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Paper Citation Record · LEDGER

Thermodynamics and Legendre Duality in Optimal Networks

As of 8 August 2026, this Paper Citation Record lists 80 of 80 outbound references and 0 inbound Pith citation observations for arXiv:2506.15727.

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

pith.paper-citation-record.v1
2506.15727 v1

Coverage vector

measured 80 of 80 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T05:33:21.307241Z

measured 80 of 80 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+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

80 of 80 outbound references displayed

  • verified exact0
  • verified fuzzy52
  • unresolved28
  • parse uncertain0
  • malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation a065bdeb-a4cb-42e5-a077-23870794e641 · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 1

Resolution
unresolved
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 66e714a7-4c9d-49b1-b0a0-329161b843af · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 2

Resolution
unresolved
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 2441017f-bb57-4ace-a239-814b219070fc · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 3

Resolution
unresolved
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation ddfbf355-55c3-4eef-a2b5-ea234c37319c · outbound

This paper cites Rodriguez-Iturbe, A.

Thermodynamics and Legendre Duality in Optimal Networks Rodriguez-Iturbe, A

Reference 4

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation f185aea9-b652-4813-8816-d45dfaab8b1d · outbound

This paper cites Santambrogio, Optimal transport for applied mathematicians, Birk¨ auser, NY 55 (58-63) (2015) 94.

Thermodynamics and Legendre Duality in Optimal Networks Santambrogio, Optimal transport for applied mathematicians, Birk¨ auser, NY 55 (58-63) (2015) 94

Reference 5

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 871c065b-6baa-430c-b3ae-c3072f4bc94b · outbound

This paper cites Van Baak, Variational alternatives to kirchhoff’s loop theorem in dc circuits, American Journal of Physics 67 (1) (1999) 36–44.

Thermodynamics and Legendre Duality in Optimal Networks Van Baak, Variational alternatives to kirchhoff’s loop theorem in dc circuits, American Journal of Physics 67 (1) (1999) 36–44

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:33.263012Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation e2d67628-56a3-4d73-8a53-15d61916df8c · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:33.094946Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:20.963790Z digest=sha256:5ac294eb58ec047bd237950441dd970dc0b7db4bbdc2357dc2d89bf566e02f04

Observation 07941dc3-f4a7-49da-910a-176a34d88b5b · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:32.932284Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:20.968823Z digest=sha256:fd54ac3cd3384ef630d4a6df078172b1bdd9cc77c9bab63454588f5917e15d25

Observation cc9e931d-dd99-4379-85ec-07371df9640f · outbound

This paper cites Barbera, On the principle of minimal entropy production for navier-stokes-fourier fluids, Continuum Mechanics and Thermodynamics 11 (5) (1999) 327–330.

Thermodynamics and Legendre Duality in Optimal Networks Barbera, On the principle of minimal entropy production for navier-stokes-fourier fluids, Continuum Mechanics and Thermodynamics 11 (5) (1999) 327–330

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:32.759519Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:20.973825Z digest=sha256:6fb50fa0dd17b59518f0eaa93b09b8309594090caa7014e7c9614da41b896cd5

Observation 96a13060-834e-4998-a5a0-afa7543327e3 · outbound

This paper cites Kondepudi, I.

Thermodynamics and Legendre Duality in Optimal Networks Kondepudi, I

Reference 10

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 8a6e7795-190b-4059-b45b-6f5e4a08f339 · outbound

This paper cites Martyushev, A.

Thermodynamics and Legendre Duality in Optimal Networks Martyushev, A

Reference 11

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 4856ca3f-f057-422e-8505-6312cde9e12e · outbound

This paper cites Millar, Cxvi.

