{"as_of":"2026-08-21T00:10:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:61820ef310d16e65c4a8cf367aca53eb3a54b0a50aa811ba961e320959b8430b","coverage":[{"denominator":31,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":31,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T12:15:28.081143Z","state":"measured"},{"denominator":31,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":31,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-20T06:33:59.587034+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2412.14605/citation-record","integrity":"/paper/2412.14605/integrity","json":"/paper/2412.14605/citation-record.json","paper":"/paper/2412.14605"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T12:15:28.629191Z","title":"Aguiar, Pre-Poisson algebras, Lett","venue":null,"work_id":"c3820a7b-4a99-4c79-9d07-4de55cd16ff0","year":2000},"citing_paper":{"arxiv_id":"2412.14605","last_updated":"2024-12-19T07:53:24Z","snapshot_observed_at":"2026-08-15T14:49:34.886847Z","submitted_at":"2024-12-19T07:53:24Z","title":"Averaging antisymmetric infinitesimal bialgebra and perm bialgebras","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-11T12:15:27.924313Z"},"links":{"citing_paper":"/paper/2412.14605"},"observation_digest":"sha256:70ffe7f530318527c3290a6c8ee3e830fb17e964e96da359ddfb5b9e767fe360","observation_id":"1252591a-6e8d-4008-bd21-a02c5b0037f3","resolution":{"observed_at":"2026-08-11T12:15:28.634128Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-11T12:15:28.613503Z","title":"Bai, Double constructions of Frobenius algebras, Connes cocycl es and their duality , J","venue":null,"work_id":"bebd4166-e77a-4873-9382-7577f3816847","year":2010},"citing_paper":{"arxiv_id":"2412.14605","last_updated":"2024-12-19T07:53:24Z","snapshot_observed_at":"2026-08-15T14:49:34.886847Z","submitted_at":"2024-12-19T07:53:24Z","title":"Averaging antisymmetric infinitesimal bialgebra and perm bialgebras","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-11T12:15:27.930572Z"},"links":{"citing_paper":"/paper/2412.14605"},"observation_digest":"sha256:0a8643d52b24c84a9763d9d832139b91ebbe7cf0875522cf90f1fb5050f62621","observation_id":"c99a4f45-6f70-429d-9813-196518c249b9","resolution":{"observed_at":"2026-08-11T12:15:28.618596Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-11T12:15:28.595923Z","title":null,"venue":null,"work_id":"5a028723-8722-430d-a2fa-2966144f5977","year":2012},"citing_paper":{"arxiv_id":"2412.14605","last_updated":"2024-12-19T07:53:24Z","snapshot_observed_at":"2026-08-15T14:49:34.886847Z","submitted_at":"2024-12-19T07:53:24Z","title":"Averaging antisymmetric infinitesimal bialgebra and perm bialgebras","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-11T12:15:27.936674Z"},"links":{"citing_paper":"/paper/2412.14605"},"observation_digest":"sha256:e65cfef41de8b2773dd09597637bace66bde7f0b315dfc32773829433e1960a3","observation_id":"cc791534-4730-4443-b2ca-cc5d7af9643b","resolution":{"observed_at":"2026-08-11T12:15:28.601199Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-11T12:15:28.580640Z","title":null,"venue":null,"work_id":"192070a0-f37e-4046-becf-9c7f1c5ad921","year":2012},"citing_paper":{"arxiv_id":"2412.14605","last_updated":"2024-12-19T07:53:24Z","snapshot_observed_at":"2026-08-15T14:49:34.886847Z","submitted_at":"2024-12-19T07:53:24Z","title":"Averaging antisymmetric infinitesimal bialgebra and perm bialgebras","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-11T12:15:27.942677Z"},"links":{"citing_paper":"/paper/2412.14605"},"observation_digest":"sha256:ff6ec791f9291919505636a1e07754f88d68de3c8619be226d8977ba1d317cb7","observation_id":"6dfd2c4f-6dcc-4a8e-83e4-ad4c6a8f916e","resolution":{"observed_at":"2026-08-11T12:15:28.585575Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-11T12:15:28.564577Z","title":null,"venue":null,"work_id":"981d8503-da8b-4734-b568-1e59f1862249","year":2012},"citing_paper":{"arxiv_id":"2412.14605","last_updated":"2024-12-19T07:53:24Z","snapshot_observed_at":"2026-08-15T14:49:34.886847Z","submitted_at":"2024-12-19T07:53:24Z","title":"Averaging