{"as_of":"2026-08-16T21:31:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:47b04979179f66f502697e41d77cba93c0283b935256bd5e8fdfa268ec12c32d","coverage":[{"denominator":43,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":43,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T15:39:03.231651Z","state":"measured"},{"denominator":43,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":43,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+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/2412.10821/citation-record","integrity":"/paper/2412.10821/integrity","json":"/paper/2412.10821/citation-record.json","paper":"/paper/2412.10821"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T15:39:02.981742Z","title":"Lewenstein, A","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:02.981742Z"},"links":{"citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:5569983169036e8bf4afde9c13499c5bd1d8b103a32daab2af025b04ee5fe93d","observation_id":"f13b80ed-78c6-4f2b-9a74-ac91ee29fd6a","resolution":{"observed_at":"2026-08-11T15:39:02.981742Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.commatsci.2012.02.002","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T15:39:04.052562Z","title":"Curtarolo, W","venue":null,"work_id":"b44b1074-9e43-4e20-bb2b-a50858db2d0d","year":2012},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:02.988996Z"},"links":{"citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:10d7c2fd3fd24961844ee0ef52aa16972b5fc33b3bc253b31def0fad650431fe","observation_id":"b30a7952-a5a1-4f94-bf4c-a18282e8302c","resolution":{"observed_at":"2026-08-11T15:39:04.058481Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1103/physrevb.99.165118","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T15:39:04.031476Z","title":null,"venue":null,"work_id":"af95a45d-18da-40f5-abf7-b7b3bb830d2f","year":2019},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:02.995184Z"},"links":{"citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:35d8f61b69246fb18f9e5d7ccbb1ade38297e58e23de520df7377ef8c3a55bd6","observation_id":"59cd64eb-df19-4456-a8f8-d04c62d84d57","resolution":{"observed_at":"2026-08-11T15:39:04.036867Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1142/9789812567840","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T15:39:04.011925Z","title":null,"venue":null,"work_id":"2b2b6232-15a8-46ca-afd4-9a4b2c9048d3","year":2004},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:03.000823Z"},"links":{"citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:519a9f635418a75aa838882eca4615f54085b4d9c8e10ee6274c8a6dc6b9023b","observation_id":"70821d61-621a-4799-8565-300a1efd6073","resolution":{"observed_at":"2026-08-11T15:39:04.017437Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1021/bi00199a029","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T15:39:03.995795Z","title":null,"venue":null,"work_id":"375616bb-34a4-42f8-9d84-74fd4aed8d3d","year":1994},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:03.008363Z"},"links":{"citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:ca62ddaad7f4677f7ebefaf0333a0e46f3016b957ddd197c98424c0bb8fead0d","observation_id":"0ffe7f07-60bd-4aa7-a3fe-51e10cc0a88a","resolution":{"observed_at":"2026-08-11T15:39:04.000901Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.3390/math7010103","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T15:39:03.967510Z","title":null,"venue":null,"work_id":"74afb040-44c5-461f-881f-b0bef8e875d5","year":2019},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:03.014022Z"},"links":{"citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:af64ea9c7335fec488fcbbd448ae9404a2d111bf95fbbfa53f69dd04ed04610f","observation_id":"24c1b928-835c-40dd-84fe-b5b5c14a61f4","resolution":{"observed_at":"2026-08-11T15:39:03.974211Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-11T15:39:04.604806Z","title":null,"venue":null,"work_id":"c17092da-dfc4-4edd-8650-f75fa4b0dfce","year":2017},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:03.019318Z"},"links":{"citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:564cc65459174aa207002acb2e19a4ef919ca5b2fd25883397805967532d0fba","observation_id":"b5e33d4c-d972-4936-818c-559663025a09","resolution":{"observed_at":"2026-08-11T15:39:04.611641Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-11T15:39:04.583330Z","title":"Toda, Theory of Nonlinear Lattices, Springer Science & Business Media,, 