{"as_of":"2026-08-10T16:18:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:ebe0b42089fb86ec04e3bba4c3771d222650e669e6412c30832bfb10583f0d97","coverage":[{"denominator":57,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":57,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-08T20:19:58.016655Z","state":"measured"},{"denominator":57,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":57,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-10T06:31:04.303077+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/2502.05137/citation-record","integrity":"/paper/2502.05137/integrity","json":"/paper/2502.05137/citation-record.json","paper":"/paper/2502.05137"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T20:19:58.999786Z","title":null,"venue":null,"work_id":"7cd82b24-bded-45c8-9ce5-f2115415d0a7","year":1996},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.767064Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:7f9f639b8e1c1232e2f82622e85250765394647bad1c7469b6813784b12ca4f8","observation_id":"a80889ae-d27c-4d6d-8194-6053dfa7e9a4","resolution":{"observed_at":"2026-08-08T20:19:59.004283Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.985696Z","title":"Agricola, (2008)","venue":null,"work_id":"2b71f9bf-932b-49a4-aba9-1166c638b3f0","year":2008},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.772569Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:6dab820cdedca47e83f62c827fb2572b9683080560753db5a36589a2ce155deb","observation_id":"44f6637d-2d93-4dcb-bbcf-e47e63eade17","resolution":{"observed_at":"2026-08-08T20:19:58.990180Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.971297Z","title":"Encyclopaedia of Mathematical Sciences, Springer Berlin Heidelberg, 2007","venue":null,"work_id":"bd7b7928-ef26-4319-8989-f0298b74b5f1","year":2007},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.777360Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:c34001226d92795b53f29660bb8cdcf8acac824c697d82ba8851e19a6f7c33b6","observation_id":"68f5caf1-a733-4f40-aabf-fbda45bbdb93","resolution":{"observed_at":"2026-08-08T20:19:58.975935Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.957188Z","title":"Pisa, Spo- erri, 1918","venue":null,"work_id":"0b2e630a-48be-419f-a62e-3242c0d41481","year":1918},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.782225Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:86a3d2b22650566b2a78535c076584ce28fc7ed0b6a160f14d9be8dda34d4115","observation_id":"1db277a1-b4b9-4abd-8d7b-340ca2af9ad5","resolution":{"observed_at":"2026-08-08T20:19:58.961726Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:57.786877Z","title":"V.: Compatible Poisson brackets on Lie algebras and completene ss of fam- ilies of functions in involution","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.786877Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:ca3fa6ad9d720242c8adbd1dbf61774d0b7988d9e4fb39e9e92636b907883550","observation_id":"98ea06d1-1863-4e63-b359-85dfcf691139","resolution":{"observed_at":"2026-08-08T20:19:57.786877Z","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.geomphys.2016.12.008","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Journal of Geometry and Physics, 114, 404-419, 2017","venue":"Journal of Geometry and Physics","work_id":"9a0caa39-69f8-4e15-b0a1-4a6aa42d10fb","year":2017},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.791406Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:567379ac58cdf5112491b03539faeb52fba43fcd728eb8119eeb8f392fdd7e70","observation_id":"0c1c8ab7-e69a-45d7-8777-876905a8941b","resolution":{"observed_at":"2026-08-08T20:19:58.166695Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.943192Z","title":null,"venue":null,"work_id":"5b551011-160e-48b0-9547-dcf29d78ea02","year":1909},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.796618Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:6d12935aa135ea7b24f854cf5d0e37099a248a6815a56f017308fd71e6295376","observation_id":"4167341d-aec5-461a-972f-ce3b11ac53aa","resolution":{"observed_at":"2026-08-08T20:19:58.947577Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2210.14289","last_updated":"2023-02-28T18:51:05Z","snapshot_observed_at":"2026-07-06T14:10:24.345006Z","submitted_at":"2022-10-25T19:21:20Z","title":"Classification of degenerate non-homogeneous Hamiltonian