antisymmetric infinitesimal bialgebra and perm bialgebras","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-11T12:15:27.948428Z"},"links":{"citing_paper":"/paper/2412.14605"},"observation_digest":"sha256:3acbafa1764a65cc58bcbdb9862edc286f01d9c670f5e605b898823905efe275","observation_id":"b3a949c6-7349-4aab-8d8d-60f1e4ee80cd","resolution":{"observed_at":"2026-08-11T12:15:28.569351Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-11T12:15:28.548453Z","title":"Bong, Some apparent connection between baxter and averaging operators, J","venue":null,"work_id":"369f0c73-1521-4281-8267-bb6ee2405a7f","year":1976},"citing_paper":{"arxiv_id":"2412.14605","last_updated":"2024-12-19T07:53:24Z","snapshot_observed_at":"2026-08-15T14:49:34.886847Z","submitted_at":"2024-12-19T07:53:24Z","title":"Averaging antisymmetric infinitesimal bialgebra and perm bialgebras","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-11T12:15:27.953980Z"},"links":{"citing_paper":"/paper/2412.14605"},"observation_digest":"sha256:bebebc2fac19522a26bf1d0b3ea309c02d193d88fb364eb0d20fab6e51b004e4","observation_id":"d15b225c-892f-4433-aa0c-262c8aa4517f","resolution":{"observed_at":"2026-08-11T12:15:28.553608Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-11T12:15:28.531197Z","title":"Cao, An algebraic study of averaging operators , Ph.D","venue":null,"work_id":"e39d1323-d296-449d-93b5-1a1d1cd25a17","year":2000},"citing_paper":{"arxiv_id":"2412.14605","last_updated":"2024-12-19T07:53:24Z","snapshot_observed_at":"2026-08-15T14:49:34.886847Z","submitted_at":"2024-12-19T07:53:24Z","title":"Averaging antisymmetric infinitesimal bialgebra and perm bialgebras","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-11T12:15:27.959662Z"},"links":{"citing_paper":"/paper/2412.14605"},"observation_digest":"sha256:0c66c675fa0729c1742f617ea52d361e44f06f18db52ece5b31dcb095c587932","observation_id":"2bb4275c-ea53-4b9a-8120-d73250517e1b","resolution":{"observed_at":"2026-08-11T12:15:28.536665Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-11T12:15:28.513695Z","title":"Chari, A","venue":null,"work_id":"ed378f4d-ed55-49fa-bb5e-d5940d3763c7","year":1994},"citing_paper":{"arxiv_id":"2412.14605","last_updated":"2024-12-19T07:53:24Z","snapshot_observed_at":"2026-08-15T14:49:34.886847Z","submitted_at":"2024-12-19T07:53:24Z","title":"Averaging antisymmetric infinitesimal bialgebra and perm bialgebras","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-11T12:15:27.964476Z"},"links":{"citing_paper":"/paper/2412.14605"},"observation_digest":"sha256:c23329fd675a71dcc3b6da1f2df9d3ae03e654b5c62440f99fb4fc1ad984a6aa","observation_id":"6f397f39-ab1e-4e9b-99f3-8ac10b0b4aae","resolution":{"observed_at":"2026-08-11T12:15:28.519957Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2303.17798","last_updated":"2023-03-31T05:11:54Z","snapshot_observed_at":"2026-08-16T15:43:53.274465Z","submitted_at":"2023-03-31T05:11:54Z","title":"Controlling structures, deformations and homotopy theory for averaging algebras","version":1},"cited_work":{"arxiv_id":"2303.17798","doi":null,"metadata_source":"pith","pith_arxiv_id":"2303.17798","snapshot_observed_at":"2026-08-11T12:15:28.156809Z","title":"Controlling structures, deformations and homotopy theory for averaging algebras","venue":"math.RA","work_id":"092fd814-a57c-43a9-8064-6ccd0b9b8c78","year":2023},"citing_paper":{"arxiv_id":"2412.14605","last_updated":"2024-12-19T07:53:24Z","snapshot_observed_at":"2026-08-15T14:49:34.886847Z","submitted_at":"2024-12-19T07:53:24Z","title":"Averaging antisymmetric infinitesimal bialgebra and perm