{"as_of":"2026-08-22T17:32:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:31927282e28c0aa520ab85b2f75d58cc29e826c7c31e5d078a9c118358f53166","coverage":[{"denominator":93,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":93,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-04T14:52:28.806078Z","state":"measured"},{"denominator":95,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":95,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-22T06:32:14.747728+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-30T23:48:18.087365Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-07-01T13:15:45.961982Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"cited_work":{"arxiv_id":"2509.22584","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2509.22584","snapshot_observed_at":"2026-07-24T02:23:50.060455Z","title":"Double categories of open systems: the cospan approach","venue":null,"work_id":"60a98774-15e9-485b-91f5-dca438fca933","year":2025},"citing_paper":{"arxiv_id":"2605.04516","last_updated":"2026-08-14T19:31:57Z","snapshot_observed_at":"2026-08-20T23:09:31.417026Z","submitted_at":"2026-05-06T05:49:02Z","title":"Enhanced $2$-categories of models of sketches as enhanced $2$-categories of algebras over monads","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-05-08T16:36:04.288905Z"},"links":{"cited_paper":"/paper/2509.22584","citing_paper":"/paper/2605.04516"},"observation_digest":"sha256:cfb2df309a496ec030b20e783bdd41ca687f5508916dbff6d40f1e3a94f03677","observation_id":"00c6f491-c932-4294-be27-960c77d3c596","resolution":{"observed_at":"2026-07-24T02:23:50.060455Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"cited_work":{"arxiv_id":"2509.22584","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2509.22584","snapshot_observed_at":"2026-07-24T02:23:50.060455Z","title":"Double categories of open systems: the cospan approach","venue":null,"work_id":"60a98774-15e9-485b-91f5-dca438fca933","year":2025},"citing_paper":{"arxiv_id":"2605.04516","last_updated":"2026-08-14T19:31:57Z","snapshot_observed_at":"2026-08-20T23:09:31.417026Z","submitted_at":"2026-05-06T05:49:02Z","title":"Enhanced $2$-categories of models of sketches as enhanced $2$-categories of algebras over monads","version":2},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-06-30T23:48:18.087365Z"},"links":{"cited_paper":"/paper/2509.22584","citing_paper":"/paper/2605.04516"},"observation_digest":"sha256:2d3739800db5fd6723674b6917f7cb750cdffe72d89b31a630d0842ecd754d14","observation_id":"98f246c4-33d9-4ad1-a63b-cf11dad2ee19","resolution":{"observed_at":"2026-07-24T02:23:50.060455Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2509.22584/citation-record","integrity":"/paper/2509.22584/integrity","json":"/paper/2509.22584/citation-record.json","paper":"/paper/2509.22584"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2301.01445","last_updated":"2024-05-05T21:26:08Z","snapshot_observed_at":"2026-08-17T19:59:14.283648Z","submitted_at":"2023-01-04T04:32:08Z","title":"A compositional account of motifs, mechanisms, and dynamics in biochemical regulatory networks","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2301.01445","snapshot_observed_at":"2026-08-04T14:52:17.019193Z","title":"Aduddell, J","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:17.019193Z"},"links":{"cited_paper":"/paper/2301.01445","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:571414c497a7ad74e31922a97c5b9651304e2b175caed6821be3bd41da3e9ed2","observation_id":"5a011351-7d8f-41e9-a29f-c496a47abc06","resolution":{"observed_at":"2026-08-04T14:52:17.019193Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1809.06940","last_updated":"2018-09-18T21:26:05Z","snapshot_observed_at":"2026-08-15T03:09:21.939924Z","submitted_at":"2018-09-18T21:26:05Z","title":"Cartesian Double Categories with an Emphasis on Characterizing Spans","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1809.06940","snapshot_observed_at":"2026-08-04T14:52:17.099972Z","title":"Aleiferi,Cartesian Double Categories with an Emphasis on Characterizing Spans, Ph.D","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:17.099972Z"},"links":{"cited_paper":"/paper/1809.06940","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:d6abacd718237c415dcd9e8bbb8667a2e932acfe1406990d93500f0cec471717","observation_id":"41ce4943-6079-42f8-b684-c20a2ec6d363","resolution":{"observed_at":"2026-08-04T14:52:17.099972Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:17.187523Z","title":"(Referred to on page 