{"as_of":"2026-08-19T18:14:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:8b5a48f17aa7389092c95776df5a84194c36bb4b5aaecd8656cd81958ee8f0cf","coverage":[{"denominator":41,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":41,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T17:06:40.469953Z","state":"measured"},{"denominator":41,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":41,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-19T06:32:44.657259+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/2508.18658/citation-record","integrity":"/paper/2508.18658/integrity","json":"/paper/2508.18658/citation-record.json","paper":"/paper/2508.18658"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T17:06:41.003255Z","title":null,"venue":null,"work_id":"19444a72-c287-4155-8975-239797c04599","year":2010},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.337370Z"},"links":{"citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:b08c9bb1bd99d7c656cd4550feeaa6b3cc7ada13374d7d0c363f845fb993426b","observation_id":"f2dd5c19-612c-404c-b2d5-cd2509a53ea0","resolution":{"observed_at":"2026-08-15T17:06:41.007008Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T17:06:40.988307Z","title":"Brouder, Trees, Renormalization and Di fferential Equations, BIT Numerical Mathematics 44 (2004), 425-438","venue":null,"work_id":"20600e0d-b45f-4342-bfb1-3ee5844be784","year":2004},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.341531Z"},"links":{"citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:5c520df462c144c5faae9595a72a13f2d6bab79d1a6c9641c50cc379d62e3ece","observation_id":"98dd6561-2237-4fc0-9682-a87ff78ee3a1","resolution":{"observed_at":"2026-08-15T17:06:40.992128Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T17:06:40.977125Z","title":"Brouder, A","venue":null,"work_id":"d29f5bcc-b682-409b-ae46-3116ae8caaa1","year":2010},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.344902Z"},"links":{"citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:3a6fd5758758c782d55af02d699cc0af4a42f294bede43f5b6e7642e4854c60e","observation_id":"8dac6d62-6752-43ce-8f7e-cab6a47ea91b","resolution":{"observed_at":"2026-08-15T17:06:40.980585Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T17:06:40.963485Z","title":"Bruned, M","venue":null,"work_id":"9212c13e-10bb-4d41-9892-c74ea6025caf","year":2019},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.348368Z"},"links":{"citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:b15ea6165318fb9f46d8d789962a4460f489187552b95166a8617a6c0d424350","observation_id":"f476ebf3-05c2-444f-9356-d876c43f6baa","resolution":{"observed_at":"2026-08-15T17:06:40.967004Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T17:06:40.949711Z","title":"Connes and D","venue":null,"work_id":"79f05031-19f4-4078-ad4e-695cc63e6069","year":1998},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.351422Z"},"links":{"citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:10a4c8148541308db376fcd94f9381e513878147094b9d0350b108fa4f25a1a7","observation_id":"b4ae513c-971f-4b56-8a1c-bc297aa1be15","resolution":{"observed_at":"2026-08-15T17:06:40.954606Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T17:06:40.936203Z","title":"Clavier, L","venue":null,"work_id":"7be1c659-281a-48ef-99eb-920b63c85bac","year":2020},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.354577Z"},"links":{"citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:61d5676c31a8057eac9ad11aad95404011041f63e0430f858d4152113bc523e3","observation_id":"f026471a-e859-4aaf-8441-df051f1d24c1","resolution":{"observed_at":"2026-08-15T17:06:40.940191Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T17:06:40.923960Z","title":"Chapoton and M","venue":null,"work_id":"0fc2d6e4-1968-4d22-91a5-dcb761a7773d","year":2001},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.358456Z"},"links":{"citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:0781737a10f3d7644867eca91127dec387850314aa981270772c8959f56805c4","observation_id":"c6564863-f10a-492d-8261-8f4607f57145","resolution":{"observed_at":"2026-08-15T17:06:40.927793Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T17:06:40.912862Z","title":"Chakraborty and F","venue":null,"work_id":"0ebd1eb3-d665-420d-b14c-902896f43d30","year":2025},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.361895Z"},"links":{"citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:7831f556031799df6f46c3e0e40a2291f7a1ea06a1f2dad04e6e7c30b05ea5e7","observation_id":"28a907a4-561f-484f-a805-0b1d099c3a35","resolution":{"observed_at":"2026-08-15T17:06:40.916243Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T17:06:40.900997Z","title":"Foissy, Introduction