{"as_of":"2026-08-13T19:20:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:76f6fd8db30034b1e8408adfa7f95b028d90127e94b7bb711a7ca6fcfa1fa346","coverage":[{"denominator":80,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":80,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T05:33:21.307241Z","state":"measured"},{"denominator":80,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":80,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-13T06:32:02.005865+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2506.15727/citation-record","integrity":"/paper/2506.15727/integrity","json":"/paper/2506.15727/citation-record.json","paper":"/paper/2506.15727"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:34.527109Z","title":null,"venue":null,"work_id":"2969871d-8f35-4558-a6ad-5dce6a60af0a","year":1953},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:20.931931Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:0a3a7bcc109da38dc882b378b71ca6572151ab78eef238063424be2ab09177fc","observation_id":"a065bdeb-a4cb-42e5-a077-23870794e641","resolution":{"observed_at":"2026-08-07T05:33:34.671565Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:34.262796Z","title":null,"venue":null,"work_id":"e0c0f1a6-8efa-4f8e-828b-d631d1bc3f53","year":2022},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:20.937923Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:5718786f1b772f0e2e83eb5be9be61ce7fc849ce0c9e252586dbb7e8fee512b0","observation_id":"66e714a7-4c9d-49b1-b0a0-329161b843af","resolution":{"observed_at":"2026-08-07T05:33:34.361239Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:33.966070Z","title":null,"venue":null,"work_id":"d6edb674-db2a-4dbc-b805-cf5c78826994","year":1987},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:20.943208Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:e94984d63496e04b668df662e5bf3b7bfe2acceefc35932fe5974d495ac05252","observation_id":"2441017f-bb57-4ace-a239-814b219070fc","resolution":{"observed_at":"2026-08-07T05:33:34.138856Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:33.642047Z","title":"Rodriguez-Iturbe, A","venue":null,"work_id":"22327bee-6a20-4f95-8341-8149ffe9cb92","year":1997},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:20.948172Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:4e59bbcdbdb7745b8890913491af58e81b7bac404400b99b845464a4cbd69f4e","observation_id":"ddfbf355-55c3-4eef-a2b5-ea234c37319c","resolution":{"observed_at":"2026-08-07T05:33:33.795775Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:33.408524Z","title":"Santambrogio, Optimal transport for applied mathematicians, Birk¨ auser, NY 55 (58-63) (2015) 94","venue":null,"work_id":"721f154a-bbd9-4857-9b92-3900cea9c35d","year":2015},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:20.953603Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:3e7cb94ff8949ecd70bc2a589fedbbb2113db5ac201ca1a3e8ef3775d4894437","observation_id":"f185aea9-b652-4813-8816-d45dfaab8b1d","resolution":{"observed_at":"2026-08-07T05:33:33.557074Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:33.164032Z","title":"Van Baak, Variational alternatives to kirchhoff’s loop theorem in dc circuits, American Journal of Physics 67 (1) (1999) 36–44","venue":null,"work_id":"dee0337d-755e-41ad-895d-0f065c63b075","year":1999},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:20.958465Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:345f8c3e7a547896268faf9dd02df503997b1cdeb3c4f60ef703dfb009cbd1e6","observation_id":"871c065b-6baa-430c-b3ae-c3072f4bc94b","resolution":{"observed_at":"2026-08-07T05:33:33.263012Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:33.009238Z","title":null,"venue":null,"work_id":"13fa7fde-cae2-4914-99c2-325d9a754779","year":2009},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:20.963790Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:cedf8a00a3b3b6ded2ac14a51fd2dd1ea7b89aaab604343cfac340c502eb0b56","observation_id":"e2d67628-56a3-4d73-8a53-15d61916df8c","resolution":{"observed_at":"2026-08-07T05:33:33.094946Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:32.868529Z","title":null,"venue":null,"work_id":"41353bee-24cb-4c0c-bc4d-f26b7373d60b","year":1998},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:20.968823Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:978a1f8b512bd2263a253b0b0238a1a3e124492b3f9dab0236105f232a739290","observation_id":"07941dc3-f4a7-49da-910a-176a34d88b5b","resolution":{"observed_at":"2026-08-07T05:33:32.932284Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:32.700843Z","title":"Barbera, On the principle of minimal entropy production for navier-stokes-fourier fluids, Continuum Mechanics and Thermodynamics 11 (5) (1999) 