operators","version":3},"cited_work":{"arxiv_id":"2210.14289","doi":null,"metadata_source":"pith","pith_arxiv_id":"2210.14289","snapshot_observed_at":"2026-08-08T20:19:58.387709Z","title":"Classification of degenerate non-homogeneous Hamiltonian operators","venue":"math-ph","work_id":"033cb0cd-7bf3-4898-a790-e70896e091fe","year":2022},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.801011Z"},"links":{"cited_paper":"/paper/2210.14289","citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:92eac0b00d5bca6f11f57b235ac18d2915853a7e674fe16785cb28d3fd33c3dd","observation_id":"c44696f6-37e7-4641-9a13-de250799a262","resolution":{"observed_at":"2026-08-08T20:19:58.392670Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.928747Z","title":"In preparation, 2024","venue":null,"work_id":"efe4e8de-dc22-4f9a-ab1d-2155634eb060","year":2024},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.805818Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:bf42eee4052d3090f0df0c98090d292cba6e6b21a426ec73a988b3b9723ed6bd","observation_id":"2f283b00-ef14-46af-9455-a05bc9c6bf32","resolution":{"observed_at":"2026-08-08T20:19:58.933223Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.914678Z","title":"Cambridge Univer- sity Press; 2020","venue":null,"work_id":"4906534b-1bf6-4dd2-b77d-049cf6a14788","year":2020},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.810371Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:0f93f64df9d1f66f53f826ef4fe7b37deb22840a575b1559ab499283d2bf73c8","observation_id":"88d62672-dfec-442c-8641-8086440c27ad","resolution":{"observed_at":"2026-08-08T20:19:58.919116Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/0550-3213(92)90137-z","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Nuclear Physics B, 379, 3, 1992, pp","venue":"Nuclear Physics B","work_id":"f9bccde1-aa57-4e6b-825d-0db2ccc0287b","year":1992},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.814887Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:d30c0c7770993161e313068335e4a61a4ca46e2fbbf3d0be163b218a1eb1864b","observation_id":"ef60c295-472f-4550-a1db-a088427c9c69","resolution":{"observed_at":"2026-08-08T20:19:58.151724Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.900501Z","title":"and Novikov, S.P.: Hamiltonian formalism of one-dimensional systems of hydrodynamic type and the Bogolyubov–Whitham averaging method","venue":null,"work_id":"71cedf49-3847-4f90-a436-39f536249e9a","year":1983},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.819568Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:8daaf3c4247e6f278392ab6725b53bdad8687b32f46934b69af8c445b683f1ba","observation_id":"5d98628a-9780-4b3e-865e-b40b7cc38a81","resolution":{"observed_at":"2026-08-08T20:19:58.905074Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.886644Z","title":null,"venue":null,"work_id":"ea0d3e18-5ab4-4c5f-8da6-283e873cf430","year":1984},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.823701Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:8ee3189f66e218161210334d6c3bc487d9c1ad8ce732bfc67ac6ece2b34cb30f","observation_id":"293860ad-39da-4331-9c03-5d8bdea4f30b","resolution":{"observed_at":"2026-08-08T20:19:58.891029Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:57.828005Z","title":null,"venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.828005Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:a5a509c7b58a59d1c6b0ef29c99c3f497c8ae2f8e84e61aaf8431ce766c2155c","observation_id":"32c5fc62-6183-4538-a7f4-35b875547353","resolution":{"observed_at":"2026-08-08T20:19:57.828005Z","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":"2026-08-08T20:19:58.872437Z","title":"A., Krichever, I","venue":null,"work_id":"7bdb5288-9382-4be0-a203-b027a9b4cfef","year":2001},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.832384Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:9557f84d2135cbc04d8ab45b554981d963f641204de37ba6729483c1866f2e52","observation_id":"a99babcc-b6a1-4cd9-b19d-4579b33ba5cb","resolution":{"observed_at":"2026-08-08T20:19:58.877066Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.geomphys.2014.05.027","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"and Vitolo, R.: Projective-geometric aspects of homogeneous third-order Hamiltonian operators","venue":"Journal of Geometry and