Thermodynamics and Legendre Duality in Optimal Networks Millar, Cxvi

Reference 12

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:20.988944Z digest=sha256:98a826ebbe6c09ea56183321e17b8c8dc3ad541e80a04ae888ee4c1539442d19

Observation f169b4f6-f3e6-4c86-b9b3-d3521fa351bd · outbound

This paper cites Cherry, Non-linear circuit theory by the methods of classical dynamics, in: Recent Developments in Network Theory, Elsevier, 1963, pp.

Thermodynamics and Legendre Duality in Optimal Networks Cherry, Non-linear circuit theory by the methods of classical dynamics, in: Recent Developments in Network Theory, Elsevier, 1963, pp

Reference 13

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:20.994288Z digest=sha256:c6a422a70f0c8b7bcd44b9bfc476a1a161c62fb467bdbda640f6e39d325b049d

Observation 6dcb97e7-6e10-4e72-ad49-22e328c03e74 · outbound

This paper cites Verh´ as, Gyarmati’s variational principle of dissipative processes, Entropy 16 (4) (2014) 2362–2383.

Thermodynamics and Legendre Duality in Optimal Networks Verh´ as, Gyarmati’s variational principle of dissipative processes, Entropy 16 (4) (2014) 2362–2383

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:31.887390Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:20.999970Z digest=sha256:0ceeacdcf4184b5a2acad5c0a790a6ffd6e896b8fff01d3157ff774f2df16ec5

Observation 98ee0a3b-686c-4cfc-9845-d8e1780c45e7 · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:31.658043Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation fa2828a4-92a0-4eac-ae42-492af6e3e2a0 · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 16

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:31.481481Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 37106f81-5467-4fc3-89ff-666da53c3f64 · outbound

This paper cites Bejan, S.

Thermodynamics and Legendre Duality in Optimal Networks Bejan, S

Reference 17

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 0d5c1ce7-94ec-498f-98e8-3386b5713e80 · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 18

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:31.049138Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 9e33c85d-b658-4372-9e29-212cb42c6ba9 · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 19

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:30.836691Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation af34757c-bef0-4203-8e21-81491eaf5ba0 · outbound

This paper cites Rinaldo, R.

Thermodynamics and Legendre Duality in Optimal Networks Rinaldo, R

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:30.607866Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.029117Z digest=sha256:ad548092d415e822ac86d41cb879f74e24aee6377aeaa791dbdd715b4c4c4f6e

Observation 57a38811-0b57-4f5b-a6dd-d50992981e4d · outbound

This paper cites Bandle, Dido’s problem and its impact on modern mathematics, Notices of the AMS 64 (9).

Thermodynamics and Legendre Duality in Optimal Networks Bandle, Dido’s problem and its impact on modern mathematics, Notices of the AMS 64 (9)

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:30.470890Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 98efe4aa-1045-4b98-91d5-fd484cf7b39a · outbound

This paper cites Hooshyar, S.

Thermodynamics and Legendre Duality in Optimal Networks Hooshyar, S

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:30.345312Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 269f0bb4-7408-460c-95bb-de1b34335bf5 · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 23

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:30.132449Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 49cff04c-5d14-4839-b166-8319817d2265 · outbound

This paper cites Facca, F.

Thermodynamics and Legendre Duality in Optimal Networks Facca, F

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:29.966668Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation fc119b5e-981d-4eb0-9510-2bde90366e80 · outbound

This paper cites Mrugala, J.

Thermodynamics and Legendre Duality in Optimal Networks Mrugala, J

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:29.792301Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 8517ec12-a603-4b54-8887-88187dbe596f · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 26

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:29.491703Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.057958Z digest=sha256:4b35b4f70cb56ad99df6162db0c6eda249e8679939df6aadacff3e038598802e

Observation 806a7299-caef-4a65-a90f-52c723fc93b3 · outbound

This paper cites Schnakenberg, Network theory of microscopic and macroscopic behavior of master equation systems, Reviews of Modern physics 48 (4) (1976) 571.