to Hopf algebra of rooted trees, URL: http: //loic.foissy.free.fr/pageperso/p11.pdf 6, 17, 19","venue":null,"work_id":"a5f45785-ae9c-4829-9d69-61c219dd22ee","year":null},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.365203Z"},"links":{"citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:dfe4c60dcfb9f3fb776fbc8c6da73b45bd29d88d42513e4a5ab08aa72ec38822","observation_id":"dc0d96eb-82d0-4d6c-98b1-941fe0023b25","resolution":{"observed_at":"2026-08-15T17:06:40.904958Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T17:06:40.888509Z","title":"Foissy, Les alg `ebres de Hopf des arbres enracin ´es d ´ecor´es","venue":null,"work_id":"3e8c49ec-fc69-4f09-abfd-bb78a369a79f","year":2002},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.368861Z"},"links":{"citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:d71b3ff026f7314b0fe806fba0f5718df918371a38a527e474f9a75ed8106663","observation_id":"ce0eb6e8-adc0-4377-b5f3-816c1bd100ee","resolution":{"observed_at":"2026-08-15T17:06:40.892757Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T17:06:40.872363Z","title":"Foissy, Algebraic structures on typed decorated rooted trees, SIGMA 17 (2021), 086, 28 pages","venue":null,"work_id":"06a75f00-1e5c-4257-a68b-bcfa4934e1f8","year":2021},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.372525Z"},"links":{"citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:1234d195f641f8113c9f9c210fa7dfa256f800ee60d3fae8415e975136615af3","observation_id":"b9150f9e-9c06-4bc5-bf1d-2df7d6576faf","resolution":{"observed_at":"2026-08-15T17:06:40.876681Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2501.07009","last_updated":"2025-01-13T02:10:07Z","snapshot_observed_at":"2026-08-11T06:57:48.209269Z","submitted_at":"2025-01-13T02:10:07Z","title":"Species of Rota-Baxter algebras by rooted trees, twisted bialgebras and Fock functors","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.07009","snapshot_observed_at":"2026-08-15T17:06:40.376313Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.376313Z"},"links":{"cited_paper":"/paper/2501.07009","citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:4e057d6a60d955f78ac64e0a3c82df6ec848828d817d6b248c0806fcaa3a5d34","observation_id":"707c3379-4147-4c4c-b8fa-fb553478b483","resolution":{"observed_at":"2026-08-15T17:06:40.376313Z","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":"2026-08-15T17:06:40.858429Z","title":"Grossman and R","venue":null,"work_id":"762bf955-3242-4381-b76c-0ba1b9b47959","year":1989},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.379919Z"},"links":{"citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:362fc4dbd8af86512aa57673e65ae3ab1036f38303221adc8160369a838ae38c","observation_id":"a34110ef-a507-44c5-a63a-786dfd8a9b46","resolution":{"observed_at":"2026-08-15T17:06:40.863071Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T17:06:40.845026Z","title":"Grossman and R","venue":null,"work_id":"024793d9-da14-4d0c-9270-c049dc35e9da","year":2005},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.383257Z"},"links":{"citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:6ba6539acc4f1bcd87370466ceb2290143d37d3485b3601eb308d5d493242ae7","observation_id":"815dc93d-54c7-4cbb-a3bf-d1670d301ac7","resolution":{"observed_at":"2026-08-15T17:06:40.849179Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T17:06:40.831239Z","title":"Guo, Operated semigroups, Motzkin paths and rooted trees, J","venue":null,"work_id":"1f50eaca-c102-4d74-9cfa-d16c33b82187","year":2009},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.386329Z"},"links":{"citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:36dcdaef0e015206480fdec58d6be6454ab51e7d219383d897d0876111e85504","observation_id":"8ae8505f-2546-4223-8d40-fc6f253e0b76","resolution":{"observed_at":"2026-08-15T17:06:40.836474Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T17:06:40.818680Z","title":null,"venue":null,"work_id":"75fad33d-0f24-4ec0-a932-c3181388cf2f","year":2011},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.389772Z"},"links":{"citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:8d4e0ef1c6e35ade3c9b77d1d861aad46be45bc3c53d680ab2944629213b3dd9","observation_id":"1ec9e1f2-d0dc-4666-976e-ecf077b11132","resolution":{"observed_at":"2026-08-15T17:06:40.822894Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T17:06:40.807307Z","title":null,"venue":null,"work_id":"5b0ac85a-6c82-4a48-ba27-efa17c13f711","year":2021},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.393004Z"},"links":{"citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:e7fa944d8bea26282c6aa921d943e23bce6e2f73879be729ad223e8d228789b6","observation_id":"b7edef94-4624-459e-9ed2-816252f9accb","resolution":{"observed_at":"2026-08-15T17:06:40.811378Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T17:06:40.796211Z","title":"Goncharov, Rota-Baxter