35.)","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:17.187523Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:6b96ffba7daaebdb6bf038e7912362f67432f15562a0673cf35ef5652754f76e","observation_id":"5475a21f-42cc-4082-8629-61b9d30ca6b1","resolution":{"observed_at":"2026-08-04T14:52:17.187523Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:17.338914Z","title":"(Referred to on page 20, 35.)","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:17.338914Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:d7c641337b03dbd04e9554f929e56fdbf89efc9eb3b4279134bcd4c74ba21ba6","observation_id":"c7539788-fcd9-430b-b345-ac6367387846","resolution":{"observed_at":"2026-08-04T14:52:17.338914Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2203.16345","last_updated":"2022-05-07T16:26:09Z","snapshot_observed_at":"2026-08-20T10:49:17.863347Z","submitted_at":"2022-02-28T17:44:55Z","title":"An Algebraic Framework for Structured Epidemic Modeling","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2203.16345","snapshot_observed_at":"2026-08-04T14:52:17.463074Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:17.463074Z"},"links":{"cited_paper":"/paper/2203.16345","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:6417f421d9200b24747ca6f1b582d14da12ef40efa14dbf8e3402044161777fb","observation_id":"708c98d7-6822-4b1e-9bbe-7f61a295060d","resolution":{"observed_at":"2026-08-04T14:52:17.463074Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:17.606120Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:17.606120Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:524161bf70d7bca20e54ea5bf3eb12dcfc86c3d90995c1dbf2224a658e97269a","observation_id":"dbaab4e7-a9d5-4601-9e40-90bc66959044","resolution":{"observed_at":"2026-08-04T14:52:17.606120Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1911.04630","last_updated":"2020-11-10T02:39:53Z","snapshot_observed_at":"2026-08-04T10:31:15.583661Z","submitted_at":"2019-11-12T01:29:09Z","title":"Structured Cospans","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1911.04630","snapshot_observed_at":"2026-08-04T14:52:17.676343Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:17.676343Z"},"links":{"cited_paper":"/paper/1911.04630","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:f59dd0e7e379a183eadd8c6756dc26ad6286baedcd8817ca88537b1f8f7fc637","observation_id":"8bf0c2f8-ba04-4788-b919-e04d2f427ae6","resolution":{"observed_at":"2026-08-04T14:52:17.676343Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:17.816125Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:17.816125Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:0227842a208677b09a9449623dc9bc158c2eb89fea761b658dbc3b44b7aa3d9f","observation_id":"ffacae2a-b4b5-4283-b174-17d51e734b8b","resolution":{"observed_at":"2026-08-04T14:52:17.816125Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2101.09363","last_updated":"2022-08-30T18:32:12Z","snapshot_observed_at":"2026-08-16T18:50:34.343729Z","submitted_at":"2021-01-22T22:18:10Z","title":"Structured versus Decorated Cospans","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2101.09363","snapshot_observed_at":"2026-08-04T14:52:18.044982Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:18.044982Z"},"links":{"cited_paper":"/paper/2101.09363","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:7fbc1e344a72faad0bc33b049c43095693bb7d9d23701ccf6fec86fd2d7ab102","observation_id":"a0f08a3b-7b5f-4482-8784-e3af256260c9","resolution":{"observed_at":"2026-08-04T14:52:18.044982Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1707.08321","last_updated":"2018-06-01T21:02:32Z","snapshot_observed_at":"2026-08-20T07:22:47.065907Z","submitted_at":"2017-07-26T08:45:47Z","title":"Props in Network Theory","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1707.08321","snapshot_observed_at":"2026-08-04T14:52:18.195141Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:18.195141Z"},"links":{"cited_paper":"/paper/1707.08321","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:c1b499fb499b21bd6bc2a3b6af4666d22b572728bf8128f863c98671a7b4d6b5","observation_id":"40adf8a0-01a3-4a95-8700-efbd0994f6db","resolution":{"observed_at":"2026-08-04T14:52:18.195141Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1405.6881","last_updated":"2015-05-20T18:23:43Z","snapshot_observed_at":"2026-08-14T23:32:35.689941Z","submitted_at":"2014-05-27T12:15:54Z","title":"Categories in