Thermodynamics and Legendre Duality in Optimal Networks Schnakenberg, Network theory of microscopic and macroscopic behavior of master equation systems, Reviews of Modern physics 48 (4) (1976) 571

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:29.262278Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation a72f3a37-5a94-4a64-9003-eb7bdad4149d · outbound

This paper cites Oster, C.

Thermodynamics and Legendre Duality in Optimal Networks Oster, C

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:29.090999Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation f3084f35-4a8f-4c52-a0e1-e97adb0823d5 · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 29

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:28.913765Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.070815Z digest=sha256:b1555377a9519a01458e7e56e9cfcb5e67efd713f952366eacb2acf3fe097943

Observation 08d11f20-9f43-4da1-ad9c-763c12919750 · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 30

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:28.706338Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.075205Z digest=sha256:29dc0f404332018a653b1fe943fd31dd33b599e269a37df1da4ba97f2b1a0a63

Observation 48cad465-364e-42a5-bd8f-52e3049dd0ad · outbound

This paper cites Onsager, S.

Thermodynamics and Legendre Duality in Optimal Networks Onsager, S

Reference 31

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:28.518735Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.079731Z digest=sha256:dde79dc942de3954506b34d9b681d37642e4d0681bca788f4e32ead3331c2cc0

Observation 3ceafdb9-7fc5-42e0-abc3-61ed0ebf4862 · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 32

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:28.297224Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.084827Z digest=sha256:1bb7f7aa816206ba256bd0a174b5c7ba34f96c06c07a15f6c7546ec34195f879

Observation 64b60d3a-6a2b-459e-8650-241000e97c65 · outbound

This paper cites Doi, Onsager’s variational principle in soft matter, Journal of Physics: Condensed Matter 23 (28) (2011) 284118.

Thermodynamics and Legendre Duality in Optimal Networks Doi, Onsager’s variational principle in soft matter, Journal of Physics: Condensed Matter 23 (28) (2011) 284118

Reference 33

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:28.121574Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.089777Z digest=sha256:3e67d926df5813994673a5594e52d2a9981bc61c8bc636b499c36ccb742ba5f5

Observation b0228743-28d2-4a5c-ac04-e844e9eb46df · outbound

This paper cites Bataille, D.

Thermodynamics and Legendre Duality in Optimal Networks Bataille, D

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:27.931097Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.094442Z digest=sha256:bb3045b0df06f9d4ab03cfcbd4a14dfe32157abf117f2d1cfa71eb50164edc3f

Observation b96c3a07-64ff-4cbd-95d2-1651b8c8f74e · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 35

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:27.723856Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.099469Z digest=sha256:1d56ad86af669606afdc68f93e52b016b8610f98338f6ea7be8a5dddf1d6cc49

Observation 5a0f92d8-7522-4992-a3a4-290b03c4520d · outbound

This paper cites Sewell, Complementary energy and catastrophes, in: Variational Methods in the Mechanics of Solids, Elsevier, 1980, pp.

Thermodynamics and Legendre Duality in Optimal Networks Sewell, Complementary energy and catastrophes, in: Variational Methods in the Mechanics of Solids, Elsevier, 1980, pp

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:27.509220Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.103871Z digest=sha256:b700a6c44d638b71aa99195cf6c14e0ef72df7666f8a3f0e202750da7659e08f

Observation c4bbc2ef-27f9-456d-a683-910328fc2600 · outbound

This paper cites Gyarmati, et al., Non-equilibrium thermodynamics, Vol.

Thermodynamics and Legendre Duality in Optimal Networks Gyarmati, et al., Non-equilibrium thermodynamics, Vol

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:27.301920Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.108691Z digest=sha256:ed8e2c2cc4d956db818218ebda9b5cd04d13aff1015e785f43cf1e2c76a9ab0e

Observation 0e017a57-89bd-469d-9aee-15b8344475fc · outbound

This paper cites Biolek, D.