operators on cocommutative Hopf algebras, J","venue":null,"work_id":"e248c3e9-6fdd-4048-b9ab-9424b699a2f2","year":2021},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.395989Z"},"links":{"citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:8c563951de6d23b3649f713d8080238ddea04cf64bf2246c8aec22a58b63eb6a","observation_id":"8c787733-0a4e-4b39-bbe0-1bf9e9cf49c0","resolution":{"observed_at":"2026-08-15T17:06:40.800153Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T17:06:40.782655Z","title":null,"venue":null,"work_id":"36305930-9b8b-498f-8b44-070a91e39079","year":1956},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.399237Z"},"links":{"citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:e98234b935ab7351e9561a270b54f8ae600d468fc82c1a8054a613b6522df30e","observation_id":"c0f9d783-8f00-44d8-93bb-d3c472aaf94a","resolution":{"observed_at":"2026-08-15T17:06:40.786817Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T17:06:40.768231Z","title":"Holtkamp, Comparison of Hopf algebras on trees, Arch","venue":null,"work_id":"dfeed8a9-6452-4519-ad33-a729b04d90da","year":2003},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.402777Z"},"links":{"citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:d99c419498794b10f67cea034289c7a12f929bca508246d519d5270ac1978ead","observation_id":"3ae64d0d-c96c-4086-8ee9-f761976484dc","resolution":{"observed_at":"2026-08-15T17:06:40.772624Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T17:06:40.755155Z","title":"Kock, Categorification of Hopf algebras of rooted trees, Cent","venue":null,"work_id":"11c10eed-af4b-4f95-b813-bc87aa89aa67","year":2013},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.405902Z"},"links":{"citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:a5e7fba925fb40c3b637ce7c213ca242ee512dbf2d643851d1b79acf43b9f9a2","observation_id":"29947fb1-cd0b-436d-bb02-e61092d73865","resolution":{"observed_at":"2026-08-15T17:06:40.759115Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T17:06:40.742980Z","title":"Kreimer, On the Hopf algebra structure of perturbative quantum field theories, Adv","venue":null,"work_id":"58d73f7c-a9a3-4a2b-9de0-e02784fc8432","year":1998},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.409198Z"},"links":{"citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:937ce0e0a7bee9e20732e66e72d89a004fb4eb3420d54ec6fff8be10ce1a3ae3","observation_id":"710e4e96-12ed-44a6-9731-ed374ad2be3e","resolution":{"observed_at":"2026-08-15T17:06:40.746754Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T17:06:40.730659Z","title":null,"venue":null,"work_id":"050759a0-affd-446b-b0aa-eeea2c788801","year":1960},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.412161Z"},"links":{"citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:85fd5455d367f0a40555478e987b9ea745a170e2acbda65a88a096202201701d","observation_id":"803b2f40-f066-44df-9dbc-0349218e3b51","resolution":{"observed_at":"2026-08-15T17:06:40.734860Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T17:06:40.718364Z","title":"Laan and I","venue":null,"work_id":"1d7e7675-c251-48f6-bfd8-9048f0f3c938","year":2006},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.415092Z"},"links":{"citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:3beb5350e6b2cc8d3e9cc5a65a484de5ef53d15d189af6f6ab22f4d85ab987ea","observation_id":"00bad6d5-be06-4367-8d59-b91fa5143cbb","resolution":{"observed_at":"2026-08-15T17:06:40.722147Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T17:06:40.704596Z","title":"Lundervold, H","venue":null,"work_id":"bffdc5ec-0a29-4617-b5ce-11bca6a156c1","year":2011},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.418160Z"},"links":{"citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:3673f3ff4a95f7b5b88c35e9a10177ab53ed39c1969561afa0d8d5e05ae26765","observation_id":"7eecbdfd-83d2-41c5-ae81-4a88e3b37dc1","resolution":{"observed_at":"2026-08-15T17:06:40.709767Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T17:06:40.693733Z","title":"Loday, Cyclic Homology, Springer-Verlag, Berlin, 