Physics","work_id":"fe5a749b-485c-4c07-903e-e51c0a911798","year":2014},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.836808Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:ad60bcdc21bc7c07f77bc6a56dcc551fa1b358faf2cc3d298d148018393da8be","observation_id":"39ca4904-5c3e-4a11-b04b-bfaf25fc59d5","resolution":{"observed_at":"2026-08-08T20:19:58.127452Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.857515Z","title":"Springer New York","venue":null,"work_id":"8d005b49-93f9-45b6-8114-32e532440979","year":1991},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.841171Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:fa6fee2c2841e24d73b4f9f834fdf06a16ed411c231d1d6242f97e6bbc0f6abf","observation_id":"6ce9f036-040f-4385-b485-e6686ddb7a96","resolution":{"observed_at":"2026-08-08T20:19:58.861903Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.843150Z","title":"Duke Math","venue":null,"work_id":"9a5dfb40-a2ef-431f-80e6-aff6023309d2","year":2002},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.845482Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:3ae06de96ed214e1cf063751882fe97022db02c1a0b0f88a2675e9362caaa67a","observation_id":"d2738c2d-9a1c-444f-9270-9fa3ccbbe9b8","resolution":{"observed_at":"2026-08-08T20:19:58.847700Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:57.849476Z","title":"Compatible Lie Brackets and Integr able Equations of the Principal Chiral Model Type","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.849476Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:4ad458eaa8aa750de2b0a8d3d0413d6b8f05a8b43e9a09473a590b5f32faa082","observation_id":"7a166447-d85d-4cc0-a854-901d01dca80c","resolution":{"observed_at":"2026-08-08T20:19:57.849476Z","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":"2024.0280","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T20:19:58.365137Z","title":null,"venue":null,"work_id":"64c3a8f2-054a-4e70-aea4-4608957688ae","year":2024},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.853924Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:d5dc307cf323736c1cb20feb67e49c6cd5a93991adf0e5593748c43a3491cffd","observation_id":"9a237070-b8a9-47ad-8e51-ce6b66774f76","resolution":{"observed_at":"2026-08-08T20:19:58.372566Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.828670Z","title":"and Casati, M.: Multidimensional nonhomogeneous quasi-linear systems an d their Hamiltonian structures","venue":null,"work_id":"2ab60c56-5aa5-4d8e-b224-cc8c1a362d49","year":2024},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.857871Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:70b2eefe5df26027ecc65592505a12d475d579b5993dfb672ef20a265b0cddb0","observation_id":"bb19418d-2a1a-48fc-b4cf-f18cbadea28a","resolution":{"observed_at":"2026-08-08T20:19:58.833339Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.813908Z","title":"Dover Publications, 2013","venue":null,"work_id":"8765fb57-a3ed-40a8-915d-80b450482216","year":2013},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.861854Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:cc67ba0b10b5b1d696724bf8212032acf5e29c90b6afe1aaacc97d3d8d33bd4d","observation_id":"73fce55f-1bfb-4c6a-8d8a-8e788671e22c","resolution":{"observed_at":"2026-08-08T20:19:58.818496Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.799731Z","title":"and Vitolo, R.: Hamiltonian structures for general PDEs","venue":null,"work_id":"68d80c69-4eab-4a9c-a206-93214afd6519","year":null},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.865632Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:c45dfe9f84ad95d6542acff5151ab2ff6a392459cf2fb70503edfa0b5e7bf755","observation_id":"72f23fb2-d256-4956-ad38-13845511cb5d","resolution":{"observed_at":"2026-08-08T20:19:58.804291Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.785310Z","title":"S., Verbovetsky, A., and Vitolo, R.: Hamiltonian Structures for General PDEs","venue":null,"work_id":"a06872d6-97d7-4044-83cc-6395cea758d7","year":null},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.869743Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:f03ae8e91dde2e70982105bc6aa4406fc35c4fd44ae5b67c48165a013eb4f3bb","observation_id":"733a7a97-af8e-4b83-9342-509e3d4f7feb","resolution":{"observed_at":"2026-08-08T20:19:58.790333Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.771453Z","title":"Cambridge University Press, 