Control","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1405.6881","snapshot_observed_at":"2026-08-04T14:52:18.317624Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:18.317624Z"},"links":{"cited_paper":"/paper/1405.6881","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:3eaf3896f4dc3054a8763ea115e9f2a89e71f62c1dd1d4ec53d1eab411277547","observation_id":"e46ae5b2-1142-4d2e-a309-139248dbed71","resolution":{"observed_at":"2026-08-04T14:52:18.317624Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1504.05625","last_updated":"2018-11-16T23:07:28Z","snapshot_observed_at":"2026-08-16T04:27:00.273794Z","submitted_at":"2015-04-22T00:40:19Z","title":"A Compositional Framework for Passive Linear Networks","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1504.05625","snapshot_observed_at":"2026-08-04T14:52:18.453716Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:18.453716Z"},"links":{"cited_paper":"/paper/1504.05625","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:6a7f8ef584119e471feb11b6641a010aa2b4a9c45f02dc29261cf1ec7ca142ce","observation_id":"f6b66a3a-6dec-4117-88a4-55e387c42ab0","resolution":{"observed_at":"2026-08-04T14:52:18.453716Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1508.06448","last_updated":"2016-03-22T00:52:25Z","snapshot_observed_at":"2026-08-15T14:30:57.271501Z","submitted_at":"2015-08-26T11:31:07Z","title":"A Compositional Framework for Markov Processes","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1508.06448","snapshot_observed_at":"2026-08-04T14:52:18.633554Z","title":null,"venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:18.633554Z"},"links":{"cited_paper":"/paper/1508.06448","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:67e65e180950fa2c81b3cedeff2f84dd2531898678a388f93a739702a8c33b0c","observation_id":"5a998653-b943-46af-affc-48d249259935","resolution":{"observed_at":"2026-08-04T14:52:18.633554Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2101.04238","last_updated":"2021-04-26T19:04:46Z","snapshot_observed_at":"2026-08-16T18:52:57.287417Z","submitted_at":"2021-01-11T23:42:14Z","title":"Categories of Nets","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2101.04238","snapshot_observed_at":"2026-08-04T14:52:18.761381Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:18.761381Z"},"links":{"cited_paper":"/paper/2101.04238","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:e70e29ba4ec0ff9cd3c07f9ead12619dad0a5ca9dd871b4f53279bd069d7b3e9","observation_id":"862200d4-03c1-4cfe-af20-a0bbe67cae80","resolution":{"observed_at":"2026-08-04T14:52:18.761381Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"0908.2469","last_updated":"2009-08-18T00:47:18Z","snapshot_observed_at":"2026-08-17T11:43:58.867586Z","submitted_at":"2009-08-18T00:47:18Z","title":"A Prehistory of n-Categorical Physics","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0908.2469","snapshot_observed_at":"2026-08-04T14:52:18.846742Z","title":null,"venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:18.846742Z"},"links":{"cited_paper":"/paper/0908.2469","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:4626379cce7cbe5a577cd5b64fec3b82956704439d6c27f5b6f749e166305675","observation_id":"a097ad3d-8872-4842-b4f1-edf5b3b03ff0","resolution":{"observed_at":"2026-08-04T14:52:18.846742Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2211.01290","last_updated":"2023-01-14T01:41:02Z","snapshot_observed_at":"2026-08-16T16:19:26.794028Z","submitted_at":"2022-11-01T16:15:54Z","title":"A Categorical Framework for Modeling with Stock and Flow Diagrams","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2211.01290","snapshot_observed_at":"2026-08-04T14:52:18.990688Z","title":null,"venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:18.990688Z"},"links":{"cited_paper":"/paper/2211.01290","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:5ab0abe7be4df1a5de2ed8736a1f87aa685edca84f8baa75521b7d8f94d641ec","observation_id":"07e01c88-35a1-4166-8219-c662ae4c2333","resolution":{"observed_at":"2026-08-04T14:52:18.990688Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:19.071512Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:19.071512Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:de865befa550e92601163b6cd0aef779731ff55ab8a28652aabc4b4966a2269e","observation_id":"103b2b15-20bf-4ccc-a033-98b3f7c86a9f","resolution":{"observed_at":"2026-08-04T14:52:19.071512Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2111.10315","last_updated":"2023-02-10T00:56:11Z","snapshot_observed_at":"2026-08-16T17:40:38.020602Z","submitted_at":"2021-11-19T16:57:02Z","title":"Compositional