bialgebras","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-11T12:15:27.969759Z"},"links":{"cited_paper":"/paper/2303.17798","citing_paper":"/paper/2412.14605"},"observation_digest":"sha256:b3a1ca5a84fa03bb060381d2fcba6d92b72733f67216a71ca35e5619320e00d4","observation_id":"6b420487-6bf5-47e1-ab21-33bcfda74442","resolution":{"observed_at":"2026-08-11T12:15:28.164358Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2403.06250","last_updated":"2024-03-10T16:23:29Z","snapshot_observed_at":"2026-08-16T14:11:12.350144Z","submitted_at":"2024-03-10T16:23:29Z","title":"Averaging operators on groups, racks and Leibniz algebras","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2403.06250","snapshot_observed_at":"2026-08-11T12:15:27.977033Z","title":"Das Averaging operators on groups, racks and Leibniz algebras , arXiv:2403.06250","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2412.14605","last_updated":"2024-12-19T07:53:24Z","snapshot_observed_at":"2026-08-15T14:49:34.886847Z","submitted_at":"2024-12-19T07:53:24Z","title":"Averaging antisymmetric infinitesimal bialgebra and perm bialgebras","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-11T12:15:27.977033Z"},"links":{"cited_paper":"/paper/2403.06250","citing_paper":"/paper/2412.14605"},"observation_digest":"sha256:86bad2fccba9ed26d6472f3ced2c45488cd3bbe48197581304673a2e04d58a1d","observation_id":"e186e8b7-270c-4c29-9b47-6ec5f819b08c","resolution":{"observed_at":"2026-08-11T12:15:27.977033Z","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":"2026-08-11T12:15:28.496467Z","title":"Das, S, Sen, 2-term averaging L∞-algebras and non-abelian extensions of averaging Lie alge bras, J","venue":null,"work_id":"2097de85-3fc8-4020-9c69-61b52dfcd6eb","year":2024},"citing_paper":{"arxiv_id":"2412.14605","last_updated":"2024-12-19T07:53:24Z","snapshot_observed_at":"2026-08-15T14:49:34.886847Z","submitted_at":"2024-12-19T07:53:24Z","title":"Averaging antisymmetric infinitesimal bialgebra and perm bialgebras","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-11T12:15:27.982363Z"},"links":{"citing_paper":"/paper/2412.14605"},"observation_digest":"sha256:4b9168f3d891a016cbe64a17c6d67719228f0319c476dcfb88a56b91881c410a","observation_id":"0f734025-3ab4-40e1-8a13-da50073217d6","resolution":{"observed_at":"2026-08-11T12:15:28.501833Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-11T12:15:28.480374Z","title":"Drinfeld, Hamiltonian structure on the Lie groups, Lie bialgebras and the geometric sense of the classical Y ang-Baxter equations, Soviet Math","venue":null,"work_id":"c5b9a6ba-69e6-4c5f-b4bc-a53701e087ee","year":1983},"citing_paper":{"arxiv_id":"2412.14605","last_updated":"2024-12-19T07:53:24Z","snapshot_observed_at":"2026-08-15T14:49:34.886847Z","submitted_at":"2024-12-19T07:53:24Z","title":"Averaging antisymmetric infinitesimal bialgebra and perm bialgebras","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-11T12:15:27.987388Z"},"links":{"citing_paper":"/paper/2412.14605"},"observation_digest":"sha256:2be07e602190a386c9d00c8ac088aaf8bc2fd2446176c2eb500c60438bc25dd0","observation_id":"f2fb2df3-03a7-4e7c-b1a3-cb95a47ae866","resolution":{"observed_at":"2026-08-11T12:15:28.485391Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-11T12:15:28.464568Z","title":"Miller, Averaging and Reynolds operators on Banach algebras II","venue":null,"work_id":"04aa684e-39f4-4a5e-8bf3-08c35d448d56","year":1968},"citing_paper":{"arxiv_id":"2412.14605","last_updated":"2024-12-19T07:53:24Z","snapshot_observed_at":"2026-08-15T14:49:34.886847Z","submitted_at":"2024-12-19T07:53:24Z","title":"Averaging antisymmetric infinitesimal bialgebra and perm