327–330","venue":null,"work_id":"c9867440-7150-4eda-9ce1-074997fb8f96","year":1999},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:20.973825Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:38cf617321a121f54bba5d6b0074d436309d0463e5f1f45ee177e5a22b4de744","observation_id":"cc9e931d-dd99-4379-85ec-07371df9640f","resolution":{"observed_at":"2026-08-07T05:33:32.759519Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:32.519343Z","title":"Kondepudi, I","venue":null,"work_id":"051fbf1c-3ac5-4afc-8f53-031a23365749","year":2014},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:20.978555Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:13ad0242e65efb8a09494c9fb6bae19bf7bf71215a6c3cbc93cf85707f7a8edd","observation_id":"96a13060-834e-4998-a5a0-afa7543327e3","resolution":{"observed_at":"2026-08-07T05:33:32.625253Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:32.389830Z","title":"Martyushev, A","venue":null,"work_id":"da6a289e-9600-4260-b462-0428ba423168","year":2006},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:20.983547Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:ad9b95b0d9c5f96ea2c9155e061cfbc7e147435ff9b4139db279e40508b34172","observation_id":"8a6e7795-190b-4059-b45b-6f5e4a08f339","resolution":{"observed_at":"2026-08-07T05:33:32.437798Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:32.163514Z","title":"Millar, Cxvi","venue":null,"work_id":"dbd29ba0-5119-45cd-8330-88df1b71b21d","year":1951},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:20.988944Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:3b8d828ea19bd092685ea645c8480740320be2e6b90855264a9aa16ccaf75087","observation_id":"4856ca3f-f057-422e-8505-6312cde9e12e","resolution":{"observed_at":"2026-08-07T05:33:32.274682Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:32.023618Z","title":"Cherry, Non-linear circuit theory by the methods of classical dynamics, in: Recent Developments in Network Theory, Elsevier, 1963, pp","venue":null,"work_id":"52701073-53ab-411c-894c-e95cba0b60f1","year":1963},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:20.994288Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:51eefa0fe497b72beeaa904f9cdd4359e531ecc45f881c252e6bcdf43b79cadb","observation_id":"f169b4f6-f3e6-4c86-b9b3-d3521fa351bd","resolution":{"observed_at":"2026-08-07T05:33:32.085372Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:31.765083Z","title":"Verh´ as, Gyarmati’s variational principle of dissipative processes, Entropy 16 (4) (2014) 2362–2383","venue":null,"work_id":"5db4edda-8f95-4c31-b92b-3ab6f2511ac3","year":2014},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:20.999970Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:e5e7e279f8aae89a8e19f54e081088d8d66db3736f68e6d65afb8fcc58f9ac0d","observation_id":"6dcb97e7-6e10-4e72-ad49-22e328c03e74","resolution":{"observed_at":"2026-08-07T05:33:31.887390Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:31.601248Z","title":null,"venue":null,"work_id":"de9d62ff-369a-4312-b4b0-52ae93340e86","year":1926},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.004952Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:18ce8aeeaf6ab7935edf15ae5147885f50dd3cf05e6fb8c40f30d4050f6bf775","observation_id":"98ee0a3b-686c-4cfc-9845-d8e1780c45e7","resolution":{"observed_at":"2026-08-07T05:33:31.658043Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:31.415841Z","title":null,"venue":null,"work_id":"ab3ac1ef-7672-4ce8-a1d3-1e03dfb05742","year":1999},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.009962Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:27c71c9cc9ecd3a6f108fba65316f79a285fadc763738de6ec9cdc9ba27a2ee9","observation_id":"fa2828a4-92a0-4eac-ae42-492af6e3e2a0","resolution":{"observed_at":"2026-08-07T05:33:31.481481Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:31.135502Z","title":"Bejan, S","venue":null,"work_id":"217ca90d-ef10-4a76-b5c2-303865f254f4","year":2004},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.014875Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:a7f9a46524d263f2b510fa914429be727184eac320883397fce3369593a2620b","observation_id":"37106f81-5467-4fc3-89ff-666da53c3f64","resolution":{"observed_at":"2026-08-07T05:33:31.263085Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:30.962594Z","title":null,"venue":null,"work_id":"c8c35c86-fb8f-4199-8b70-8f1b7f099fa0","year":2007},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.019363Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:43a4837dff6ee89960f9d69f0fa6a421f6b3bd60f2f29852090791b0aac63aeb","observation_id":"0d5c1ce7-94ec-498f-98e8-3386b5713e80","resolution":{"observed_at":"2026-08-07T05:33:31.049138Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:30.691926Z","title":null,"venue":null,"work_id":"43d3968e-e543-4579-8619-70dd0970f72b","year":2007},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.024393Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:e7e9799c5c1bf3e65fab9107694e8d785d110cb9a2efa7c0ba6c92b654337791","observation_id":"9e33c85d-b658-4372-9e29-212cb42c6ba9","resolution":{"observed_at":"2026-08-07T05:33:30.836691Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:30.558000Z","title":"Rinaldo, R","venue":null,"work_id":"55eba264-383d-4fe5-abd7-567cf6ae4904","year":2014},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.029117Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:b889440efb8284c41a1d55878dc35b1edeb6f26283e20820eb485b465403c510","observation_id":"af34757c-bef0-4203-8e21-81491eaf5ba0","resolution":{"observed_at":"2026-08-07T05:33:30.607866Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:30.416030Z","title":"Bandle, Dido’s