Thermostatics","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2111.10315","snapshot_observed_at":"2026-08-04T14:52:19.145851Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:19.145851Z"},"links":{"cited_paper":"/paper/2111.10315","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:dd2de386c996d297f2050e626632c7b1abfecf073e81fb075441408d0c6d53a1","observation_id":"74a3ece8-dd3e-4998-8eb8-c0c62c7f6365","resolution":{"observed_at":"2026-08-04T14:52:19.145851Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1808.05415","last_updated":"2022-07-25T02:08:16Z","snapshot_observed_at":"2026-08-16T03:09:43.428087Z","submitted_at":"2018-08-16T11:04:45Z","title":"Open Petri Nets","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1808.05415","snapshot_observed_at":"2026-08-04T14:52:19.305801Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:19.305801Z"},"links":{"cited_paper":"/paper/1808.05415","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:66b403b3234efa27d93d3d962247d1639d073a0122aa6226f679b6e5c2234b21","observation_id":"677e1a38-b9d4-4391-94be-c3f475525a2b","resolution":{"observed_at":"2026-08-04T14:52:19.305801Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1704.02051","last_updated":"2020-09-08T22:15:53Z","snapshot_observed_at":"2026-08-17T10:56:35.052467Z","submitted_at":"2017-04-06T23:38:44Z","title":"A Compositional Framework for Reaction Networks","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1704.02051","snapshot_observed_at":"2026-08-04T14:52:19.409604Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:19.409604Z"},"links":{"cited_paper":"/paper/1704.02051","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:5f62937aaded74b6ffac3ab687eb4416c32b2a5aefcd2c899cee05dfe27ff260","observation_id":"a3a6b9c4-da86-4ff8-9f12-d6cd192d1ccf","resolution":{"observed_at":"2026-08-04T14:52:19.409604Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"0903.0340","last_updated":"2009-06-06T00:45:58Z","snapshot_observed_at":"2026-08-20T13:54:59.188408Z","submitted_at":"2009-03-02T20:38:42Z","title":"Physics, Topology, Logic and Computation: A Rosetta Stone","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0903.0340","snapshot_observed_at":"2026-08-04T14:52:19.552196Z","title":null,"venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:19.552196Z"},"links":{"cited_paper":"/paper/0903.0340","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:1cb6e0915d7a3134d15a8cc6ec21521189ea17c817b74e9b62755b132dc50d3a","observation_id":"45710931-9039-4589-a40c-817c523d916e","resolution":{"observed_at":"2026-08-04T14:52:19.552196Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1710.11392","last_updated":"2021-03-15T23:00:13Z","snapshot_observed_at":"2026-08-14T20:18:31.931228Z","submitted_at":"2017-10-31T09:51:54Z","title":"Open Systems in Classical Mechanics","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1710.11392","snapshot_observed_at":"2026-08-04T14:52:19.662016Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:19.662016Z"},"links":{"cited_paper":"/paper/1710.11392","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:0ce73a7b4ba8a7df67965a88f81f5d9e2deeb612d7e3558bcaecf49e3471c5f5","observation_id":"7257069f-eab1-4794-b081-eaf79d4f19ff","resolution":{"observed_at":"2026-08-04T14:52:19.662016Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:19.795981Z","title":"Bonchi, P","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:19.795981Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:41af20bb8e35d56f579a04cbe22afdd357cdf5e43f1f63dff18f855ccfcf9ede","observation_id":"b0c9cfd2-7027-4363-ab6e-18ee63d09be1","resolution":{"observed_at":"2026-08-04T14:52:19.795981Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:19.887933Z","title":"Carboni, Matrices, relations, and group representations,J","venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:19.887933Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:06fb391c7b553895df716eacfaae41c2cbf9a8c6dff35079daf83c4398298c07","observation_id":"0dab1f46-3b49-4086-8b33-3715496d5083","resolution":{"observed_at":"2026-08-04T14:52:19.887933Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:19.969969Z","title":"Available at https://catcolab.org/help","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:19.969969Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:7eeb0c74b78c1c2980ab8fe413bc180951ff67ac5946e7228009a08247ad9464","observation_id":"a83c8f98-96f6-4e87-9d0c-04e152ddb0d5","resolution":{"observed_at":"2026-08-04T14:52:19.969969Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:20.101964Z","title":"Available at