2012","venue":null,"work_id":"e8f50444-ce3f-41a8-9942-8b56452ba090","year":2012},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:03.024946Z"},"links":{"citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:1b22f6482035e055d4f791cf8c84554c72914eebc1fe7b3f01137ed20e3c9042","observation_id":"c377c292-975f-4615-8ec0-83253b971836","resolution":{"observed_at":"2026-08-11T15:39:04.589312Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-11T15:39:04.567634Z","title":null,"venue":null,"work_id":"fd5fce27-7477-4fb5-8127-8716b8949c16","year":2016},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:03.031917Z"},"links":{"citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:0a8bea8ecb0508bac02190982bbcafe2db3370beab2fb0413136c3a6d2868629","observation_id":"48ad0f10-d1db-4550-a391-5e0ab0f452fb","resolution":{"observed_at":"2026-08-11T15:39:04.572645Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T15:39:03.037265Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:03.037265Z"},"links":{"citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:da6be7ca409961392ca6f0c55972b6f7bcdbc2eb326d39105e9e335398f5e2f9","observation_id":"eb43d6e1-7916-47cf-b538-a1419d5cd1be","resolution":{"observed_at":"2026-08-11T15:39:03.037265Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1038/nrd1280","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T15:39:03.929445Z","title":"Datta, D","venue":null,"work_id":"40a6c549-3e9b-4ab8-bbf6-6a297b32a09c","year":2004},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:03.042633Z"},"links":{"citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:5099b283c5f75e7bbcc9e8c6432913000d666ebe049a74fa0acbf46578675aa3","observation_id":"9ea4487e-36d8-46c4-8abd-c1b087b61ae1","resolution":{"observed_at":"2026-08-11T15:39:03.937278Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/978-3-030-44992-6","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T11:03:20.376878Z","title":null,"venue":"Nonlinear systems and complexity","work_id":"10f63f75-3129-4788-a95d-192a3e483844","year":2020},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:03.049325Z"},"links":{"citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:01bb16da73ac530e41d8b03600cc03c11d52e6133cd124e69cf50d65c1e095d7","observation_id":"48c03c0f-1b1f-4d06-bada-98cd193ea88d","resolution":{"observed_at":"2026-08-11T15:39:03.915752Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-11T15:39:04.550885Z","title":"Teki´ c, P","venue":null,"work_id":"5770addb-1317-4b80-bfa0-849f46354a36","year":2016},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:03.054123Z"},"links":{"citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:a32a1daa48f756b3a8309457d5260af43c13c1c9a3526c994b61c935f952cfdb","observation_id":"7e7a92b7-785f-4056-b9ca-9b41995959d6","resolution":{"observed_at":"2026-08-11T15:39:04.557080Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T15:39:03.060807Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:03.060807Z"},"links":{"citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:c08e6cb1c4753035b9e09917302cc1bbc463782b61d4a12d4696375fafef1814","observation_id":"ec3a0c35-ea4f-4edd-9f7e-bc22aae4afaf","resolution":{"observed_at":"2026-08-11T15:39:03.060807Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2009.1123","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T15:39:04.440327Z","title":"Maci´ a, Charge transfer in DNA: e ffective Hamiltonian approaches, Zeitschrift f¨ ur Kristallographie-Crystalline Materials 224 (1-2) (2009) 91–95","venue":null,"work_id":"cd253302-2ab5-47ae-8f99-84576c797122","year":2009},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:03.067355Z"},"links":{"citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:20622a13f382b788dc6c20935c7e6d67428ccd3e25f4863a2abd47ce02d46e00","observation_id":"268da267-e4d1-4939-9ba2-22898ccc9645","resolution":{"observed_at":"2026-08-11T15:39:04.449309Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T15:39:03.073488Z","title":"Saqlain, W","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:03.073488Z"},"links":{"citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:c3adb8e858eea9ff81a0208349e9fde55f3aa116f0f2e36e6630903e36530d17","observation_id":"c5a02272-cc02-440f-9468-7efabf332ea5","resolution":{"observed_at":"2026-08-11T15:39:03.073488Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1038/s42005-021-00755-5","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T15:39:03.868050Z","title":"Zvyagintseva, H","venue":null,"work_id":"d3e02359-1f96-4326-a514-2cf89a9e98f8","year":2022},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:03.081651Z"},"links":{"citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:a9ec7a1246939744fc0e7d9955d2dd21df63f71f523b70e8b5e5148ba514d868","observation_id":"1cbf3243-3662-483a-b7f1-308a4f59f6b3","resolution":{"observed_at":"2026-08-11T15:39:03.875321Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s11071-021-06996-x","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T15:39:03.829497Z","title":null,"venue":null,"work_id":"450d9cde-6175-4b0d-8e00-4cbf501ce33d","year":2022},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