Thermodynamics and Legendre Duality in Optimal Networks Biolek, D

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:27.082729Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.113035Z digest=sha256:056be9c479c0d3021f580b69c5724443b843f9b7ee94144ed2f92c7d2050af5f

Observation e4078341-e11c-4077-82b9-82fff929b02a · outbound

This paper cites Ziegler, An introduction to thermomechanics, Elsevier, 2012.

Thermodynamics and Legendre Duality in Optimal Networks Ziegler, An introduction to thermomechanics, Elsevier, 2012

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:26.900967Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.117427Z digest=sha256:05176366e8c243bf8215c4ed6bbc039590a713c311ab9a8137be4f65b2f08ba7

Observation 7c85d655-e8a5-403b-9cc3-c2ca9a73fa29 · outbound

This paper cites Gallavotti, Statistical mechanics: A short treatise, Springer Science & Business Media, 2013.

Thermodynamics and Legendre Duality in Optimal Networks Gallavotti, Statistical mechanics: A short treatise, Springer Science & Business Media, 2013

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:26.708417Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.121810Z digest=sha256:040e225efe0dedd60623efb932516089c9ccd0efe4b1330e2938ec5656c5c18b

Observation 430b49dc-171b-4840-b91a-6054721dc72e · outbound

This paper cites ˇZupanovi´ c, D.

Thermodynamics and Legendre Duality in Optimal Networks ˇZupanovi´ c, D

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:26.459542Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.126049Z digest=sha256:dafbfb12fa06ef7472de100b693275266f2e9d06894d83728aae7e118272b94b

Observation 56e76cdd-8d5e-4091-8f5d-234b5bb3b954 · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 42

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:26.204696Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.130308Z digest=sha256:a621f82f4a7618d2707d0ffc59b221eb932ef36182965b481fa507ad18a662c3

Observation 8a14c1b8-a2f9-4fca-acdd-1b21703d49fd · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 43

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:25.979268Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.135222Z digest=sha256:9ed96729b202f79169e4d77a71b2e087e515ef7192b7ebe2d93b7c6b64cf62e1

Observation fd6e830b-285a-4d15-88eb-7de1eef2b467 · outbound

This paper cites Porporato, S.

Thermodynamics and Legendre Duality in Optimal Networks Porporato, S

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:25.781269Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.140079Z digest=sha256:f67137871fef603fc095aa11eb98d567bc88d32794d3a26e24988cab451a2cfb

Observation 30299500-509f-4caf-aa22-91ce3512e3bc · outbound

This paper cites Schl¨ ogl, Thermodynamic metric and stochastic measures, Zeitschrift f¨ ur Physik B Condensed Matter 59 (4) (1985) 449–454.

Thermodynamics and Legendre Duality in Optimal Networks Schl¨ ogl, Thermodynamic metric and stochastic measures, Zeitschrift f¨ ur Physik B Condensed Matter 59 (4) (1985) 449–454

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:25.588584Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.144813Z digest=sha256:353e08c372a9cc22068a6dbe4bc04477eff96ed4c01a1710104ff3b85a3895b5

Observation b06a446c-fdd5-42b1-add3-1895bbe63e6a · outbound

This paper cites Mrugala, J.

Thermodynamics and Legendre Duality in Optimal Networks Mrugala, J

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:25.336653Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.149261Z digest=sha256:89bff40381c45cb829cd4b9ef2b4a61457b83e3b4e93fcffcf640d986319cc95

Observation 092520c9-0ca6-4cce-a728-1f0a214821cb · outbound

This paper cites Brody, N.

Thermodynamics and Legendre Duality in Optimal Networks Brody, N

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:25.110479Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.154078Z digest=sha256:08f0336612d2d720fa32deeba4925c10a42fac9ebe24ef5e7820a9f2f03207aa

Observation 7590a5c9-3d7c-44d2-ba8d-8947d98b2944 · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 48

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:24.879402Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.158804Z digest=sha256:2ae29ad5e9c1508bc26f4d2fa64dd0ad75822ed3c93ce8e4cceacf1d101c69fc

Observation b9074e50-eb92-4f5b-9f5c-32c0ac788904 · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 49

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:24.760150Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.163390Z digest=sha256:01c08f9b969cc4ead4bbc9b05139e70f790a2c0747f8ddff06922cf531ec9558

Observation 22e66c23-6678-4062-a0e8-4b8725b11eb3 · outbound

This paper cites Ercan, On kirchhoff’s equations and variational approaches to electrical network analysis, American Journal of Physics 84 (3) (2016) 231–233.