https://github.com/AlgebraicJulia/Catlab.jl","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:20.101964Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:a1311d56fd2958943995a88fa792b4d4dda575389f152acbdf0f8224db656d2e","observation_id":"c969de5e-a0ba-4857-b04b-61d7c59f5b24","resolution":{"observed_at":"2026-08-04T14:52:20.101964Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1605.08100","last_updated":"2017-09-19T16:58:01Z","snapshot_observed_at":"2026-08-14T21:55:40.778986Z","submitted_at":"2016-05-25T23:07:59Z","title":"A bicategory of decorated cospans","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1605.08100","snapshot_observed_at":"2026-08-04T14:52:20.182291Z","title":"Courser, A bicategory of decorated cospans,Theory Appl","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:20.182291Z"},"links":{"cited_paper":"/paper/1605.08100","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:09194101c20fd6ce1c016374ff3e0564572a9ba79b5fba7158a236e7cf1e7757","observation_id":"d7f125b9-9a17-49cb-8287-a2aa5fcfd545","resolution":{"observed_at":"2026-08-04T14:52:20.182291Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2008.02394","last_updated":"2020-08-05T23:40:35Z","snapshot_observed_at":"2026-08-18T18:43:17.098945Z","submitted_at":"2020-08-05T23:40:35Z","title":"Open Systems: A Double Categorical Perspective","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2008.02394","snapshot_observed_at":"2026-08-04T14:52:20.289078Z","title":"Courser,Open Systems: a Double Categorical Perspective, Ph.D","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:20.289078Z"},"links":{"cited_paper":"/paper/2008.02394","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:f6c343069d185922a225c4ba46202b68bb42897e52ec6c009eb797f41cc14cdc","observation_id":"7817ad45-b02b-471a-8f0c-9b0e35cc4d2c","resolution":{"observed_at":"2026-08-04T14:52:20.289078Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1601.02307","last_updated":"2016-01-30T03:27:44Z","snapshot_observed_at":"2026-08-19T20:24:53.213791Z","submitted_at":"2016-01-11T02:47:33Z","title":"Corelations are the prop for extraspecial commutative Frobenius monoids","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1601.02307","snapshot_observed_at":"2026-08-04T14:52:20.343443Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:20.343443Z"},"links":{"cited_paper":"/paper/1601.02307","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:4bb2c2a04053535075d80154515e4657dbad609213e7a82becd660e4e7b9d79d","observation_id":"67db2cf2-a365-48ca-b305-4aa6d3c0fd88","resolution":{"observed_at":"2026-08-04T14:52:20.343443Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1710.00098","last_updated":"2017-09-29T21:27:24Z","snapshot_observed_at":"2026-08-14T20:28:11.230044Z","submitted_at":"2017-09-29T21:27:24Z","title":"A Compositional Framework for Bond Graphs","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1710.00098","snapshot_observed_at":"2026-08-04T14:52:20.452528Z","title":"Coya, A compositional framework for bond graphs","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:20.452528Z"},"links":{"cited_paper":"/paper/1710.00098","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:5d469c1f86df7c7461ba0473362baacefc77fdcb17446bbc6d3e260d59026f92","observation_id":"6ca974d1-297a-4340-bb61-a9436470f8a7","resolution":{"observed_at":"2026-08-04T14:52:20.452528Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1805.08290","last_updated":"2018-05-21T21:11:01Z","snapshot_observed_at":"2026-08-14T19:12:47.201747Z","submitted_at":"2018-05-21T21:11:01Z","title":"Circuits, Bond Graphs, and Signal-Flow Diagrams: A Categorical Perspective","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1805.08290","snapshot_observed_at":"2026-08-04T14:52:20.654839Z","title":"Coya,Circuits, Bond Graphs, and Signal-Flow Diagrams: A Categorical Perspective, Ph.D","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:20.654839Z"},"links":{"cited_paper":"/paper/1805.08290","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:f1c19d6fa5866434a609ebdd1531afa1269ae1dc94ccc484b23e1a720c9cdc03","observation_id":"e6b6aff8-73ee-4cfa-954c-3abbd19046b8","resolution":{"observed_at":"2026-08-04T14:52:20.654839Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1501.02860","last_updated":"2016-01-09T02:47:42Z","snapshot_observed_at":"2026-08-14T23:04:19.538885Z","submitted_at":"2015-01-13T01:44:10Z","title":"Toric Differential Inclusions and a Proof of the Global Attractor Conjecture","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1501.02860","snapshot_observed_at":"2026-08-04T14:52:20.835536Z","title":"Craciun, Toric differential inclusions and a proof of the Global Attractor