bialgebras","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-11T12:15:27.992206Z"},"links":{"citing_paper":"/paper/2412.14605"},"observation_digest":"sha256:0988de0cf559a744fb4386dc69e4d11e6cd4f7e820513b04fa97368a0586eb24","observation_id":"4b78f3fa-3feb-4a75-a49c-fda786ecf7a4","resolution":{"observed_at":"2026-08-11T12:15:28.469976Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-11T12:15:28.448471Z","title":null,"venue":null,"work_id":"ac11474a-f913-41fa-b838-9f872f38c29b","year":2018},"citing_paper":{"arxiv_id":"2412.14605","last_updated":"2024-12-19T07:53:24Z","snapshot_observed_at":"2026-08-15T14:49:34.886847Z","submitted_at":"2024-12-19T07:53:24Z","title":"Averaging antisymmetric infinitesimal bialgebra and perm bialgebras","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-11T12:15:27.997065Z"},"links":{"citing_paper":"/paper/2412.14605"},"observation_digest":"sha256:73d26d233ba838e9c61cb21e28b81eb473e31eb6a51dd6ef7b32a567da509efc","observation_id":"f2ada03d-7c88-4d8e-8aef-975fbc0b3731","resolution":{"observed_at":"2026-08-11T12:15:28.453480Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-11T12:15:28.432507Z","title":"Guo, An Introduction to Rota-Baxter Algebra , International Press and Higher Education Press (China), 2 012","venue":null,"work_id":"517c949d-48f2-4c19-b4d2-6db12a200609","year":null},"citing_paper":{"arxiv_id":"2412.14605","last_updated":"2024-12-19T07:53:24Z","snapshot_observed_at":"2026-08-15T14:49:34.886847Z","submitted_at":"2024-12-19T07:53:24Z","title":"Averaging antisymmetric infinitesimal bialgebra and perm bialgebras","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-11T12:15:28.001839Z"},"links":{"citing_paper":"/paper/2412.14605"},"observation_digest":"sha256:d7003e2a27fdbcef4f7e68d9304085b95fc97ca30c095e041a910867557274c4","observation_id":"54e83406-aef2-4ff0-b026-6c9838fd7171","resolution":{"observed_at":"2026-08-11T12:15:28.437505Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-11T12:15:28.415894Z","title":"Hou, Extending structures for perm algebras and perm bialgebras , J","venue":null,"work_id":"d3dcb72b-55b4-447a-9b97-b36c39ae9a9d","year":2024},"citing_paper":{"arxiv_id":"2412.14605","last_updated":"2024-12-19T07:53:24Z","snapshot_observed_at":"2026-08-15T14:49:34.886847Z","submitted_at":"2024-12-19T07:53:24Z","title":"Averaging antisymmetric infinitesimal bialgebra and perm bialgebras","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-11T12:15:28.006961Z"},"links":{"citing_paper":"/paper/2412.14605"},"observation_digest":"sha256:565f9aaee1e80462d8f512a8280ec8c36dc72b3dcfc2b7e939987fea0986a2d5","observation_id":"6962d86b-005f-4b85-97de-f50d7cb0b018","resolution":{"observed_at":"2026-08-11T12:15:28.421472Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-11T12:15:28.395164Z","title":"Kamp´ e de F´ eriet,L’´ etat actuel du probl` eme de la turbulence (I and II) , La Sci","venue":null,"work_id":"c8916277-d89b-40ad-bb48-9bd5747888b8","year":1934},"citing_paper":{"arxiv_id":"2412.14605","last_updated":"2024-12-19T07:53:24Z","snapshot_observed_at":"2026-08-15T14:49:34.886847Z","submitted_at":"2024-12-19T07:53:24Z","title":"Averaging antisymmetric infinitesimal bialgebra and perm bialgebras","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-11T12:15:28.011973Z"},"links":{"citing_paper":"/paper/2412.14605"},"observation_digest":"sha256:6e593b73ac40d6029c6b29f0688f11e332e2eb76be55f1aa88c2df92dffe1e96","observation_id":"2a96b4e8-7895-4a2d-8dfd-b7c02f8053cd","resolution":{"observed_at":"2026-08-11T12:15:28.400839Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-11T12:15:28.377491Z","title":"Kamp´ e de F´ eriet,Introduction to the statistical theory of turbulence, correlation and spectrum, in The Institute of Fluid Dynamics and Applied Mathematics, Lecture Series No","venue":null,"work_id":"dd7e4ca9-5131-46b9-804a-5aec2e954db8","year":1950},"citing_paper":{"arxiv_id":"2412.14605","last_updated":"2024-12-19T07:53:24Z","snapshot_observed_at":"2026-08-15T14:49:34.886847Z","submitted_at":"2024-12-19T07:53:24Z","title":"Averaging antisymmetric infinitesimal bialgebra and perm