:03.087745Z"},"links":{"citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:1d3ae6645b56aaf87837460dc9b9ba88839947f179be9dac05cf3b8d780b9034","observation_id":"2f1280d1-d81e-45d8-9511-d5e855747400","resolution":{"observed_at":"2026-08-11T15:39:03.840416Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2022.13326","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T15:39:04.252320Z","title":null,"venue":null,"work_id":"53e9bf02-cf6f-48cf-95cd-ee694f625b11","year":2022},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:03.096459Z"},"links":{"citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:cfa8ab52112604b45e5a191c69e6be8e609f75fc13d4121914a4d23106b09963","observation_id":"f362cfa0-159f-428e-b033-bfba8a5554a7","resolution":{"observed_at":"2026-08-11T15:39:04.265077Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T15:39:03.102986Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:03.102986Z"},"links":{"citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:ec8574126bcf9484be280783f67ce948be2a34342a994c21c6b9359153222b18","observation_id":"ec8ce2a1-69ff-4f1c-9c4d-86d06ec3fff0","resolution":{"observed_at":"2026-08-11T15:39:03.102986Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1909.12264","last_updated":"2019-09-26T17:19:16Z","snapshot_observed_at":"2026-08-10T03:12:45.536051Z","submitted_at":"2019-09-26T17:19:16Z","title":"Quantum Graph Neural Networks","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1909.12264","snapshot_observed_at":"2026-08-11T15:39:03.108079Z","title":"V erdon, T","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:03.108079Z"},"links":{"cited_paper":"/paper/1909.12264","citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:e0cd6c3eedd4204a54db404204bb33ea444ce4f754b6610c266e38a347da6041","observation_id":"ddc7c3ce-749b-4c8a-8d42-7d5fc9d463ac","resolution":{"observed_at":"2026-08-11T15:39:03.108079Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.48550/arxiv.2110.0639","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T15:39:03.759766Z","title":"Kochkov, T","venue":null,"work_id":"8cd4bf31-e0d3-484a-9a4b-616bc0cebe93","year":2021},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:03.114278Z"},"links":{"citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:998834f89764049e041838e23f56ddbd782c100eefa00c67b668302ff0463097","observation_id":"39543aef-6365-47ac-8224-382f2d8c6373","resolution":{"observed_at":"2026-08-11T15:39:03.777442Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-11T15:39:04.523747Z","title":"Bishnoi, R","venue":null,"work_id":"980e6d98-519f-4c4f-8402-007dbfe223b6","year":2023},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:03.119779Z"},"links":{"citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:3123c0093dddd14b189410729b9aa167b3966d2fac04127858e3d39a9342974b","observation_id":"a03e4638-0825-4f7e-9931-c72d6b5557b3","resolution":{"observed_at":"2026-08-11T15:39:04.528881Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1909.12790","last_updated":"2019-09-27T16:54:04Z","snapshot_observed_at":"2026-08-11T04:53:32.321020Z","submitted_at":"2019-09-27T16:54:04Z","title":"Hamiltonian Graph Networks with ODE Integrators","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1909.12790","snapshot_observed_at":"2026-08-11T15:39:03.125491Z","title":"Sanchez-Gonzalez, V","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:03.125491Z"},"links":{"cited_paper":"/paper/1909.12790","citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:321c361876504c09ccbb941f86fbd70c02341c955a37342174f1092b3b79678b","observation_id":"7ea6c09f-c8f6-4b7e-94e8-5e8ce7e468fc","resolution":{"observed_at":"2026-08-11T15:39:03.125491Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T15:39:04.504188Z","title":null,"venue":null,"work_id":"0b916be4-ca24-4ac4-919f-ca63e6b57592","year":2024},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:03.132721Z"},"links":{"citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:8d9e5321bbbac691707cc352291aa7269b7e757217c96e319c4847080e343c2f","observation_id":"30e4a7a9-b5d0-45d5-b60d-77003987cfaa","resolution":{"observed_at":"2026-08-11T15:39:04.510952Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-11T15:39:04.482362Z","title":"V eliˇ ckovi´ c, G","venue":null,"work_id":"25d264fe-4357-48eb-9584-78daad3a363f","year":2018},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:03.141380Z"},"links":{"citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:325b34bc3c87c35cb76db02cc67a4b421fd36c6100fa0d0b43e4b912e3d8f863","observation_id":"fc5d0d0c-5589-46f2-9a7b-1609956117a3","resolution":{"observed_at":"2026-08-11T15:39:04.488665Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1609.02907","last_updated":"2017-02-22T09:55:36Z","snapshot_observed_at":"2026-08-13T11:38:10.906031Z","submitted_at":"2016-09-09T19:48:41Z","title":"Semi-Supervised