Conjecture","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:20.835536Z"},"links":{"cited_paper":"/paper/1501.02860","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:006efe188008df40529892469a5415f5bf339178086c56d1514c337715e792b9","observation_id":"738579bb-58f4-4d0a-832d-f5ee1d903b38","resolution":{"observed_at":"2026-08-04T14:52:20.835536Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2105.07321","last_updated":"2021-05-16T00:50:55Z","snapshot_observed_at":"2026-08-16T18:24:28.996700Z","submitted_at":"2021-05-16T00:50:55Z","title":"A graph-theoretic condition for delay stability of reaction systems","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2105.07321","snapshot_observed_at":"2026-08-04T14:52:20.970315Z","title":"Craciun, M","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:20.970315Z"},"links":{"cited_paper":"/paper/2105.07321","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:fc192b0a11dda4cfebacea34dc56d5eca78d19f3d019806dd385fecabcb46508","observation_id":"1f42ea3a-94c9-45aa-ac80-f92c21ea1e4f","resolution":{"observed_at":"2026-08-04T14:52:20.970315Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:21.157328Z","title":"Craciun, F","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:21.157328Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:0b4e752594856d3b8e52b89358078e1331b214b3bf130a9c8d594b4c8a4897ff","observation_id":"4f4ba75d-b5fe-4eae-b845-4988ff3fbb1f","resolution":{"observed_at":"2026-08-04T14:52:21.157328Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:21.332910Z","title":"Craciun, Y","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:21.332910Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:52835b2838243616d59caa0c6c2c8038721216a295f8dbc00c093f628ab824de","observation_id":"0b96fd76-f904-4c37-91d2-0ba5079cb1e7","resolution":{"observed_at":"2026-08-04T14:52:21.332910Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:21.523972Z","title":"Day and R","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:21.523972Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:085f0446aaba1d4dfb9ac4adcfac26c15c010b94806c5eeb946160d08b6a78ea","observation_id":"d48ac0ae-a389-4c2e-8854-e82541c4fd2b","resolution":{"observed_at":"2026-08-04T14:52:21.523972Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:21.691090Z","title":null,"venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:21.691090Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:12be9026439909b6509442db1c4f4a29ffd0b7fe0bcd9215694533fecdf7091d","observation_id":"85f0292a-0a53-45a6-9317-221e26fbb035","resolution":{"observed_at":"2026-08-04T14:52:21.691090Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:21.847080Z","title":null,"venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:21.847080Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:13708c033430a3374ae61220f71cbd633ea9ddb6988a0674eddd5064003dfc4f","observation_id":"f4363ddd-fc78-4696-863b-d814a747f34a","resolution":{"observed_at":"2026-08-04T14:52:21.847080Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:22.144008Z","title":"Feinberg, Chemical reaction network structure and the stability of complex isothermal reactors: I","venue":null,"work_id":null,"year":1987},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:22.144008Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:392e3d28d9a289bb5561a1b3aa416928c6724013e96f513425d442db6b468422","observation_id":"08ea2d38-903d-4cd4-81d5-420eec30ad76","resolution":{"observed_at":"2026-08-04T14:52:22.144008Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:22.337121Z","title":"Feinberg,Foundations of Chemical Reaction Network Theory, Springer, Berlin, 2019","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:22.337121Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:3b7efa6b4a2509742aa2777fa3ff7d4e5130a841ddf41d8c81897f5fe8df6dcc","observation_id":"39ddacba-b858-480d-9f02-d00dba213d62","resolution":{"observed_at":"2026-08-04T14:52:22.337121Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:22.441600Z","title":null,"venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:22.441600Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:595757288d5528972189c6989cad2e1751577315c03ca032761ad3e464babc67","observation_id":"71558bbe-be5c-4c49-b3e6-f669b50fd2fc","resolution":{"observed_at":"2026-08-04T14:52:22.441600Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1502.00872","last_updated":"2015-08-11T06:41:30Z","snapshot_observed_at":"2026-08-17T05:55:38.900385Z","submitted_at":"2015-02-03T14:26:36Z","title":"Decorated Cospans","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1502.00872","snapshot_observed_at":"2026-08-04T14:52:22.553817Z","title":"Fong, Decorated