bialgebras","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-11T12:15:28.016928Z"},"links":{"citing_paper":"/paper/2412.14605"},"observation_digest":"sha256:3aebcbda8801b5bb7f3a976f2135d36de652a96d263bbd7404b1cfeb2f3928e4","observation_id":"00306963-57a4-4587-97c4-c1a89b2270cd","resolution":{"observed_at":"2026-08-11T12:15:28.383346Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-11T12:15:28.357854Z","title":"Kelley, Averaging operators on C ∞(X), Illinois J","venue":null,"work_id":"d9bcaa4e-1766-4124-ab94-44f32242d32a","year":1958},"citing_paper":{"arxiv_id":"2412.14605","last_updated":"2024-12-19T07:53:24Z","snapshot_observed_at":"2026-08-15T14:49:34.886847Z","submitted_at":"2024-12-19T07:53:24Z","title":"Averaging antisymmetric infinitesimal bialgebra and perm bialgebras","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-11T12:15:28.021905Z"},"links":{"citing_paper":"/paper/2412.14605"},"observation_digest":"sha256:ac96013360455310c23e99d2f099e969550d4dd741f49747a77c842e68835049","observation_id":"4b83569a-1041-4551-b3c3-3a7e9e1d34f2","resolution":{"observed_at":"2026-08-11T12:15:28.364212Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-11T12:15:28.340834Z","title":null,"venue":null,"work_id":"951257bc-9006-4706-8c4e-16e5198370cb","year":2023},"citing_paper":{"arxiv_id":"2412.14605","last_updated":"2024-12-19T07:53:24Z","snapshot_observed_at":"2026-08-15T14:49:34.886847Z","submitted_at":"2024-12-19T07:53:24Z","title":"Averaging antisymmetric infinitesimal bialgebra and perm bialgebras","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-11T12:15:28.026618Z"},"links":{"citing_paper":"/paper/2412.14605"},"observation_digest":"sha256:26db99281e355dda28f412010c31ffce6efde0026a32e148ef5ed3316732743e","observation_id":"80b435a7-69d2-4e6e-a7a8-956d4bece05b","resolution":{"observed_at":"2026-08-11T12:15:28.345660Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-11T12:15:28.324160Z","title":null,"venue":null,"work_id":"7d595dac-f123-4d44-9336-59f64c5e6973","year":2025},"citing_paper":{"arxiv_id":"2412.14605","last_updated":"2024-12-19T07:53:24Z","snapshot_observed_at":"2026-08-15T14:49:34.886847Z","submitted_at":"2024-12-19T07:53:24Z","title":"Averaging antisymmetric infinitesimal bialgebra and perm bialgebras","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-11T12:15:28.031642Z"},"links":{"citing_paper":"/paper/2412.14605"},"observation_digest":"sha256:269a8eb4f5efe87fd2dbd820a0e4956f2524bcb7f23d3416f7c02eb8d615605b","observation_id":"15eda8fd-2187-43f8-b33d-93178a50e4dc","resolution":{"observed_at":"2026-08-11T12:15:28.329980Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-11T12:15:28.306833Z","title":"Miller, Averaging and Reynolds operators on Banach algebra I, Repre sentation by derivation and an- tiderivations, J","venue":null,"work_id":"68f8e8df-f9cd-410b-a287-f7c9ac6e0cf3","year":1966},"citing_paper":{"arxiv_id":"2412.14605","last_updated":"2024-12-19T07:53:24Z","snapshot_observed_at":"2026-08-15T14:49:34.886847Z","submitted_at":"2024-12-19T07:53:24Z","title":"Averaging antisymmetric infinitesimal bialgebra and perm bialgebras","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-11T12:15:28.036347Z"},"links":{"citing_paper":"/paper/2412.14605"},"observation_digest":"sha256:39b94b18a7437a69314ce3d47136fc5d89a2c7ef53b585e1db01ecd1c0cc8ef0","observation_id":"67955cbc-6f28-44e1-9b23-f8475a2e58ca","resolution":{"observed_at":"2026-08-11T12:15:28.312632Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-11T12:15:28.289260Z","title":"Moy, Characterizations of conditional expectation as a transfo rmation on function spaces , Paciﬁc J","venue":null,"work_id":"1d35da6b-5dc5-4859-a724-1ace401bf072","year":1954},"citing_paper":{"arxiv_id":"2412.14605","last_updated":"2024-12-19T07:53:24Z","snapshot_observed_at":"2026-08-15T14:49:34.886847Z","submitted_at":"2024-12-19T07:53:24Z","title":"Averaging