Thermodynamics and Legendre Duality in Optimal Networks Ercan, On kirchhoff’s equations and variational approaches to electrical network analysis, American Journal of Physics 84 (3) (2016) 231–233

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:24.592563Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.167842Z digest=sha256:a8b0fb18adea14caa76a5f0b5e04ad6f437b17afdd84802aef111121c3144607

Observation 75d696d1-abe1-420d-b1bb-3b4fb409ee1b · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 51

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:24.417598Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.172481Z digest=sha256:ef2d5e6926519a50d9405f9cf6028632803cab089d4ac4863762a7cca7b67be9

Observation 5350e943-4ae1-4917-bc0d-e9f0dbec3098 · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 52

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:24.254134Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.176876Z digest=sha256:c4ab966edf1861f9283151968f5da4f6d33a86ff23e25c5200789975554cad20

Observation e90ecb08-25e2-44fd-9d1c-ef98f5c51b27 · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 53

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:24.054150Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.181606Z digest=sha256:2fdce41c1650301e01c31544702f3e0357b4a6e14cfe5047cdb724e2a1924829

Observation 9d4b41be-2d01-4f95-81a8-ffb2c56b3b7f · outbound

This paper cites Kawazura, Z.

Thermodynamics and Legendre Duality in Optimal Networks Kawazura, Z

Reference 54

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:23.892350Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.185987Z digest=sha256:89a9aea7946bcfc84758fafe23dd2eeff46d9dcc4a06fb97ef3fa5b13bf3c23f

Observation 0d25b65e-077f-4e0e-a033-6828adb2e852 · outbound

This paper cites Martyushev, Some interesting consequences of the maximum entropy production principle, Journal of Experimental and Theoretical Physics 104 (2007) 651–654.

Thermodynamics and Legendre Duality in Optimal Networks Martyushev, Some interesting consequences of the maximum entropy production principle, Journal of Experimental and Theoretical Physics 104 (2007) 651–654

Reference 55

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:23.642601Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.190487Z digest=sha256:db655d225b91c7ca9170e79b97e3036de0aa4558b41bf369dbc1ab3021b23e6b

Observation 4f8a2d9a-fbfd-4b77-a843-c3631bb48c72 · outbound

This paper cites Hill, Entropy production as the selection rule between different growth morphologies, Nature 348 (1990) 426–428.

Thermodynamics and Legendre Duality in Optimal Networks Hill, Entropy production as the selection rule between different growth morphologies, Nature 348 (1990) 426–428

Reference 56

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:23.358734Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.195131Z digest=sha256:f4fd49dd4695333ad0e999e85509d07e917b3126b394e0ccc3b7011e269a6e47

Observation e76c3b84-6bb4-4186-8ce8-4c93ff9cc540 · outbound

This paper cites Ozawa, S.

Thermodynamics and Legendre Duality in Optimal Networks Ozawa, S

Reference 57

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:23.142761Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.199386Z digest=sha256:a67202273bb807611489ab4a4c2ac494ea470d920e935e33eb93cfc37396bb28

Observation 194763ac-27ff-4c24-ac0d-04e81a939ec3 · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 58

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:22.918614Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.204078Z digest=sha256:80856624368807ab20ff3c4436ce45ad11bd1919003d115ef14794c6f3447453

Observation 0b04e7e7-d5ea-48fb-a05e-e839e3a6067f · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 59

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:22.758594Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.208743Z digest=sha256:6a0ea332b665594cb55df2b66d58e92eae267b855bb54e627bbd22c40cac198f

Observation d0d156cc-d1eb-4519-9fc4-c98fca579516 · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 60

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:22.553892Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.213392Z digest=sha256:4327b040c25c3c31ccacac697a3fff292158431239a0b91d39dfc3e618280412

Observation e19a255b-ab4e-40c6-86d0-92f34b4dd316 · outbound

This paper cites Yoshida, S.