cospans,Theory Appl","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:22.553817Z"},"links":{"cited_paper":"/paper/1502.00872","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:3819b851287914233e165555a2fe382c02d7802bba999b766f74eab47700d809","observation_id":"62f5bd1f-2a54-48f6-b1da-632a488a895f","resolution":{"observed_at":"2026-08-04T14:52:22.553817Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1609.05382","last_updated":"2016-09-17T19:52:39Z","snapshot_observed_at":"2026-08-14T21:39:23.661452Z","submitted_at":"2016-09-17T19:52:39Z","title":"The Algebra of Open and Interconnected Systems","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1609.05382","snapshot_observed_at":"2026-08-04T14:52:22.732111Z","title":"Fong,The Algebra of Open and Interconnected Systems, Ph.D","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:22.732111Z"},"links":{"cited_paper":"/paper/1609.05382","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:b6f6d62648c3533e59eaabfb35f1d29376dde6ff3659051fd311a1c873bbbd7b","observation_id":"01ced556-6e7f-4f8a-8b37-28af1887f413","resolution":{"observed_at":"2026-08-04T14:52:22.732111Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1510.05076","last_updated":"2016-02-02T19:09:53Z","snapshot_observed_at":"2026-08-17T01:48:00.821827Z","submitted_at":"2015-10-17T06:26:04Z","title":"A categorical approach to open and interconnected dynamical systems","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1510.05076","snapshot_observed_at":"2026-08-04T14:52:22.901899Z","title":null,"venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:22.901899Z"},"links":{"cited_paper":"/paper/1510.05076","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:ab53bda9490c76c8a19756644314c36448b68dd5ab9e7305ba5503a898a3b352","observation_id":"84c8a141-4b62-4b57-abd1-b7b550ef49e8","resolution":{"observed_at":"2026-08-04T14:52:22.901899Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1806.08304","last_updated":"2019-01-18T23:06:25Z","snapshot_observed_at":"2026-08-14T19:00:54.214890Z","submitted_at":"2018-06-21T16:03:04Z","title":"Hypergraph Categories","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1806.08304","snapshot_observed_at":"2026-08-04T14:52:23.081435Z","title":"Fong and D","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:23.081435Z"},"links":{"cited_paper":"/paper/1806.08304","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:79ce16d8f58a4aa60a3ffb7c251bfda7073374a55c5edfae27559955bccdeabf","observation_id":"ede3adb0-aee2-477a-8379-9f100652f063","resolution":{"observed_at":"2026-08-04T14:52:23.081435Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:23.224440Z","title":"Gadducci and R","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:23.224440Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:75f7db2888d4d8b187c1527a76420efc6ea4a9b4a3b37b868d9882aa0a516533","observation_id":"b7777dba-041e-4890-8449-26a210592abd","resolution":{"observed_at":"2026-08-04T14:52:23.224440Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:23.358670Z","title":"Girault and R","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:23.358670Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:13a9d84db6b6637dc39e8859dd8076e206394eeea03f3dc7470cc5f48fad9e8f","observation_id":"fc925c22-4493-41be-a2a9-c58b8bec3ddc","resolution":{"observed_at":"2026-08-04T14:52:23.358670Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:23.448541Z","title":"Grandis and R","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:23.448541Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:0b5d73d0f30c06e10fab886b78b52966a3c992196169a9e6e9f9ae975e29ffe6","observation_id":"c747896f-20a4-4c9a-8ceb-b10483599494","resolution":{"observed_at":"2026-08-04T14:52:23.448541Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:23.597171Z","title":"Grandis and R","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:23.597171Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:dd282fe68371db7583494d9acc06f3141e05841f1cc4fd4a1c2f72fd52038182","observation_id":"80e711dd-e925-4d03-9322-fcfcecf576ac","resolution":{"observed_at":"2026-08-04T14:52:23.597171Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:23.717117Z","title":"Gordon, A","venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:23.717117Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:d7d4c3de6acd955e8dd798bf8fb345a50485d5d5013367807f46c810133bac4b","observation_id":"90e89f11-aeba-4f23-b0de-1f003f6cd373","resolution":{"observed_at":"2026-08-04T14:52:23.717117Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:23.780478Z","title":null,"venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:23.780478Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:10e91903e773316b189cec9d2e9ce190c68e55340ec1dc74f6dbcc3024be4dbd","observation_id":"f0a4dbca-1a17-42f0-80b2-7d5301332584","resolution":{"observed_at":"2026-08-04T14:52:23.780478Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:23.879865Z","title":"Halter