{"as_of":"2026-08-22T21:56:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:f6b9681e3b94e86d9266dc71e830106560dafbee58b18920a1346871b0ce5fbb","coverage":[{"denominator":13,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":13,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T05:53:51.209171Z","state":"measured"},{"denominator":13,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":13,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-22T06:32:14.747728+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2506.07061/citation-record","integrity":"/paper/2506.07061/integrity","json":"/paper/2506.07061/citation-record.json","paper":"/paper/2506.07061"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:53:55.266681Z","title":"Aguiar, On the associative analog of Lie bialgebras","venue":null,"work_id":"db17f79d-6f26-4d29-b5ef-5181e30d7f7b","year":2001},"citing_paper":{"arxiv_id":"2506.07061","last_updated":"2025-06-08T09:44:25Z","snapshot_observed_at":"2026-08-13T09:50:31.124184Z","submitted_at":"2025-06-08T09:44:25Z","title":"Bialgebras induced by special left Alia algebras","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T05:53:49.136554Z"},"links":{"citing_paper":"/paper/2506.07061"},"observation_digest":"sha256:6a7a0fa9c0ca98e086d1b00aa4308b18edb8c6291444dead27ef6a94eb55833e","observation_id":"c68792b9-e855-4007-8b67-c1bc9477bd3c","resolution":{"observed_at":"2026-08-07T05:53:55.411546Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:53:54.839662Z","title":"Bai, Double constructions of Frobenius algebras, Connes cocycles and their duality","venue":null,"work_id":"f39ab8e0-568d-473c-b3e7-49875f00261e","year":2010},"citing_paper":{"arxiv_id":"2506.07061","last_updated":"2025-06-08T09:44:25Z","snapshot_observed_at":"2026-08-13T09:50:31.124184Z","submitted_at":"2025-06-08T09:44:25Z","title":"Bialgebras induced by special left Alia algebras","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T05:53:49.286066Z"},"links":{"citing_paper":"/paper/2506.07061"},"observation_digest":"sha256:054e23e783641cc83707dc8054d08206127969906eb667682f1c4caaed417128","observation_id":"ec70ddb7-0eab-464d-bd23-bd8bec876695","resolution":{"observed_at":"2026-08-07T05:53:55.062496Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:53:54.508670Z","title":null,"venue":null,"work_id":"d5c45db2-5431-452b-b02b-80e9ab30b0fe","year":2008},"citing_paper":{"arxiv_id":"2506.07061","last_updated":"2025-06-08T09:44:25Z","snapshot_observed_at":"2026-08-13T09:50:31.124184Z","submitted_at":"2025-06-08T09:44:25Z","title":"Bialgebras induced by special left Alia algebras","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T05:53:49.427867Z"},"links":{"citing_paper":"/paper/2506.07061"},"observation_digest":"sha256:15444e72050c5a09964ac14b88af75aa90caffe3123f386be64086dda4c054b1","observation_id":"5463f5f1-763c-4f95-aa5d-25da4cfa3da9","resolution":{"observed_at":"2026-08-07T05:53:54.663532Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:53:54.199894Z","title":null,"venue":null,"work_id":"527ab6d6-5bb3-4b74-85d7-359408d4c529","year":2024},"citing_paper":{"arxiv_id":"2506.07061","last_updated":"2025-06-08T09:44:25Z","snapshot_observed_at":"2026-08-13T09:50:31.124184Z","submitted_at":"2025-06-08T09:44:25Z","title":"Bialgebras induced by special left Alia algebras","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T05:53:49.612486Z"},"links":{"citing_paper":"/paper/2506.07061"},"observation_digest":"sha256:9c6de925d902950fc862b0c8bab70dbf2ff64988da32b98993d4d13fcafc779b","observation_id":"17e68398-6fec-41b0-975d-b265f7a409f1","resolution":{"observed_at":"2026-08-07T05:53:54.302559Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:53:53.859256Z","title":null,"venue":null,"work_id":"02902e47-5508-46b2-99c6-b65694ad399e","year":2024},"citing_paper":{"arxiv_id":"2506.07061","last_updated":"2025-06-08T09:44:25Z","snapshot_observed_at":"2026-08-13T09:50:31.124184Z","submitted_at":"2025-06-08T09:44:25Z","title":"Bialgebras