problem and its impact on modern mathematics, Notices of the AMS 64 (9)","venue":null,"work_id":"a839592f-d411-4efd-b494-f5875855f125","year":null},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.034175Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:d053724843878914d9a7d00964f9b0b910ea0d5fd479a7a9c03e11d8d56338d3","observation_id":"57a38811-0b57-4f5b-a6dd-d50992981e4d","resolution":{"observed_at":"2026-08-07T05:33:30.470890Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:30.214529Z","title":"Hooshyar, S","venue":null,"work_id":"d2b0a049-e659-42a4-b1bd-f6e0e2946de3","year":2020},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.039302Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:9e2e0d516d4307c509f80ec5378001397cbf79c5ee3f7aea07ff02a3e7a4085d","observation_id":"98efe4aa-1045-4b98-91d5-fd484cf7b39a","resolution":{"observed_at":"2026-08-07T05:33:30.345312Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:30.054754Z","title":null,"venue":null,"work_id":"34ff4986-2b6e-46a8-a828-590fa07ab0ed","year":2023},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.044301Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:b5e32aeb145abeb1b473dd4dbecf9927decf25401d0d3e191265d08250f470db","observation_id":"269f0bb4-7408-460c-95bb-de1b34335bf5","resolution":{"observed_at":"2026-08-07T05:33:30.132449Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:29.915294Z","title":"Facca, F","venue":null,"work_id":"02e62211-cea1-4533-b4c1-cbdc414102db","year":2018},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.048772Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:ad03261c81fbf174b3b77f7ece3adc24433a7e321d44bb1d219da977dfc59c97","observation_id":"49cff04c-5d14-4839-b166-8319817d2265","resolution":{"observed_at":"2026-08-07T05:33:29.966668Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:29.638381Z","title":"Mrugala, J","venue":null,"work_id":"8951ac32-80b2-40fc-980f-c0bd31b5357b","year":1991},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.053599Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:f2be2d59d9d34a531fd777ec84124be20525d981ad7a5d806fff4b0987e6bd0e","observation_id":"fc119b5e-981d-4eb0-9510-2bde90366e80","resolution":{"observed_at":"2026-08-07T05:33:29.792301Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:29.403194Z","title":null,"venue":null,"work_id":"ee3441d9-e336-4386-95cb-2f6816795b30","year":2006},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.057958Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:3f332653328136d29b3d26e08fbd80d8918de912266536904aafd647771ae872","observation_id":"8517ec12-a603-4b54-8887-88187dbe596f","resolution":{"observed_at":"2026-08-07T05:33:29.491703Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:29.200879Z","title":"Schnakenberg, Network theory of microscopic and macroscopic behavior of master equation systems, Reviews of Modern physics 48 (4) (1976) 571","venue":null,"work_id":"a84c2bda-797d-45ab-8c09-adfda1a952dd","year":1976},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.062233Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:eb0b9db5f1ed20ea8e0e139a417e5e80bec3fec60634c015935421719cd2ad33","observation_id":"806a7299-caef-4a65-a90f-52c723fc93b3","resolution":{"observed_at":"2026-08-07T05:33:29.262278Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:28.990157Z","title":"Oster, C","venue":null,"work_id":"bbcd33bc-decc-4cac-8e31-564bc1aed8bd","year":1971},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.066399Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:09bd25daf2acd1283f39a876609e456ec93abdf8749f01be96cde66e5f897409","observation_id":"a72f3a37-5a94-4a64-9003-eb7bdad4149d","resolution":{"observed_at":"2026-08-07T05:33:29.090999Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:28.792927Z","title":null,"venue":null,"work_id":"73d6c7c6-e9a4-4b30-ae56-78892b9599a9","year":2006},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.070815Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:ec24026c1287d1a787b941ce94a023fedb1533a5ea05e68be2f4f4238fd18f42","observation_id":"f3084f35-4a8f-4c52-a0e1-e97adb0823d5","resolution":{"observed_at":"2026-08-07T05:33:28.913765Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:28.628557Z","title":null,"venue":null,"work_id":"1538ca03-e424-452b-9262-a9fd3c32cc63","year":1980},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.075205Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:988d3ad07479ded749041a30fdb3faac45f62cf773e9627906a5cb42206fec51","observation_id":"08d11f20-9f43-4da1-ad9c-763c12919750","resolution":{"observed_at":"2026-08-07T05:33:28.706338Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