2008","venue":null,"work_id":"84b98849-9418-4130-884f-254377e8f3fd","year":2008},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.873634Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:5903efe4df791a1835e9013ab30fac0fab75c6ff70c36f16eb9940d7d6d500da","observation_id":"409e3a5f-deb5-4dde-a9ac-72052454498d","resolution":{"observed_at":"2026-08-08T20:19:58.775900Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2112.05635","last_updated":"2021-12-10T16:08:39Z","snapshot_observed_at":"2026-08-07T22:52:46.718750Z","submitted_at":"2021-12-10T16:08:39Z","title":"Geometry of inhomogeneous Poisson brackets, multicomponent Harry Dym hierarchies and multicomponent Hunter-Saxton equations","version":1},"cited_work":{"arxiv_id":"2112.05635","doi":null,"metadata_source":"pith","pith_arxiv_id":"2112.05635","snapshot_observed_at":"2026-08-08T20:19:58.212879Z","title":"Geometry of inhomogeneous Poisson brackets, multicomponent Harry Dym hierarchies and multicomponent Hunter-Saxton equations","venue":"math-ph","work_id":"5169b925-9790-422c-ab76-0f873620dae3","year":2021},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.877257Z"},"links":{"cited_paper":"/paper/2112.05635","citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:df2078582a11abb504805a28a570a59c0e93e754de52ae343d78050c424eab69","observation_id":"de22873c-9006-4bca-87cf-075b353802db","resolution":{"observed_at":"2026-08-08T20:19:58.217967Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/978-3-642-31090-4_4","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":null,"venue":"Grundlehren der mathematischen Wissenschaften","work_id":"aededaf9-3f7f-4519-b6e4-1f7e476113ff","year":2013},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.882149Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:a1df22f834ea0e3a4ddae5ee8100e1f4edae855ec8faf973d6f1c0f1c44b6ac0","observation_id":"76fbc55d-ee83-4036-8064-392340d10ecd","resolution":{"observed_at":"2026-08-08T20:19:58.103051Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.756565Z","title":"Vol.1–3, Leipzig, 1888, 1890, 1893","venue":null,"work_id":"6459108d-c086-4d4a-89b2-bf82c1bb10ba","year":null},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.886761Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:6474811c6638a51f29278f6c25468182d94655277fe94deabd5a716ac36e2fce","observation_id":"e1a3ab09-7f89-4e5b-a081-47b382bbc462","resolution":{"observed_at":"2026-08-08T20:19:58.761368Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.742408Z","title":"and Vitolo, R.: Bi-Hamiltonian structures of KdV type, cyclic Frobenius algebrae and Monge metrics","venue":null,"work_id":"807d0073-9377-4383-af62-f02d917d1a51","year":2024},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.891247Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:908a8b71a18f7fb49acb9b3ef2ffb797b166ddeb3955b1f18a2396fcc73c5fbe","observation_id":"64764da8-17b0-440c-89d9-d78a5788e5be","resolution":{"observed_at":"2026-08-08T20:19:58.747039Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.727983Z","title":"In Nonlinearity 37 (2024), no","venue":null,"work_id":"2db3401b-6208-48c3-960a-e9ff4c77433a","year":2024},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.895510Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:2bf0c87a6f66094ee751122156df091a97e4162eb683c48ae70abf6b9a16b84f","observation_id":"0b1b6dbf-7479-431e-ac69-63b6f2225a53","resolution":{"observed_at":"2026-08-08T20:19:58.732493Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.713860Z","title":null,"venue":null,"work_id":"181a6981-188e-4370-bf53-5c4269faf675","year":1978},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.899961Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:fa3f73475049b7248270f872d9cddf6d72cfced8c3f896f769ef95a092490fc7","observation_id":"ae31c50a-0c65-45db-96cf-a24a72395094","resolution":{"observed_at":"2026-08-08T20:19:58.718300Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.698961Z","title":"Uspekhi