Thermodynamics and Legendre Duality in Optimal Networks Yoshida, S

Reference 61

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:22.392772Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.218367Z digest=sha256:c44c85f418f89bcb5e78e2ec69edf41efd8f9af4006e05ba5e9f524ceba226ef

Observation f8fa01c8-198a-4c3b-9c02-e6b19737102f · outbound

This paper cites Yoshida, Y.

Thermodynamics and Legendre Duality in Optimal Networks Yoshida, Y

Reference 62

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:22.218248Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.223616Z digest=sha256:9969a960ed3aaee980f8a9cdbd6f546b5e183a589543d49120f109c254891cd5

Observation a57dc63a-43e2-45e1-ba77-b4158bcb0ce1 · outbound

This paper cites Kawazura, Z.

Thermodynamics and Legendre Duality in Optimal Networks Kawazura, Z

Reference 63

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:22.105747Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.228557Z digest=sha256:2993537c7553fc41e0494112e65201ea71408d220ac621d58ccdbf16d46bc2b9

Observation 1f91d8a3-f994-47b6-9fd1-7aa647d2a717 · outbound

This paper cites Glansdorff, I.

Thermodynamics and Legendre Duality in Optimal Networks Glansdorff, I

Reference 64

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:21.982485Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.233777Z digest=sha256:49decd994f6b0d23d6eb81567ef79de29d2c41e146870ca4e1e18beda75d347f

Observation f69d556d-9383-4d1d-b98b-b097c46546a1 · outbound

This paper cites Landauer, Stability and entropy production in electrical circuits, Journal of Statistical Physics 13 (1975) 1–16.

Thermodynamics and Legendre Duality in Optimal Networks Landauer, Stability and entropy production in electrical circuits, Journal of Statistical Physics 13 (1975) 1–16

Reference 65

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:21.845645Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.238383Z digest=sha256:55c77cbbcb14611bcf68e6742372016cc741b9fb74e9bd9df38cdf8566e5749a

Observation 6385e238-4510-422c-800d-4474f07b6aa4 · outbound

This paper cites Bodineau, B.

Thermodynamics and Legendre Duality in Optimal Networks Bodineau, B

Reference 66

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:21.740057Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.242842Z digest=sha256:9a3ce989bc0391f3e67c0d99e3c4e57a8554375e07de4a85d4143bbcc773a7f4

Observation 7ec3b028-4229-4bf6-a242-db0e702724ca · outbound

This paper cites Derrida, J.

Thermodynamics and Legendre Duality in Optimal Networks Derrida, J

Reference 67

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:21.676082Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.247409Z digest=sha256:712c6a057a528b7c1c855bce02af6c08e369c1e7069a1c6a1c57d506cb272429

Observation 2caff210-ba5e-4e17-b44c-6fd61ebcbb73 · outbound

This paper cites Bertini, A.

Thermodynamics and Legendre Duality in Optimal Networks Bertini, A

Reference 68

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:21.615529Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.251904Z digest=sha256:d23fd36bd2ef8f5780bdbb556a39ee32e8f58ff924064a42499bcc1f9e8affe6

Observation 68ec7cd6-0360-4b24-bd4a-b61eb5c71e31 · outbound

This paper cites Torquato, Optimal design of heterogeneous materials, Annual review of materials research 40 (1) (2010) 101–129.