:28.417345Z","title":"Onsager, S","venue":null,"work_id":"4d517b35-30ec-4ffe-b306-396f1475acd6","year":1953},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.079731Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:0e268d51bae09ee449c03070551d2150d4066d195cc51ec75af8032f8289fa2a","observation_id":"48cad465-364e-42a5-bd8f-52e3049dd0ad","resolution":{"observed_at":"2026-08-07T05:33:28.518735Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:28.209754Z","title":null,"venue":null,"work_id":"70c082b2-6139-4724-8717-4ee896044b91","year":null},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.084827Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:593cedc474929f5fe0ce340948bfca250b1ca6da94803e8964a7b52d2ccdf1bf","observation_id":"3ceafdb9-7fc5-42e0-abc3-61ed0ebf4862","resolution":{"observed_at":"2026-08-07T05:33:28.297224Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:28.026774Z","title":"Doi, Onsager’s variational principle in soft matter, Journal of Physics: Condensed Matter 23 (28) (2011) 284118","venue":null,"work_id":"5f42baed-e9f6-40ba-868d-e6b5d25b856e","year":2011},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.089777Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:4b8b618e2cb7c755c871e7665f7faffdfaf7aa6d3fcb31622df3e3280153f61f","observation_id":"64b60d3a-6a2b-459e-8650-241000e97c65","resolution":{"observed_at":"2026-08-07T05:33:28.121574Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:27.822304Z","title":"Bataille, D","venue":null,"work_id":"5e7036f0-03f6-4db7-8af1-7533d5fcf3ef","year":1979},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.094442Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:7e14a7f18b6822dac1b03eb79bebcf43f492823019f59f5efb74223281219488","observation_id":"b0228743-28d2-4a5c-ac04-e844e9eb46df","resolution":{"observed_at":"2026-08-07T05:33:27.931097Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:27.628617Z","title":null,"venue":null,"work_id":"15befed4-2f47-4783-8453-bb3f86fc4a9e","year":1953},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.099469Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:dfac881233646f13e57937c8c7eec209f49d2b991f331a84c49cbf7b009a1b7d","observation_id":"b96c3a07-64ff-4cbd-95d2-1651b8c8f74e","resolution":{"observed_at":"2026-08-07T05:33:27.723856Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:27.406091Z","title":"Sewell, Complementary energy and catastrophes, in: Variational Methods in the Mechanics of Solids, Elsevier, 1980, pp","venue":null,"work_id":"13d4e82f-c119-4066-a3d7-9b8a9a04bfa0","year":1980},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.103871Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:2af0f7dc7139a935ee58697902af48930e6d283d877da23b42c30b49f82645c0","observation_id":"5a0f92d8-7522-4992-a3a4-290b03c4520d","resolution":{"observed_at":"2026-08-07T05:33:27.509220Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:27.215232Z","title":"Gyarmati, et al., Non-equilibrium thermodynamics, Vol","venue":null,"work_id":"6cbb6b45-b77f-4ad0-b8d6-32be517c7f0f","year":1970},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.108691Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:a74ac066953e13ce3fd8437678585d2f8d930f29b3aeff984f82a41dca64e5f5","observation_id":"c4bbc2ef-27f9-456d-a683-910328fc2600","resolution":{"observed_at":"2026-08-07T05:33:27.301920Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:27.022864Z","title":"Biolek, D","venue":null,"work_id":"605359b4-09a2-40bc-bd64-6e98032ff9b8","year":2014},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.113035Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:506ada0c2bc5c565cd5cc7ca824cc1e93f5dc8e5f56c1368525a6450fe1be6cd","observation_id":"0e017a57-89bd-469d-9aee-15b8344475fc","resolution":{"observed_at":"2026-08-07T05:33:27.082729Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:26.800774Z","title":"Ziegler, An introduction to thermomechanics, Elsevier, 2012","venue":null,"work_id":"8f0d25f8-65bb-49fa-894f-2cc7e7acc704","year":2012},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.117427Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:3093c06577e72cba46a167d635114a6a6a864f1437c0f78cc4becdda488d1e1c","observation_id":"e4078341-e11c-4077-82b9-82fff929b02a","resolution":{"observed_at":"2026-08-07T05:33:26.900967Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:26.595277Z","title":"Gallavotti, Statistical mechanics: A short treatise, Springer Science & Business Media, 2013","venue":null,"work_id":"1fa8640a-c8f5-42cd-a09b-8f6955dc5d4b","year":2013},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.121810Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:7e6f9caf7d10397f0f6472e2f5de4d1339fd84c801b90faf0972a1e61997f46d","observation_id":"7c85d655-e8a5-403b-9cc3-c2ca9a73fa29","resolution":{"observed_at":"2026-08-07T05:33:26.708417Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:26.347347Z","title":"ˇZupanovi´ c, D","venue":null,"work_id":"260e64f6-7536-4446-9da0-f9d634afcf0c","year":2004},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.126049Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:18c1b6d797de1fb39c05c079dee6e73d30670ed0e2cf41e4270c873248d3ad6e","observation_id":"430b49dc-171b-4840-b91a-6054721dc72e","resolution":{"observed_at":"2026-08-07T05:33:26.459542Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:26.088808Z","title":null,"venue":null,"work_id":"88b325fa-1968-4ebd-9021-b20f22e3d397","year":1972},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.130308Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:bdb0a0d3808955227c43abb2906f16adcd1248412b5956be79754ee02bab48f4","observation_id":"56e76cdd-8d5e-4091-8f5d-234b5bb3b954","resolution":{"observed_at":"2026-08-07T05:33:26.204696Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:25.853427Z","title":null,"venue":null,"work_id":"caed1189-b816-47bf-9494-2b797056554a","year":2013},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.135222Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:aa580ea6aa8b78ab0f60650b87e02cd326c0fb8c6f2151629387ddb5cca0970a","observation_id":"8a14c1b8-a2f9-4fca-acdd-1b21703d49fd","resolution":{"observed_at":"2026-08-07T05:33:25.979268Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:25.680053Z","title":"Porporato, S","venue":null,"work_id":"3fc2a5bc-bc8c-4099-895c-7e1bd671fc14","year":2024},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.140079Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:cec6b2ff01be99e71e8dc626a5f81861690310b4c88ca83f0cba3e7bcded2d92","observation_id":"fd6e830b-285a-4d15-88eb-7de1eef2b467","resolution":{"observed_at":"2026-08-07T05:33:25.781269Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:25.450505Z","title":"Schl¨ ogl, Thermodynamic metric and stochastic measures, Zeitschrift f¨ ur Physik B Condensed Matter 59 (4) (1985) 449–454","venue":null,"work_id":"1f638540-57e1-40de-b79c-ae5538177cef","year":1985},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.144813Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:a0946656c7c896c9d973842037fe0447f7595e09d42c0a77802f1cde3b71520f","observation_id":"30299500-509f-4caf-aa22-91ce3512e3bc","resolution":{"observed_at":"2026-08-07T05:33:25.588584Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:25.237690Z","title":"Mrugala, J","venue":null,"work_id":"499be766-7655-4d1f-aeb1-322f68b82f1d","year":1990},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.149261Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:c65eaf5396233caf21fdaffa94b94c01965baedd376375b71f3e9a3f1a2e2cc9","observation_id":"b06a446c-fdd5-42b1-add3-1895bbe63e6a","resolution":{"observed_at":"2026-08-07T05:33:25.336653Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:25.038561Z","title":"Brody, N","venue":null,"work_id":"eee70e61-acce-4991-bcdf-29e70d3e9a96","year":1995},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.154078Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:4e5fab218d7c7129770157b4dc9e99057bab12de1dfa3cc894c9bbc51c76d030","observation_id":"092520c9-0ca6-4cce-a728-1f0a214821cb","resolution":{"observed_at":"2026-08-07T05:33:25.110479Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:24.843392Z","title":null,"venue":null,"work_id":"1d0937e3-17a1-42f5-8d5f-c78906c0ca92","year":2007},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.158804Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:0531c453d9d3608a8b61da9c6590761c385f6e6ce78f145932d1034cc8a63416","observation_id":"7590a5c9-3d7c-44d2-ba8d-8947d98b2944","resolution":{"observed_at":"2026-08-07T05:33:24.879402Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:24.673176Z","title":null,"venue":null,"work_id":"a331edb7-8d50-47a0-8fc5-9d9cade0b548","year":2010},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.163390Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:2727f4896da85b09fd4fa2f33075ca1886de326d0e97ede24aae1760f4355665","observation_id":"b9074e50-eb92-4f5b-9f5c-32c0ac788904","resolution":{"observed_at":"2026-08-07T05:33:24.760150Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:24.501700Z","title":"Ercan, On kirchhoff’s equations and variational approaches to electrical network analysis, American Journal of Physics 84 (3) (2016) 231–233","venue":null,"work_id":"3b541c17-e943-49ef-9c7e-ad5f07b1fc96","year":2016},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.167842Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:3f0d023ec57cc4ba956ede3ce466677fe5ac72ebfe6eaa5a26569b27435ab122","observation_id":"22e66c23-6678-4062-a0e8-4b8725b11eb3","resolution":{"observed_at":"2026-08-07T05:33:24.592563Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:24.332453Z","title":null,"venue":null,"work_id":"2b94ddfb-d6e4-4fa8-995f-6426b79118e9","year":1951},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.172481Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:ff529c9debfda1564917e82ff5095a0befdc68c7670fb7eaa600299f3c59de74","observation_id":"75d696d1-abe1-420d-b1bb-3b4fb409ee1b","resolution":{"observed_at":