antisymmetric infinitesimal bialgebra and perm bialgebras","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-11T12:15:28.040923Z"},"links":{"citing_paper":"/paper/2412.14605"},"observation_digest":"sha256:9df0f889ae35fbe2b3917261c5ad059f737f96276ef8ca319cd8c9c25dbb85b0","observation_id":"116243e0-651f-49b3-8a5e-33b901b4e18a","resolution":{"observed_at":"2026-08-11T12:15:28.295292Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-11T12:15:28.273221Z","title":null,"venue":null,"work_id":"9d2edad7-ba88-4f53-b7cb-f070e6e02afc","year":2015},"citing_paper":{"arxiv_id":"2412.14605","last_updated":"2024-12-19T07:53:24Z","snapshot_observed_at":"2026-08-15T14:49:34.886847Z","submitted_at":"2024-12-19T07:53:24Z","title":"Averaging antisymmetric infinitesimal bialgebra and perm bialgebras","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-11T12:15:28.046031Z"},"links":{"citing_paper":"/paper/2412.14605"},"observation_digest":"sha256:b846019a4d2a988dc91b56c0d0f2a87e160834741cf89eb4b6c39cd6e45be3b0","observation_id":"97bb5bc6-9e71-46cf-a2c3-ebd798064c9e","resolution":{"observed_at":"2026-08-11T12:15:28.278090Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-11T12:15:28.051468Z","title":"Reshetikhin, M.A","venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"2412.14605","last_updated":"2024-12-19T07:53:24Z","snapshot_observed_at":"2026-08-15T14:49:34.886847Z","submitted_at":"2024-12-19T07:53:24Z","title":"Averaging antisymmetric infinitesimal bialgebra and perm bialgebras","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-11T12:15:28.051468Z"},"links":{"citing_paper":"/paper/2412.14605"},"observation_digest":"sha256:ba13b455e08044b95b11ff9597cf8ecdc53c2161e2ac566aa8aa2fbced9a460e","observation_id":"edacaaca-7be9-47e3-908d-ab31e0b62181","resolution":{"observed_at":"2026-08-11T12:15:28.051468Z","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":"2026-08-11T12:15:28.244630Z","title":"Reynolds, On the dynamic theory of incompressible viscous ﬂuids and th e determination of the criterion, Phil","venue":null,"work_id":"390cfcae-c99f-4090-a9be-1279c85207c2","year":null},"citing_paper":{"arxiv_id":"2412.14605","last_updated":"2024-12-19T07:53:24Z","snapshot_observed_at":"2026-08-15T14:49:34.886847Z","submitted_at":"2024-12-19T07:53:24Z","title":"Averaging antisymmetric infinitesimal bialgebra and perm bialgebras","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-11T12:15:28.056127Z"},"links":{"citing_paper":"/paper/2412.14605"},"observation_digest":"sha256:b29e93e13d4a47eb652548b290b663f76088ceea788453d0ad6055937f7c5c11","observation_id":"1c2ece25-083e-444a-882e-a50a05f20d95","resolution":{"observed_at":"2026-08-11T12:15:28.249970Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-11T12:15:28.227816Z","title":"Rota, Reynolds operators, Proceedings of Symposia in Applied Mathematics, V ol","venue":null,"work_id":"c3e59b76-0a95-4645-92d9-9c8d0d293cfc","year":1964},"citing_paper":{"arxiv_id":"2412.14605","last_updated":"2024-12-19T07:53:24Z","snapshot_observed_at":"2026-08-15T14:49:34.886847Z","submitted_at":"2024-12-19T07:53:24Z","title":"Averaging antisymmetric infinitesimal bialgebra and perm bialgebras","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-11T12:15:28.060891Z"},"links":{"citing_paper":"/paper/2412.14605"},"observation_digest":"sha256:1e264e3925205e9c7b5c905e31d55aeba70f24dc738fa99e6514c5f92510b1ab","observation_id":"1cf63f76-d587-43e8-8254-372feb0d1359","resolution":{"observed_at":"2026-08-11T12:15:28.233371Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-11T12:15:28.210785Z","title":"Sheng, R","venue":null,"work_id":"fce51ae9-2e11-4995-ba27-80ab650bb3fc","year":2021},"citing_paper":{"arxiv_id":"2412.14605","last_updated":"2024-12-19T07:53:24Z","snapshot_observed_at":"2026-08-15T14:49:34.886847Z","submitted_at":"2024-12-19T07:53:24Z","title":"Averaging