1992","venue":null,"work_id":"0feaa61e-4b34-4448-a936-9a1d73d65902","year":1992},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.421395Z"},"links":{"citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:acb2057909b91e6569a231b1582f5756cdf91a5ea270f7e1ac684ca1b9c7a296","observation_id":"52e8d131-3f9f-45d2-8491-b71d44996756","resolution":{"observed_at":"2026-08-15T17:06:40.696973Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T17:06:40.683447Z","title":"Loday and M","venue":null,"work_id":"9eada52e-6da0-44c9-8126-aa0aee564abd","year":1998},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.424447Z"},"links":{"citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:537598ce9dac2a4f45a70d7b8b0190bc1d4d92c101de246965a401e05a1d8ae9","observation_id":"c71addc7-db6a-46f2-a388-c3c958bcc5f2","resolution":{"observed_at":"2026-08-15T17:06:40.687395Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T17:06:40.673157Z","title":"Murua, The Hopf algebra of rooted trees, free Lie algebras, and Lie series, Found Comput Math 6, (2006) 387-426","venue":null,"work_id":"a061e570-c8a9-49bf-91a8-65d253e3ab7f","year":2006},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.427638Z"},"links":{"citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:6723dddb5db4754f3661037618b9426938501c62fde2c07e28b5474f19623ab7","observation_id":"662524d8-dc85-49e8-89c2-af94bba21444","resolution":{"observed_at":"2026-08-15T17:06:40.676535Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2306.10270","last_updated":"2023-06-17T06:31:36Z","snapshot_observed_at":"2026-08-16T15:23:10.796089Z","submitted_at":"2023-06-17T06:31:36Z","title":"Old and New Minimalism: a Hopf algebra comparison","version":1},"cited_work":{"arxiv_id":"2306.10270","doi":null,"metadata_source":"pith","pith_arxiv_id":"2306.10270","snapshot_observed_at":"2026-08-15T17:06:40.501323Z","title":"Old and New Minimalism: a Hopf algebra comparison","venue":"cs.CL","work_id":"e96d95ae-6e4f-4121-9354-5e6e46d4d634","year":2023},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.430746Z"},"links":{"cited_paper":"/paper/2306.10270","citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:1e308a979cecebed7df91a696ced5b89ddef7c2ebab2d1e0606e43429219046b","observation_id":"bd18a579-86c1-4ea1-b825-66192917d69f","resolution":{"observed_at":"2026-08-15T17:06:40.507082Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T17:06:40.662548Z","title":"Marcolli, R","venue":null,"work_id":"f1137cb3-4b71-4c73-9fbc-a0b628371e51","year":2025},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.434459Z"},"links":{"citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:247819e1c8844051924ec325b5d3dd82c76534bf9ef568da08c7cd8235267e87","observation_id":"10a81c14-9c2a-4bee-a999-dcf82d8c3914","resolution":{"observed_at":"2026-08-15T17:06:40.665987Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T17:06:40.652238Z","title":"Moerdijk, On the Connes-Kreimer construction of Hopf algebras, Contemp","venue":null,"work_id":"63712581-1e35-4278-bbec-ddafa30982ea","year":2001},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.437566Z"},"links":{"citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:d73f5a3fdf08479a6fcf84ccfa256d881c80d8de8e639ceab2183bff2c8f44d4","observation_id":"1661386b-f5e9-4cac-b653-01f87b1e9fd6","resolution":{"observed_at":"2026-08-15T17:06:40.655811Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T17:06:40.640373Z","title":null,"venue":null,"work_id":"91e2f41d-0c76-4242-9588-47ed9494bc61","year":2020},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.440503Z"},"links":{"citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:86d943932d08253c66ba44e1093e08234479a1732cac8b4fa6f546ff136dcb66","observation_id":"3ac94c7c-2607-49a0-bea4-8bf51ab1fb73","resolution":{"observed_at":"2026-08-15T17:06:40.644577Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T17:06:40.629798Z","title":null,"venue":null,"work_id":"b2b98233-adf2-40a3-a484-48e58ebf0084","year":1997},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.443620Z"},"links":{"citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:6788f2f19489e49fa11ec0aa81062453647a4677c44e22baa9da8bafaca286f1","observation_id":"5a15e3e2-147a-4610-b18b-896756d06b34","resolution":{"observed_at":"2026-08-15T17:06:40.633342Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T17:06:40.617566Z","title":"Takeuchi, Free Hopf algebras generated by