"2026-08-07T05:33:24.417598Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:24.145621Z","title":null,"venue":null,"work_id":"382bdf0a-dbfe-450b-801d-5c717d0ce9a9","year":2010},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.176876Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:51ddc02e55d54bac7d772514597e6b687f34618d0e12c83a3c0cdf11138312c3","observation_id":"5350e943-4ae1-4917-bc0d-e9f0dbec3098","resolution":{"observed_at":"2026-08-07T05:33:24.254134Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:23.973163Z","title":null,"venue":null,"work_id":"056de713-7959-45c1-9660-04e3a3f52ff2","year":2019},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.181606Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:245a3b6f690cb470fabd2e48d3ec51aca37bec569da6d59e819104cba538db84","observation_id":"e90ecb08-25e2-44fd-9d1c-ef98f5c51b27","resolution":{"observed_at":"2026-08-07T05:33:24.054150Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:23.806015Z","title":"Kawazura, Z","venue":null,"work_id":"09566bb5-3c1d-4cbb-85bd-7e9a66845110","year":2012},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.185987Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:50894230d9f1ecfa09a1cc665fd8b809eefbc38d4961f19c48ab6ed1bd8e750e","observation_id":"9d4b41be-2d01-4f95-81a8-ffb2c56b3b7f","resolution":{"observed_at":"2026-08-07T05:33:23.892350Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:23.515241Z","title":"Martyushev, Some interesting consequences of the maximum entropy production principle, Journal of Experimental and Theoretical Physics 104 (2007) 651–654","venue":null,"work_id":"0b49e4b7-ef05-47b9-9bda-04ad7844e213","year":2007},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.190487Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:601d98a3ed8ce39a4f59180ac7681658fe4272a997acb1a7e2d25e856453ef7f","observation_id":"0d25b65e-077f-4e0e-a033-6828adb2e852","resolution":{"observed_at":"2026-08-07T05:33:23.642601Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:23.267066Z","title":"Hill, Entropy production as the selection rule between different growth morphologies, Nature 348 (1990) 426–428","venue":null,"work_id":"cf0a13e3-8452-4acf-9e7e-d4a944f81a5e","year":1990},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.195131Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:370ce379995bb3f0184ac04b65c7a0656fe10df4e47e69b11c70cd27951aa078","observation_id":"4f8a2d9a-fbfd-4b77-a843-c3631bb48c72","resolution":{"observed_at":"2026-08-07T05:33:23.358734Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:23.054798Z","title":"Ozawa, S","venue":null,"work_id":"4aa94687-15c5-4af0-9954-c8959f7d955f","year":2001},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.199386Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:85f40621aa6b055962b707457a0377f0246d3b1f57d7f920f79cacf4947be1ae","observation_id":"e76c3b84-6bb4-4186-8ce8-4c93ff9cc540","resolution":{"observed_at":"2026-08-07T05:33:23.142761Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:22.849650Z","title":null,"venue":null,"work_id":"55074da9-86ca-449b-b2f9-27cf767741ba","year":2010},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.204078Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:01b4ad435c2a008a161e3680d2835739fd43da73ae540c2f05d8a0d6a597b192","observation_id":"194763ac-27ff-4c24-ac0d-04e81a939ec3","resolution":{"observed_at":"2026-08-07T05:33:22.918614Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:22.679122Z","title":null,"venue":null,"work_id":"89bab958-1b50-4a48-8602-754a12e41b22","year":2016},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.208743Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:b05e10db1b51dfd7745d2b875d1e1f490ff7110f09e4f98bcc692d296c910607","observation_id":"0b04e7e7-d5ea-48fb-a05e-e839e3a6067f","resolution":{"observed_at":"2026-08-07T05:33:22.758594Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:22.505816Z","title":null,"venue":null,"work_id":"b70841ac-eb9b-46d2-aabc-16802c67ea93","year":2009},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.213392Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:8cad6f3dd83f2e36d06186bcd771098fef89d13798efa370c0f5b4d35b387bc0","observation_id":"d0d156cc-d1eb-4519-9fc4-c98fca579516","resolution":{"observed_at":"2026-08-07T05:33:22.553892Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:22.330465Z","title":"Yoshida, S","venue":null,"work_id":"7a3c57af-e8e5-45e6-b3cd-c8d570aa687a","year":2008},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.218367Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:29fe015c91c4f96f91670427ad2b9ad6ff7166ecc373b410002729490ebd6f01","observation_id":"e19a255b-ab4e-40c6-86d0-92f34b4dd316","resolution":{"observed_at":"2026-08-07T05:33:22.392772Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:22.162109Z","title":"Yoshida, Y","venue":null,"work_id":"5ee587d1-8469-4e55-ac22-573f535672fd","year":2014},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.223616Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:78374a1d9aaa50ced701d9d92b0a2ea18f1f8f94d746edec92b3dd978265a2db","observation_id":"f8fa01c8-198a-4c3b-9c02-e6b19737102f","resolution":{"observed_at":"2026-08-07T05:33:22.218248Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:22.091113Z","title":"Kawazura, Z","venue":null,"work_id":"cbf463d5-7955-4b57-b80b-3ded2b637bd6","year":2010},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.228557Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:06fa7919ec6231fe8f19b38f3790e8b016762b8050efbd6735783834b2d7408f","observation_id":"a57dc63a-43e2-45e1-ba77-b4158bcb0ce1","resolution":{"observed_at":"2026-08-07T05:33:22.105747Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:21.921954Z","title":"Glansdorff, I","venue":null,"work_id":"c62cbf19-1d27-4d32-945d-f02a1830c171","year":1964},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.233777Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:27e45dcb9b6da5e6f9a3416bdad5b0551cd3ca5593b701d473507ef8dbfe50fa","observation_id":"1f91d8a3-f994-47b6-9fd1-7aa647d2a717","resolution":{"observed_at":"2026-08-07T05:33:21.982485Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:21.783883Z","title":"Landauer, Stability and entropy production in electrical circuits, Journal of Statistical Physics 13 (1975) 1–16","venue":null,"work_id":"4773f566-f078-43e6-ace9-babf263fc92e","year":1975},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.238383Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:fa08820bb5ff8c38bd419e333d012a17f482ba2707a9a19ba43e996a33a33b6a","observation_id":"f69d556d-9383-4d1d-b98b-b097c46546a1","resolution":{"observed_at":"2026-08-07T05:33:21.845645Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:21.712544Z","title":"Bodineau, B","venue":null,"work_id":"1abe2328-0651-434c-8286-309daa83018b","year":2025},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.242842Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:ee36ab9434855a5e11e1f5fbdcfec36c526db41dd7b817d43daf3ed293b62c81","observation_id":"6385e238-4510-422c-800d-4474f07b6aa4","resolution":{"observed_at":"2026-08-07T05:33:21.740057Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:21.648366Z","title":"Derrida, J","venue":null,"work_id":"7cd62370-3cfa-42c5-8428-347a629be038","year":2001},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.247409Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:8680214d8981748b73054ff56206cf8ad2f080a81ebd55ade5f6afe4843fca15","observation_id":"7ec3b028-4229-4bf6-a242-db0e702724ca","resolution":{"observed_at":"2026-08-07T05:33:21.676082Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:21.598222Z","title":"Bertini, A","venue":null,"work_id":"a82df591-3cbf-462a-af98-225bf4674106","year":2002},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":68,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.251904Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:072aaeeaf287cafbdcac3f48a9c17be378165dc4383af2bc234851d3e570d51f","observation_id":"2caff210-ba5e-4e17-b44c-6fd61ebcbb73","resolution":{"observed_at":"2026-08-07T05:33:21.615529Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:21.572417Z","title":"Torquato, Optimal design of heterogeneous materials, Annual review of materials research 40 (1) (2010) 101–129","venue":null,"work_id":"904b7a4b-359a-490d-9e43-b641ed1b119f","year":2010},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":69,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.256917Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:d80b75ed44a3300633a91270d04c0ecd270856ac872fbe0f0192c45831b06f9c","observation_id":"68ec7cd6-0360-4b24-bd4a-b61eb5c71e31","resolution":{"observed_at":"2026-08-07T05:33:21.580139Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:21.548900Z","title":"Waldherr, D","venue":null,"work_id":"67732855-1965-4065-b702-d33f0cb19466","year":2015},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":70,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.261139Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:44efe65d4d4bcc0acba2670ddabb223f12bd31358f21c7a8b349d52332e3bbb3","observation_id":"574d4ea4-09b1-42c3-92a3-257bfbf7ead4","resolution":{"observed_at":"2026-08-07T05:33:21.557838Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:21.523405Z","title":"Franklin, S","venue":null,"work_id":"d4615704-eb2a-4c7e-a394-f41155d891fa","year":2020},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":71,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.265258Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:76dc5a4fbc859e7fb3acbaa0bd9e21aa57167c14a6e236e4fb70633c2ca93f45","observation_id":"988a15a6-96e3-499b-bb44-50210b31ccff","resolution":{"observed_at":"2026-08-07T05:33:21.533585Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:21.498111Z","title":"Calabrese, B","venue":null,"work_id":"c5a9e9cd-74ab-4132-8838-3f2c7db9b295","year":2022},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":72,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.269652Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:53cee2b8876c08e420d53459bcdba847834f5baa2b3eb838fb42ccd2c590a2dd","observation_id":"973005cd-66be-4c31-95b3-7cac2cbfbf12","resolution":{"observed_at":"2026-08-07T05:33:21.507547Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:21.473483Z","title":"Witelski, M","venue":null,"work_id":"3a2a4074-338a-426f-9081-2b2fa2ed9dc1","year":2015},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":73,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.274297Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:17ccf7c8e15e547da5a9fe5adcef0bc021ba051322ec73d2f1e14584a1ac8269","observation_id":"26caf9fe-689f-475d-936f-54dff3aff9ce","resolution":{"observed_at":"2026-08-07T05:33:21.481941Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:21.450940Z","title":null,"venue":null,"work_id":"717ad8b5-63ae-494d-b9cd-9bbc088cc8ab","year":2021},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":74,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.278618Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:c30d3b14085f94949f1cc2717a6157dc67b2961d298673f0c49bada204461b6e","observation_id":"7550b0c6-3660-47ab-93da-84cb728d5346","resolution":{"observed_at":"2026-08-07T05:33:21.460848Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:21.428108Z","title":"Giaccone, S","venue":null,"work_id":"6bd21824-79e0-4155-9ee1-ec147c3b3659","year":2025},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":75,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.283029Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:e58346574fba36649855b4327e018d9c429a46023a4681bb2b96d098a4e96ee5","observation_id":"f366eb38-1e2a-4965-9342-6de5ed467b35","resolution":{"observed_at":"2026-08-07T05:33:21.435638Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:21.406997Z","title":null,"venue":null,"work_id":"b0199f53-bbaa-4a6f-8440-c9e978b72b50","year":2001},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":76,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.287674Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:774b0978e3fb40a41b2ba835feb60015413807d30396dd4a041fe9e386e147ae","observation_id":"73b80792-d2a1-48af-b70f-70e962a15f23","resolution":{"observed_at":"2026-08-07T05:33:21.414149Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:21.389767Z","title":"Burger, J","venue":null,"work_id":"981b2420-8370-4d17-8b06-4840f9b41a76","year":null},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":77,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.292634Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:f04b9519b19caa60cf7569fad16746f5046d69def013c30ec4b17e95300e8302","observation_id":"25bc5904-daa7-42ff-b4be-50250aa95aa1","resolution":{"observed_at":"2026-08-07T05:33:21.394832Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:21.374322Z","title":null,"venue":null,"work_id":"916ad8d5-9d88-483e-b1d0-ea20767688ae","year":2013},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":78,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.297764Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:3898b603e93a042710a604f2622efca11e5ad123fa46d6b341c3342942e6ab22","observation_id":"68c65f00-4840-460c-9726-0e8fb01527f6","resolution":{"observed_at":"2026-08-07T05:33:21.379227Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:21.358373Z","title":"Bonetti, M","venue":null,"work_id":"232d8033-4be1-41fc-8d4f-06dc8300c994","year":2020},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":79,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.302767Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:7c96877b5d3f8dc635773bc661a45105dc339602f69a8a80f70e2ad7331ecf6c","observation_id":"9f4750d6-7403-4824-b1f2-fa4163915783","resolution":{"observed_at":"2026-08-07T05:33:21.362961Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:33:21.340874Z","title":"Maritan, F","venue":null,"work_id":"601c5e28-9c1a-4b6a-9e42-9dc09f97a3d4","year":1996},"citing_paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks","version":1},"reference_index":80,"source":"pdf_text","source_observed_at":"2026-08-07T05:33:21.307241Z"},"links":{"citing_paper":"/paper/2506.15727"},"observation_digest":"sha256:c440f7beb22927c6cc7d5453856cb82021982d5c7ee6028654b4a3af4e977dea","observation_id":"104fbc02-6dab-41a2-b8ca-e95f914c2665","resolution":{"observed_at":"2026-08-07T05:33:21.346917Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.15727","last_updated":"2025-06-09T16:51:33Z","latest_version":1,"primary_category":"cond-mat.stat-mech","snapshot_observed_at":"2026-08-13T10:31:56.904804Z","submitted_at":"2025-06-09T16:51:33Z","title":"Thermodynamics and Legendre Duality in Optimal Networks"},"reference_resolution":{"displayed":80,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":28,"verified_exact":0,"verified_fuzzy":52},"total_outbound_references":80},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 80 of 80 outbound references and 0 inbound Pith citation observations for arXiv:2506.15727."}