Classification with Graph Convolutional Networks","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1609.02907","snapshot_observed_at":"2026-08-11T15:39:03.147519Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:03.147519Z"},"links":{"cited_paper":"/paper/1609.02907","citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:16bbedf4a80285f0c6ee8311d44e49f9c2cd5ed55e6d7d272021d12e71dd3afb","observation_id":"afaf56c7-9a61-4c44-ba59-16994c17ef1a","resolution":{"observed_at":"2026-08-11T15:39:03.147519Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T15:39:03.153566Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:03.153566Z"},"links":{"citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:8bcfe2076f63bcec98606fa9b70333c7ad9b7a3689176c10809ff6bdf3abce74","observation_id":"e1f63235-b5a1-4cb1-93a2-50bdbb47fa21","resolution":{"observed_at":"2026-08-11T15:39:03.153566Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.physd.2019.06.002","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T15:39:03.541310Z","title":"Penati, V","venue":null,"work_id":"0f7ff1c8-4a50-4196-a53d-f0ec65db6453","year":2019},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:03.159801Z"},"links":{"citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:fe95730990df18877ce881e80836375d99a47047781596f619909668657411a8","observation_id":"b16a43b4-5036-4349-b286-76dff479e0eb","resolution":{"observed_at":"2026-08-11T15:39:03.548371Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.physd.2012.08.011","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T15:39:03.517847Z","title":"Koukouloyannis, P","venue":null,"work_id":"3c3bae9e-7850-4c5e-af05-b3db7093ee03","year":2013},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:03.164754Z"},"links":{"citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:990edcd4a1d801a03547c9092227147001cbd5ce4fd047513ba29a0a908d6e22","observation_id":"74df4f07-6321-4cf8-8118-781fce55e4b4","resolution":{"observed_at":"2026-08-11T15:39:03.524147Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1103/physreve.65.056607","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T15:39:03.496041Z","title":null,"venue":null,"work_id":"33906b68-f22e-4ffd-8f0c-8297a6c6854d","year":2002},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:03.170508Z"},"links":{"citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:110601c14436ec2c6c1201ae2686592fead3df910bf8957c0291e92b37330436","observation_id":"e6e27bc7-4e16-483f-b1bb-3f6451d66e82","resolution":{"observed_at":"2026-08-11T15:39:03.502501Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1063/1.1854273","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T15:39:03.472873Z","title":"Dauxois, R","venue":null,"work_id":"cba7b932-0777-489e-9229-d293f627c973","year":2005},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:03.174977Z"},"links":{"citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:1a4499517ddc91b768c2fe21af6800fd917623cbb5b17289c4f7686b8e7bee99","observation_id":"0653f45f-d288-4163-9e73-64b3afd099d3","resolution":{"observed_at":"2026-08-11T15:39:03.478671Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2207.10142","last_updated":"2022-07-20T18:45:10Z","snapshot_observed_at":"2026-08-16T16:44:27.753457Z","submitted_at":"2022-07-20T18:45:10Z","title":"KP-II approximation for a scalar FPU system on a 2D square lattice","version":1},"cited_work":{"arxiv_id":"2207.10142","doi":"10.48550/arxiv.2207.10142","metadata_source":"pith","pith_arxiv_id":"2207.10142","snapshot_observed_at":"2026-08-11T18:16:15.004306Z","title":"KP-II approximation for a scalar FPU system on a 2D square lattice","venue":"nlin.SI","work_id":"52eb17dd-c3fc-4c37-b9ca-b3fad4d29021","year":2022},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:03.179367Z"},"links":{"cited_paper":"/paper/2207.10142","citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:3da6ffe82bf571918d9e0fb54b764a26771c594b82f0e696787a443233a7667b","observation_id":"2970a1bc-d017-4d92-824b-4ebc91bc3a0e","resolution":{"observed_at":"2026-08-11T15:39:03.458068Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1143/ptp.50.1547","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T15:39:03.416662Z","title":null,"venue":null,"work_id":"e02e7f1e-5f7b-4954-b0b0-74a2098e13a5","year":1973},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:03.185015Z"},"links":{"citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:534db56499880f4870106b2b742e011f50a4d13356c8ac7f4b03048ccafc07ba","observation_id":"051bee38-3afe-4d1a-ade6-2222a9eaff82","resolution":{"observed_at":"2026-08-11T15:39:03.422021Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T15:39:03.191046Z","title":"Montavon, G","