coalgebras, J","venue":null,"work_id":"489151b8-4049-4669-b748-ca3ad9778fcc","year":1971},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.446755Z"},"links":{"citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:2d3884dbc9bf356dbb5e53418437de7837fdb3c6e2ca51f29a039c3af1869064","observation_id":"f92006a1-3108-4b8b-bbc8-cc5f8ba47850","resolution":{"observed_at":"2026-08-15T17:06:40.621471Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T17:06:40.607086Z","title":"Vinberg, The theory of homogeneous convex cones, Transl","venue":null,"work_id":"a897525f-4909-42b2-95fe-585fe92b2d3a","year":1963},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.449741Z"},"links":{"citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:36026bd2328223eb44fc3ead737c4ea73a1cf1abb932d89fa25e4152a27520ef","observation_id":"e80a06ac-99e7-48a2-baa5-a06ad71df213","resolution":{"observed_at":"2026-08-15T17:06:40.610765Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T17:06:40.594252Z","title":"Zhang, X","venue":null,"work_id":"0aaae7e7-ad7e-4511-9438-75871dc1847d","year":2016},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.453808Z"},"links":{"citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:8d3972e47c65d59602f4e59d4ba145d8ce82723a2f17b526750f57e70c2b52f0","observation_id":"23a820e4-f30e-43b4-a7db-86c257d21486","resolution":{"observed_at":"2026-08-15T17:06:40.598871Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T17:06:40.579793Z","title":"Zhang, A","venue":null,"work_id":"8abb0488-b241-46de-bf47-1cacf05784f7","year":2022},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.456989Z"},"links":{"citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:e2f6c7e097a753a5b62d8cff7760865695cc989d113b16387b0c4982b62c242a","observation_id":"cfd322b5-a804-46c9-b495-4464e78951ad","resolution":{"observed_at":"2026-08-15T17:06:40.584589Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T17:06:40.567409Z","title":"Algebraic Combin","venue":null,"work_id":"a63a3a16-c09c-4fa9-8ede-a660342c78be","year":2020},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.460088Z"},"links":{"citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:64cbd957a48c45c2c9242110fc55c66903f74ff253a2ed08909ba94aa2242505","observation_id":"ac6abf7a-fdd2-43f2-8188-641774a41d3e","resolution":{"observed_at":"2026-08-15T17:06:40.571025Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T17:06:40.554622Z","title":"Zhang, D","venue":null,"work_id":"d0911baf-342b-4e9f-a9dd-db9e77396870","year":2019},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.463228Z"},"links":{"citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:05026e7c61c2b72a67f37bacc96f360583b97af43c3cf709f41917583be07355","observation_id":"870b81f0-4c8b-4da0-a787-94a4a8630ff7","resolution":{"observed_at":"2026-08-15T17:06:40.558700Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T17:06:40.542318Z","title":"Zhang, X Gao and L Guo, Hopf algebra of multidecorated rooted forests, free matching Rota-Baxter algebras and Gr¨obner-Shirshov bases, Pacific J","venue":null,"work_id":"e9f36975-a536-4419-a2d3-fefc2a6fd7ce","year":2022},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.466787Z"},"links":{"citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:ada31f22f6d422e8cdc4df49bab009e086ed7d78999f6b47c650a5bb4deb0a53","observation_id":"f2d17baa-272d-4598-8ff5-3a14cebedcc0","resolution":{"observed_at":"2026-08-15T17:06:40.546619Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T17:06:40.529459Z","title":"Zheng, Y","venue":null,"work_id":"6338df13-2b40-4006-8c8b-50d68589630a","year":2025},"citing_paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-15T17:06:40.469953Z"},"links":{"citing_paper":"/paper/2508.18658"},"observation_digest":"sha256:6a5662019866524d75ab4df99d41f11873a5919c01adbddc726294cd40a2c43b","observation_id":"10e25ac4-2f74-45a0-a8cc-87f0ca7c4d69","resolution":{"observed_at":"2026-08-15T17:06:40.533657Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2508.18658","last_updated":"2025-08-26T04:04:30Z","latest_version":1,"primary_category":"math.RA","snapshot_observed_at":"2026-08-15T16:52:16.516052Z","submitted_at":"2025-08-26T04:04:30Z","title":"Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach"},"reference_resolution":{"displayed":41,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":8,"verified_exact":1,"verified_fuzzy":32},"total_outbound_references":41},"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":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"thesis":"As of 19 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 0 inbound Pith citation observations for arXiv:2508.18658."}