Thermodynamics and Legendre Duality in Optimal Networks Torquato, Optimal design of heterogeneous materials, Annual review of materials research 40 (1) (2010) 101–129

Reference 69

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:21.580139Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.256917Z digest=sha256:e0254b5d8228786492f5065ff3deafb5ad87696cf4401625285b5338b447eb44

Observation 574d4ea4-09b1-42c3-92a3-257bfbf7ead4 · outbound

This paper cites Waldherr, D.

Thermodynamics and Legendre Duality in Optimal Networks Waldherr, D

Reference 70

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:21.557838Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.261139Z digest=sha256:dd622338a87e6277373569178bb688c01e6fbc8d8a8576fe859e4be2fc25e738

Observation 988a15a6-96e3-499b-bb44-50210b31ccff · outbound

This paper cites Franklin, S.

Thermodynamics and Legendre Duality in Optimal Networks Franklin, S

Reference 71

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:21.533585Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.265258Z digest=sha256:ab7a5efadcad183c7fd744d63564a6239e2ddfa6279a7059046f25d87fad24a2

Observation 973005cd-66be-4c31-95b3-7cac2cbfbf12 · outbound

This paper cites Calabrese, B.

Thermodynamics and Legendre Duality in Optimal Networks Calabrese, B

Reference 72

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:21.507547Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.269652Z digest=sha256:875a97af74496d78d5d3e5dd20e895dfb61ef44e43608829e142d3c26b0a0f38

Observation 26caf9fe-689f-475d-936f-54dff3aff9ce · outbound

This paper cites Witelski, M.

Thermodynamics and Legendre Duality in Optimal Networks Witelski, M

Reference 73

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:21.481941Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.274297Z digest=sha256:e68d9b3976ce24b39d3e953717e033bfbc5b8cf254f289845d69271d9d5b3274

Observation 7550b0c6-3660-47ab-93da-84cb728d5346 · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 74

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:21.460848Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.278618Z digest=sha256:4a36b132d98e143379a4f896073994e16db6c8047e311b6bd1eb1d9fbfb26e9b

Observation f366eb38-1e2a-4965-9342-6de5ed467b35 · outbound

This paper cites Giaccone, S.

Thermodynamics and Legendre Duality in Optimal Networks Giaccone, S

Reference 75

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:21.435638Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.283029Z digest=sha256:84170f06ead80e8463d7b3c10e9682567946f67eceaa4efd379c762a7cee5463

Observation 73b80792-d2a1-48af-b70f-70e962a15f23 · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 76

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:21.414149Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.287674Z digest=sha256:3c17a2304f1ce912ad4c795b644dd56a7e2c18da3fdc97da6c6794e37ef7dfdb

Observation 25bc5904-daa7-42ff-b4be-50250aa95aa1 · outbound

This paper cites Burger, J.

Thermodynamics and Legendre Duality in Optimal Networks Burger, J

Reference 77

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:21.394832Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.292634Z digest=sha256:5c50873ce3e7e7be3a1c11d2f097ace30fc14bb7140c99df7e4757ecbf0188da

Observation 68c65f00-4840-460c-9726-0e8fb01527f6 · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 78

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:21.379227Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.297764Z digest=sha256:bf46db4c6309fee61662ebc445db2d8f625bd4177fe2a680be51a38bfb2a9bdd

Observation 9f4750d6-7403-4824-b1f2-fa4163915783 · outbound

This paper cites Bonetti, M.

Thermodynamics and Legendre Duality in Optimal Networks Bonetti, M

Reference 79

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:21.362961Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.302767Z digest=sha256:75cf18fdde62a3b2b5f799884bde8c5eed31abe67defcd9ca1132fadd6c719da

Observation 104fbc02-6dab-41a2-b8ca-e95f914c2665 · outbound

This paper cites Maritan, F.

Thermodynamics and Legendre Duality in Optimal Networks Maritan, F

Reference 80

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:21.346917Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T05:33:21.307241Z digest=sha256:53b4ed22f1d2110932353a0906aafcd19d52d3025ce640c13c2f374243cd520b

Pith citing papers

No inbound Pith citation observations are available.