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:03.191046Z"},"links":{"citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:24ababd98ca3e66d4ac92afc556239077f64ee1c90d299e345b38a788261d645","observation_id":"ab36bc11-6b98-4475-a0d2-2b11e616441f","resolution":{"observed_at":"2026-08-11T15:39:03.191046Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T15:39:04.460499Z","title":"Popescu, V","venue":null,"work_id":"63a1bbf7-81df-4540-a8b0-405aa67647f6","year":2009},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:03.196333Z"},"links":{"citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:be335eeb2db45823de52eb6fe94d4083950c0841f098582dd94b4baddd0533b2","observation_id":"a330996b-28a1-42f1-8824-e7b80799203f","resolution":{"observed_at":"2026-08-11T15:39:04.466456Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1906.01563","last_updated":"2019-09-05T04:20:28Z","snapshot_observed_at":"2026-08-14T16:21:01.276672Z","submitted_at":"2019-06-04T16:27:55Z","title":"Hamiltonian Neural Networks","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1906.01563","snapshot_observed_at":"2026-08-11T15:39:03.200717Z","title":"Greydanus, M","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:03.200717Z"},"links":{"cited_paper":"/paper/1906.01563","citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:042a566c78cf0e5732ed9d6f181198d828410da99740a6fa3b41df03f069a1d4","observation_id":"164838b0-b876-4da0-9a9a-485434c07b82","resolution":{"observed_at":"2026-08-11T15:39:03.200717Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T15:39:03.206060Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:03.206060Z"},"links":{"citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:37e9d57fe38436533be9dd2fc96491aabd490174d31dc56d87f53c7d22c9d065","observation_id":"0169fffa-9df1-49be-8fdf-ab843850c27c","resolution":{"observed_at":"2026-08-11T15:39:03.206060Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1126/sciadv.16030","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T15:39:03.340322Z","title":"Chmiela, A","venue":null,"work_id":"120e3f9a-4913-4d9b-85fb-a612ea1c8410","year":2017},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:03.211175Z"},"links":{"citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:73f4632caf88df95a973bc423e1d0400bb38001e390cb5f9d9734d1405ebce64","observation_id":"af163b4b-f09b-4c0d-9976-ff53d8cdd5e4","resolution":{"observed_at":"2026-08-11T15:39:03.347364Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T15:39:03.216882Z","title":"Chmiela, V","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:03.216882Z"},"links":{"citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:06448aee3b4f7262da49f658af990c598dca76a8c745d7f8d4f37087cbcf2a9a","observation_id":"4eee087d-b36a-4861-a7e9-e8ea13ce2072","resolution":{"observed_at":"2026-08-11T15:39:03.216882Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T15:39:03.221846Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:03.221846Z"},"links":{"citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:111656276c12098b61f3c9a495e5cfb725b7001da485dd76a4a9a97ffd4997f1","observation_id":"bc2ace9f-1324-4e05-8f7f-55a710bee7b4","resolution":{"observed_at":"2026-08-11T15:39:03.221846Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T15:39:03.226960Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:03.226960Z"},"links":{"citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:72e1f1e9a7843b8087d0bff89cbdae349d2647bbb345ec84f5544188cdbc9596","observation_id":"2bb93dd6-be1b-45b7-8a08-51f5defed2e3","resolution":{"observed_at":"2026-08-11T15:39:03.226960Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T15:39:03.231651Z","title":"Chmiela, H","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-11T15:39:03.231651Z"},"links":{"citing_paper":"/paper/2412.10821"},"observation_digest":"sha256:1a3e80ab99153e8ce20e5e4ac3157820f149833f957cfe8d094c9af7aec860f1","observation_id":"d0c65b17-0974-4c48-b7ac-b196435860b4","resolution":{"observed_at":"2026-08-11T15:39:03.231651Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2412.10821","last_updated":"2024-12-14T13:03:15Z","latest_version":1,"primary_category":"hep-lat","snapshot_observed_at":"2026-08-15T09:16:39.333564Z","submitted_at":"2024-12-14T13:03:15Z","title":"Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning"},"reference_resolution":{"displayed":43,"state_counts":{"malformed_identifier":0,"metadata_mismatch":1,"parse_uncertain":0,"unresolved":19,"verified_exact":18,"verified_fuzzy":5},"total_outbound_references":43},"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":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 16 August 2026, this Paper Citation Record lists 43 of 43 outbound references and 0 inbound Pith citation observations for arXiv:2412.10821."}