induced by special left Alia algebras","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T05:53:49.773868Z"},"links":{"citing_paper":"/paper/2506.07061"},"observation_digest":"sha256:693b852fcf74626019d1b97d9156753b1ab60a02be653aaa0d43e8b999bf07cb","observation_id":"60025f08-8426-4782-866d-5ceadd363089","resolution":{"observed_at":"2026-08-07T05:53:54.052326Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2502.18717","last_updated":"2025-07-28T09:40:12Z","snapshot_observed_at":"2026-08-19T19:10:02.879170Z","submitted_at":"2025-02-26T00:21:41Z","title":"Classical Yang-Baxter equations and Nijenhuis operators for Lie algebras","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.18717","snapshot_observed_at":"2026-08-07T05:53:49.963210Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2506.07061","last_updated":"2025-06-08T09:44:25Z","snapshot_observed_at":"2026-08-13T09:50:31.124184Z","submitted_at":"2025-06-08T09:44:25Z","title":"Bialgebras induced by special left Alia algebras","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T05:53:49.963210Z"},"links":{"cited_paper":"/paper/2502.18717","citing_paper":"/paper/2506.07061"},"observation_digest":"sha256:ae55165ca5e4027d60e72f2f4cfec0467a4086f92306b6b2eab8ff1eb2ed54c0","observation_id":"b8424d14-7d2d-46ae-8c9a-b40e525216f7","resolution":{"observed_at":"2026-08-07T05:53:49.963210Z","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":"2026-08-07T05:53:53.525740Z","title":null,"venue":null,"work_id":"8c647eec-2eb2-44a1-92ff-edb279e8136c","year":2022},"citing_paper":{"arxiv_id":"2506.07061","last_updated":"2025-06-08T09:44:25Z","snapshot_observed_at":"2026-08-13T09:50:31.124184Z","submitted_at":"2025-06-08T09:44:25Z","title":"Bialgebras induced by special left Alia algebras","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T05:53:50.133708Z"},"links":{"citing_paper":"/paper/2506.07061"},"observation_digest":"sha256:d4c8d0ea2a775fde8c3057971bc1b5ab5036e185c4142056292b1b4a9cffc580","observation_id":"a73d0734-aa62-4cd3-802d-817a72c3066d","resolution":{"observed_at":"2026-08-07T05:53:53.676395Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:53:53.099662Z","title":null,"venue":null,"work_id":"c7ca7637-4a43-40d8-956e-8f0ea6114992","year":2024},"citing_paper":{"arxiv_id":"2506.07061","last_updated":"2025-06-08T09:44:25Z","snapshot_observed_at":"2026-08-13T09:50:31.124184Z","submitted_at":"2025-06-08T09:44:25Z","title":"Bialgebras induced by special left Alia algebras","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T05:53:50.263274Z"},"links":{"citing_paper":"/paper/2506.07061"},"observation_digest":"sha256:860fd9f02c233190899153854df75e58d93324af839b2c6b2fe3aac73401f491","observation_id":"6b2fe126-75d3-4f54-a437-4463e41dbdf8","resolution":{"observed_at":"2026-08-07T05:53:53.317867Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:53:52.828923Z","title":null,"venue":null,"work_id":"3d0cd3ee-c163-4869-aab7-0ef4c6411e67","year":1969},"citing_paper":{"arxiv_id":"2506.07061","last_updated":"2025-06-08T09:44:25Z","snapshot_observed_at":"2026-08-13T09:50:31.124184Z","submitted_at":"2025-06-08T09:44:25Z","title":"Bialgebras induced by special left Alia