983-8bc9-4879484fb307 · outbound

This paper cites an unresolved cited work.

Integrating Neural Networks and Tensor Networks for Computing Free Energy Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-16T12:40:29.336204Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 4812cf1f-8f5c-4739-8fb4-f0288d77198a · outbound

This paper cites Festa, P.

Integrating Neural Networks and Tensor Networks for Computing Free Energy Festa, P

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:40:29.318676Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation cc5d61ae-e5a6-4df4-a5b9-6d149fe2c051 · outbound

This paper cites Gray and S.

Integrating Neural Networks and Tensor Networks for Computing Free Energy Gray and S

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-16T12:40:28.885913Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f7d05af2-5564-4a2e-a823-032d50ffdaab · outbound

This paper cites Classical Simulation of Intermediate-Size Quantum Circuits.

Integrating Neural Networks and Tensor Networks for Computing Free Energy Classical Simulation of Intermediate-Size Quantum Circuits

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-16T12:40:28.891595Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 78c7e0bf-d4fc-401f-89ea-b9aff047f5ce · outbound

This paper cites Villalonga, S.

Integrating Neural Networks and Tensor Networks for Computing Free Energy Villalonga, S

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:40:29.290989Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 53a9b9ca-cd58-4451-9574-27d3f1645a86 · outbound

This paper cites Pan and P.

Integrating Neural Networks and Tensor Networks for Computing Free Energy Pan and P

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-16T12:40:28.901908Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5dad2553-f8bc-4851-8944-82a718a2a24c · outbound

This paper cites an unresolved cited work.

Integrating Neural Networks and Tensor Networks for Computing Free Energy Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-16T12:40:29.275063Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c20bd890-5030-45be-a52d-69d88842518d · outbound

This paper cites NP-Hardness of Tensor Network Contraction Ordering.

Integrating Neural Networks and Tensor Networks for Computing Free Energy NP-Hardness of Tensor Network Contraction Ordering

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-16T12:40:28.912147Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 607d6aac-49e7-4faf-9a2f-298e35c09f30 · outbound

This paper cites an unresolved cited work.

Integrating Neural Networks and Tensor Networks for Computing Free Energy Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-16T12:40:29.257278Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 83ad0d6d-0368-4baa-9a09-d518f14f58c5 · outbound

This paper cites Multi-Tensor Contraction for XEB Verification of Quantum Circuits.

Integrating Neural Networks and Tensor Networks for Computing Free Energy Multi-Tensor Contraction for XEB Verification of Quantum Circuits

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-16T12:40:28.923283Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f0cc7eaf-0656-4393-b35b-83ee104024df · outbound

This paper cites Kalchbrenner, A.

Integrating Neural Networks and Tensor Networks for Computing Free Energy Kalchbrenner, A

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:40:29.239860Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 6a517ff2-9459-4865-b8fb-9116392f3a23 · outbound

This paper cites Vaswani, N.

Integrating Neural Networks and Tensor Networks for Computing Free Energy Vaswani, N

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:40:29.222661Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 652314db-42c3-4996-806e-952caa1ad857 · outbound

This paper cites an unresolved cited work.

Integrating Neural Networks and Tensor Networks for Computing Free Energy Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-16T12:40:29.206931Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 15e88d87-b5b4-46fa-bcd7-7d88a71a2d16 · outbound

This paper cites an unresolved cited work.

Integrating Neural Networks and Tensor Networks for Computing Free Energy Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-16T12:40:29.191105Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c1180e47-c629-4815-aa46-cfab3ec15d93 · outbound

This paper cites Kac and J.

Integrating Neural Networks and Tensor Networks for Computing Free Energy Kac and J

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:40:29.174759Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation e86d1c4a-d964-4cf1-be48-b115f046949c · outbound

This paper cites an unresolved cited work.

Integrating Neural Networks and Tensor Networks for Computing Free Energy Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-16T12:40:29.155813Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 5683db5b-6a8d-41a3-828f-772b571ee624 · outbound

This paper cites an unresolved cited work.

Integrating Neural Networks and Tensor Networks for Computing Free Energy Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-16T12:40:29.137589Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation d0a6a5b0-fc51-4087-88f1-0b7035b1ed88 · outbound

This paper cites Viana and A.

Integrating Neural Networks and Tensor Networks for Computing Free Energy Viana and A

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:40:29.121409Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 78e0a77c-3e84-4414-848d-5814e28861fa · outbound

This paper cites Sherrington and S.

Integrating Neural Networks and Tensor Networks for Computing Free Energy Sherrington and S

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:40:29.105280Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 322ed811-0e2e-4c17-9f27-73cc99f5c1e7 · outbound

This paper cites an unresolved cited work.

Integrating Neural Networks and Tensor Networks for Computing Free Energy Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-08-16T12:40:29.088239Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Pith citing papers

No inbound Pith citation observations are available.