antisymmetric infinitesimal bialgebra and perm bialgebras","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-11T12:15:28.065756Z"},"links":{"citing_paper":"/paper/2412.14605"},"observation_digest":"sha256:2e6c5eb55bb8f934c8fe31141685725c6f632908f7eea1e61e8e8b62aaa9ba2d","observation_id":"96667973-9a0a-40a8-a881-0f8df036ae52","resolution":{"observed_at":"2026-08-11T12:15:28.215952Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-11T12:15:28.193077Z","title":"Sheng, Y","venue":null,"work_id":"9719ee8b-4403-4aa0-88f7-46c0b8d78aa4","year":2023},"citing_paper":{"arxiv_id":"2412.14605","last_updated":"2024-12-19T07:53:24Z","snapshot_observed_at":"2026-08-15T14:49:34.886847Z","submitted_at":"2024-12-19T07:53:24Z","title":"Averaging antisymmetric infinitesimal bialgebra and perm bialgebras","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-11T12:15:28.070609Z"},"links":{"citing_paper":"/paper/2412.14605"},"observation_digest":"sha256:c43e8fef77345aeace279f8d625ea32495e357c62d4a0b1e371804b4342f33fd","observation_id":"97f996a0-a3b9-4338-b761-6ba6a6d01357","resolution":{"observed_at":"2026-08-11T12:15:28.198881Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-11T12:15:28.176369Z","title":"Triki, Extensions of positive projections and averaging operator s, J","venue":null,"work_id":"29235e44-2a2c-469d-8fcb-67013b7c462f","year":1990},"citing_paper":{"arxiv_id":"2412.14605","last_updated":"2024-12-19T07:53:24Z","snapshot_observed_at":"2026-08-15T14:49:34.886847Z","submitted_at":"2024-12-19T07:53:24Z","title":"Averaging antisymmetric infinitesimal bialgebra and perm bialgebras","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-11T12:15:28.075528Z"},"links":{"citing_paper":"/paper/2412.14605"},"observation_digest":"sha256:e377b1eb95e9cf0391881ce08902dcca136b0e51c768c0459610d1f237752fdc","observation_id":"f1a3d26b-8ae8-4e7c-99ce-7876d8007ccc","resolution":{"observed_at":"2026-08-11T12:15:28.181809Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2009.11618","last_updated":"2020-09-24T11:49:40Z","snapshot_observed_at":"2026-08-14T13:19:38.451634Z","submitted_at":"2020-09-24T11:49:40Z","title":"Cohomology theory of averaging algebras, $L_\\infty$-structures and homotopy averaging algebras","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2009.11618","snapshot_observed_at":"2026-08-11T12:15:28.081143Z","title":"Wang, G, Zhou, Cohomology theory of averaging algebras, L ∞-structures and homotopy averaging algebras, arXiv:2009.11618","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2412.14605","last_updated":"2024-12-19T07:53:24Z","snapshot_observed_at":"2026-08-15T14:49:34.886847Z","submitted_at":"2024-12-19T07:53:24Z","title":"Averaging antisymmetric infinitesimal bialgebra and perm bialgebras","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-11T12:15:28.081143Z"},"links":{"cited_paper":"/paper/2009.11618","citing_paper":"/paper/2412.14605"},"observation_digest":"sha256:94eff0a3d1eddbffee60585db8e88319109748162838e31c8d4d57927d0a89d1","observation_id":"8679cce0-96bb-4a96-9673-63f296305b92","resolution":{"observed_at":"2026-08-11T12:15:28.081143Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2412.14605","last_updated":"2024-12-19T07:53:24Z","latest_version":1,"primary_category":"math.RA","snapshot_observed_at":"2026-08-15T14:49:34.886847Z","submitted_at":"2024-12-19T07:53:24Z","title":"Averaging antisymmetric infinitesimal bialgebra and perm bialgebras"},"reference_resolution":{"displayed":31,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":10,"verified_exact":1,"verified_fuzzy":20},"total_outbound_references":31},"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":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"thesis":"As of 21 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 0 inbound Pith citation observations for arXiv:2412.14605."}