algebras","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T05:53:50.419370Z"},"links":{"citing_paper":"/paper/2506.07061"},"observation_digest":"sha256:bb7ae25fa2f25b632c74f82645bf0065a7bd145422c63686ee78991d8c8fdff9","observation_id":"d3711399-431c-4e93-9c33-dfc668edb9d7","resolution":{"observed_at":"2026-08-07T05:53:52.946651Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:53:52.469544Z","title":null,"venue":null,"work_id":"5da70803-5d78-46b6-bc4f-112f17543819","year":1997},"citing_paper":{"arxiv_id":"2506.07061","last_updated":"2025-06-08T09:44:25Z","snapshot_observed_at":"2026-08-13T09:50:31.124184Z","submitted_at":"2025-06-08T09:44:25Z","title":"Bialgebras induced by special left Alia algebras","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T05:53:50.615024Z"},"links":{"citing_paper":"/paper/2506.07061"},"observation_digest":"sha256:07497d70b33c4500f364a912e4300e92f146842fb63f81279918192bebed53ef","observation_id":"a0fb673d-c7ca-415c-91a1-0de9a2451b73","resolution":{"observed_at":"2026-08-07T05:53:52.699576Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:53:52.144067Z","title":null,"venue":null,"work_id":"7509601c-6025-44c9-8d2b-10bf55e8347b","year":1966},"citing_paper":{"arxiv_id":"2506.07061","last_updated":"2025-06-08T09:44:25Z","snapshot_observed_at":"2026-08-13T09:50:31.124184Z","submitted_at":"2025-06-08T09:44:25Z","title":"Bialgebras induced by special left Alia algebras","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T05:53:50.851409Z"},"links":{"citing_paper":"/paper/2506.07061"},"observation_digest":"sha256:739db0ace313875ff6efce2e17c7c5f879f4155bd6a97f238a57e1288f6193ec","observation_id":"dc5af05a-0f29-4f45-b5bb-84a94dceee3a","resolution":{"observed_at":"2026-08-07T05:53:52.331015Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:53:51.742502Z","title":"Zusmanovich, Special and exceptional mock-lie algebras","venue":null,"work_id":"6e72da83-bc8c-47ea-b4b0-a793620ad2b6","year":2017},"citing_paper":{"arxiv_id":"2506.07061","last_updated":"2025-06-08T09:44:25Z","snapshot_observed_at":"2026-08-13T09:50:31.124184Z","submitted_at":"2025-06-08T09:44:25Z","title":"Bialgebras induced by special left Alia algebras","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T05:53:51.059112Z"},"links":{"citing_paper":"/paper/2506.07061"},"observation_digest":"sha256:50de6954152c3ed489c4cb12cebc2c5f2a4b118aa8ad91de0e6807cd7866d570","observation_id":"7d6ed4bb-e838-4502-9df2-fefe7ccc9e15","resolution":{"observed_at":"2026-08-07T05:53:51.964173Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:53:51.459292Z","title":null,"venue":null,"work_id":"8dad9fb9-0944-4aae-a5b1-d9adde37a613","year":null},"citing_paper":{"arxiv_id":"2506.07061","last_updated":"2025-06-08T09:44:25Z","snapshot_observed_at":"2026-08-13T09:50:31.124184Z","submitted_at":"2025-06-08T09:44:25Z","title":"Bialgebras induced by special left Alia algebras","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T05:53:51.209171Z"},"links":{"citing_paper":"/paper/2506.07061"},"observation_digest":"sha256:7503f79936c560adf6893a5e129d57fa54d260735514d59cd224748e51526f4e","observation_id":"d7fd1c8e-99c9-4524-b286-30655050a3b1","resolution":{"observed_at":"2026-08-07T05:53:51.578032Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.07061","last_updated":"2025-06-08T09:44:25Z","latest_version":1,"primary_category":"math.RA","snapshot_observed_at":"2026-08-13T09:50:31.124184Z","submitted_at":"2025-06-08T09:44:25Z","title":"Bialgebras induced by special left Alia algebras"},"reference_resolution":{"displayed":13,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":10,"verified_exact":0,"verified_fuzzy":3},"total_outbound_references":13},"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":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"thesis":"As of 22 August 2026, this Paper Citation Record lists 13 of 13 outbound references and 0 inbound Pith citation observations for arXiv:2506.07061."}