Matemat","venue":null,"work_id":"2918397f-bf55-4978-82f8-5cb6d5f318f0","year":1997},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.904369Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:bb243ba7883a13d8efd510f4e5d20ac0b0c98b58114fa7a36710d3723c21697c","observation_id":"3bc38aaf-7f0c-4c03-80a8-b6512655c3e2","resolution":{"observed_at":"2026-08-08T20:19:58.703566Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.684644Z","title":null,"venue":null,"work_id":"c465625f-0d31-4120-8ced-9164203b2c0d","year":1998},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.908764Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:1ebd52bb6fd9299c8c2195bd44b1165f0d323d8ce34b0e847837833a7e44f0ca","observation_id":"74b5e164-9241-49f2-a96e-e5f3686419de","resolution":{"observed_at":"2026-08-08T20:19:58.689012Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.670544Z","title":"I., Ferapontov, E","venue":null,"work_id":"a3909215-dfcc-48e8-96d2-ae5dcd333c9e","year":1994},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.912960Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:29e36ff7eb0c885b43fd732feb802ee9bc1ea67af80335eab82c53c898c68a31","observation_id":"a8837bd2-2ad9-430d-b2a9-becbd061d358","resolution":{"observed_at":"2026-08-08T20:19:58.675239Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.656248Z","title":null,"venue":null,"work_id":"6b3551c1-e3d6-4eaa-9ea6-f6b77e18084b","year":1994},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.917524Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:8d1f2382fb4c62246514bfcdae966087e94e1eb40860503818f45dcd9e3525f5","observation_id":"a800fda5-8b6b-49b2-b43a-26d8ec1b9e91","resolution":{"observed_at":"2026-08-08T20:19:58.660721Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.641692Z","title":"M.: On solvable Lie algebras","venue":null,"work_id":"60cd7228-8c3d-46b1-8dc8-9ac6e5894fc8","year":1963},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.922282Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:573eb76ef057c70304f04a3d4339ad76e698ca60d7f8701a026e140fb48d1cc5","observation_id":"532177e9-9591-4eb6-a28d-c4e4d1b4082b","resolution":{"observed_at":"2026-08-08T20:19:58.646235Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.626816Z","title":"M.: The classiﬁcation of the real structure of ﬁve-dimensional Lie algebras","venue":null,"work_id":"90632f67-007b-46d6-a8a9-6466054fb89e","year":1963},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.926757Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:51f5d5fa62bf042ec70783e60e859f7ec9b26b5889a1ab488f82c00762fb2d74","observation_id":"3f4a2bf6-b6f5-45ae-908e-38a3124ca55e","resolution":{"observed_at":"2026-08-08T20:19:58.631528Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.612470Z","title":"M.: Classiﬁcation of solvable Lie algebras of sixth order with a non- nilpotent basis element","venue":null,"work_id":"aa21e556-6799-4651-8e34-94569e71b7ed","year":1963},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.931113Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:f2321ad1c475dc0af64f0447ba3b5ded13f3b8bd7043f643589bbed194973d9c","observation_id":"27bfa948-bbdd-48b7-9c0c-3c763b1ed8fc","resolution":{"observed_at":"2026-08-08T20:19:58.617038Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.598580Z","title":"M.: Certain theorems on solvable Lie algebras","venue":null,"work_id":"b1f7dcb2-abf2-4c8c-b375-138a8e8f09fe","year":1966},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.935721Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:f26993aa0fdca37e5e83785d9ed870536efd02df82aba957a7af3511beff63f0","observation_id":"a8635df2-2d26-43af-a167-87330f7b9f53","resolution":{"observed_at":"2026-08-08T20:19:58.603081Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.583856Z","title":"P., Manakov, S","venue":null,"work_id":"7f4190c0-1525-4ac6-8bc7-05299d6d5a3e","year":1984},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.940220Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:a65066125def8bff4f144c31285b4f601e580f289c9387b4516a59a605b42074","observation_id":"87512a74-ecd5-4fd3-beea-ac949d232457","resolution":{"observed_at":"2026-08-08T20:19:58.588571Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.569289Z","title":"V., Sokolov, V","venue":null,"work_id":"da05c1fa-b8e1-47b5-a391-a4db72e9c527","year":2006},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.944678Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:fef69bda5c321f34f30de9238e213eb9b681907a23d2a4a73c0c985d6b6c6bda","observation_id":"455547c9-165a-42fb-9169-607e2f70e4c0","resolution":{"observed_at":"2026-08-08T20:19:58.573974Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.554248Z","title":"Springer-Verlag, 2nd edition, 1993","venue":null,"work_id":"c97732fe-1123-4765-863a-35961ac479bc","year":1993},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.949161Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:4b53d63d13ae3f54c1e468c9d7daad8373c5ccf02f28a13dbc1a5f7fdb61fef0","observation_id":"13743e00-ea08-4710-99bc-999b9157327e","resolution":{"observed_at":"2026-08-08T20:19:58.559140Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.539597Z","title":"V., Vergallo, P., Vitolo, R.: Classiﬁcation of bi-Hamiltonian pairs extended by isometries","venue":null,"work_id":"e46e7cfd-895b-41cf-8840-ca177150c002","year":2021},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.953583Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:bbbe9a168cece5f04c3669987e7f6d478b57201ff678ed5aac6c986dabedd9ef","observation_id":"cb48d194-d7fb-4ce7-8cb3-01133b5663de","resolution":{"observed_at":"2026-08-08T20:19:58.544210Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.524969Z","title":"and Winternitz, P.: Subalgebras of real three and four–dimensional Lie algebra s","venue":null,"work_id":"74e96600-255a-4844-87d6-ec9227ffa546","year":1977},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.958142Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:ff1022141e1993a4b96797921fe4d96d062f03ed3f5003296c3c299deb3973c5","observation_id":"44ee96e1-b173-4924-ba14-117d0903d069","resolution":{"observed_at":"2026-08-08T20:19:58.529789Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.510586Z","title":"O., Boyko1, V","venue":null,"work_id":"2bd9bd43-f4fc-4a20-8020-206ebd255ea8","year":2003},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.962539Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:c4ea17410cc1b914471d073406f4a3a65ef4309b250dbcc6e984b4010a010c99","observation_id":"8affa488-81e0-40c1-9d0b-16c6d86f533d","resolution":{"observed_at":"2026-08-08T20:19:58.514942Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2410.22455","last_updated":"2025-04-12T09:41:47Z","snapshot_observed_at":"2026-07-06T19:41:50.722534Z","submitted_at":"2024-10-29T18:42:13Z","title":"Classification of 1+0 two-dimensional Hamiltonian operators","version":2},"cited_work":{"arxiv_id":"2410.22455","doi":null,"metadata_source":"pith","pith_arxiv_id":"2410.22455","snapshot_observed_at":"2026-08-08T20:19:58.191553Z","title":"Classification of 1+0 two-dimensional Hamiltonian operators","venue":"math-ph","work_id":"1d284227-61f5-4f9c-9f54-5b5a2bcdfe37","year":2024},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.967091Z"},"links":{"cited_paper":"/paper/2410.22455","citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:52e9dc9336a3f2b55c8c61126c94543b90ecde03be939ad4b3bee694a682a64e","observation_id":"e15c7de7-2188-49e9-8299-4dd0b9986e6c","resolution":{"observed_at":"2026-08-08T20:19:58.196647Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1063/1.3698087","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"P.: Hidden symmetries and supergravity solutions","venue":"Journal of Mathematical Physics","work_id":"bd3920b1-da00-4ba0-8919-de4242d42f32","year":2012},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.972117Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:672ea372b81ceabb6ea61d371bdd4c47d77c7bf4e191d6c7067c456df00dac92","observation_id":"6798ccac-454b-4261-b675-5eb13026ab06","resolution":{"observed_at":"2026-08-08T20:19:58.088690Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.495934Z","title":"H.: Two-step nilpotent Lie algebras","venue":null,"work_id":"b91c6fb7-ddb8-422d-bf9a-64a614247363","year":1966},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.976634Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:fe85fe27ad2841f72d11307e30b7679cd712be2dd0a919f42db252a3dafdce69","observation_id":"1f68c94e-aa00-48ef-9c07-9a0b7ce47b8c","resolution":{"observed_at":"2026-08-08T20:19:58.500636Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.480832Z","title":"and Winternitz, P.: Classiﬁcation and Identiﬁcation of Lie Al- gebras","venue":null,"work_id":"4447b7de-9276-4395-b321-b72041675006","year":2014},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.980942Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:c8fbc9a41fe9c51bad91facf90d807e04130436e6f9da3cd13e23d4e07a7748e","observation_id":"8bd02391-cea7-4345-8af6-09b8e39bc49d","resolution":{"observed_at":"2026-08-08T20:19:58.485601Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.465673Z","title":"Soviet Math","venue":null,"work_id":"4c36a172-2a3c-4999-ba93-f78a7004b199","year":1985},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.985658Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:ef25e17eea97822791ce22a4972ff03d60fed7fba6fd4e7a4c41478aafce9a73","observation_id":"d16213c0-3f68-4279-9289-6286006b47b3","resolution":{"observed_at":"2026-08-08T20:19:58.470102Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.451144Z","title":"P.: The hamiltonian property of stationary and inverse equatio ns of condensed matter mechanics and mathematical physics","venue":null,"work_id":"dfa16cd1-a1c8-44fa-911f-a96227202ead","year":1989},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.990246Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:51b86ecf2497e9bd57c1676c4bc81aa334f3850b7b47680d9343a82661def2d7","observation_id":"185380d0-d40e-4a9f-810f-13fcea99538f","resolution":{"observed_at":"2026-08-08T20:19:58.455836Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.436735Z","title":"T he general- ized hodograph method","venue":null,"work_id":"57a03bc5-9f82-4b3d-af3e-13a89355b64f","year":1991},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.994909Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:1aa9f2e116a4f4abc77cc40084f2f2cfc50d49fa0923954eb1ed1513e7572942","observation_id":"63ab6c54-9256-4eaa-a218-c1582e3592b8","resolution":{"observed_at":"2026-08-08T20:19:58.441561Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.421339Z","title":null,"venue":null,"work_id":"2c5b44d6-b301-4a8a-b400-3cd1d33ac8d7","year":1990},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:57.999352Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:e47f929aa6db301a49bff3602b18649a662ecd95e231ad01ba62fc81e1510a2d","observation_id":"5998da49-433a-4b4f-9246-ccd466cc5171","resolution":{"observed_at":"2026-08-08T20:19:58.426619Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.404476Z","title":"Lecture Notes in Mathematics, Springer, pp","venue":null,"work_id":"1662cc17-5b7a-4248-baf4-efe93ab31785","year":2013},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:58.003766Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:f4c61e226e041a7974776e35a2879687d32ef32bf95e10489a8736fd466c8b8f","observation_id":"d12406ba-7036-424b-b489-8eba46e7c96b","resolution":{"observed_at":"2026-08-08T20:19:58.409086Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.008104Z","title":"Boll Unione Mat Ital 17, 513–526 (2024)","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:58.008104Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:14a468784389df6ec5cdf72d32f99c825edbe014188b60cc38b95895beaf29f1","observation_id":"fa1ff2f0-1227-461f-a6b6-f473965de7fd","resolution":{"observed_at":"2026-08-08T20:19:58.008104Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1088/1361-6544/ac","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T20:19:58.057768Z","title":"and Vitolo, R.: Projective geometry of homogeneous second order Hamilto- nian operators","venue":null,"work_id":"4a8849c1-4d79-4df6-9331-84b4080a6091","year":2023},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:58.012392Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:ec8c156737166f29b2fc5dc60a65797243924888beb5149a1e9c2a5af113bb58","observation_id":"0515e79a-f300-49ae-a3a7-dcdc1ae4db33","resolution":{"observed_at":"2026-08-08T20:19:58.063688Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-08T20:19:58.016655Z","title":"Annals of Mathematics, vol","venue":null,"work_id":null,"year":1952},"citing_paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-08T20:19:58.016655Z"},"links":{"citing_paper":"/paper/2502.05137"},"observation_digest":"sha256:9e448bdfd42405421d7e71ebda90f9c499bb87404635befaae8aa9cb5de97e86","observation_id":"d23160fe-44b0-4f2d-980f-991dedd7d9bc","resolution":{"observed_at":"2026-08-08T20:19:58.016655Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2502.05137","last_updated":"2025-02-07T18:14:12Z","latest_version":1,"primary_category":"math-ph","snapshot_observed_at":"2026-08-08T20:04:19.445833Z","submitted_at":"2025-02-07T18:14:12Z","title":"Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators"},"reference_resolution":{"displayed":57,"state_counts":{"malformed_identifier":3,"metadata_mismatch":2,"parse_uncertain":0,"unresolved":10,"verified_exact":8,"verified_fuzzy":34},"total_outbound_references":57},"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":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"thesis":"As of 10 August 2026, this Paper Citation Record lists 57 of 57 outbound references and 0 inbound Pith citation observations for arXiv:2502.05137."}