and E","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:23.879865Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:b89ce26595329cb1d0372d80119a22480be40a6958aa3b7e6230554f13f6a41a","observation_id":"37b3558c-a029-4cad-a919-c78cdbbd56cd","resolution":{"observed_at":"2026-08-04T14:52:23.879865Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1910.09240","last_updated":"2019-11-24T08:00:57Z","snapshot_observed_at":"2026-08-06T15:57:45.838457Z","submitted_at":"2019-10-21T09:57:16Z","title":"Constructing symmetric monoidal bicategories functorially","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1910.09240","snapshot_observed_at":"2026-08-04T14:52:23.938721Z","title":null,"venue":null,"work_id":null,"year":1910},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:23.938721Z"},"links":{"cited_paper":"/paper/1910.09240","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:ee66dbc57218f88ed4df52d724b760f792ceb5cbcd4485d48832c13870e7ab26","observation_id":"67ccbd1f-1a43-4e61-a6d5-16f6f70b35f0","resolution":{"observed_at":"2026-08-04T14:52:23.938721Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:24.070989Z","title":"Heunen and J","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:24.070989Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:a2b645d7457df9812663162368ebd895079a4d225a89feaff2684fffef53a3dd","observation_id":"b5e1ee11-f876-4c95-8c27-af4a93a55696","resolution":{"observed_at":"2026-08-04T14:52:24.070989Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:24.232550Z","title":"Horn and R","venue":null,"work_id":null,"year":1972},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:24.232550Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:3815e6c9c749ffd14da089145b92c285ced136a8bedf67fea51c709668ab8396","observation_id":"33294fe9-0484-4313-96db-a7436aa970e8","resolution":{"observed_at":"2026-08-04T14:52:24.232550Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:24.324117Z","title":null,"venue":null,"work_id":null,"year":1982},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:24.324117Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:6d50c4ec77e7306522122c315304d0f16128cbca3097aa2742af1b6e197ba713","observation_id":"5b882409-f48e-49de-9430-f46718413da1","resolution":{"observed_at":"2026-08-04T14:52:24.324117Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1406.5942","last_updated":"2015-08-19T08:31:21Z","snapshot_observed_at":"2026-08-14T23:29:23.878445Z","submitted_at":"2014-06-23T15:25:28Z","title":"Finite matrices are complete for (dagger-)hypergraph categories","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1406.5942","snapshot_observed_at":"2026-08-04T14:52:24.476341Z","title":"Kissinger, Finite matrices are complete for (dagger-)hypergraph categories","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:24.476341Z"},"links":{"cited_paper":"/paper/1406.5942","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:2a6cc63a27fbd0879047eaa5d8863980ae5bdcd24677a2da389f19921737b1ed","observation_id":"87dd7697-7a8d-497a-a8f9-cdbb707141a5","resolution":{"observed_at":"2026-08-04T14:52:24.476341Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:24.642773Z","title":"Koch, Petri nets—a mathematical formalism to analyze chemical reaction networks,Mol","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:24.642773Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:9b93a3c74274aa9bfc45351dd8554248d2101bc5e458a1da8069323c75cf82ef","observation_id":"08594ae6-e00a-4d1a-81a9-5b016ab86e09","resolution":{"observed_at":"2026-08-04T14:52:24.642773Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:24.758171Z","title":"Kock,Frobenius Algebras and 2D Topological Quantum Field Theories, Cambridge U","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:24.758171Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:db6f6a96e57bbdda5ca4668f130756c0e92d46cd60ea7eacd1cea27d2bfcfd30","observation_id":"533866b6-bed5-4e24-8e1d-a77beb2ba9b1","resolution":{"observed_at":"2026-08-04T14:52:24.758171Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2005.05108","last_updated":"2023-01-05T17:43:23Z","snapshot_observed_at":"2026-08-15T04:15:04.360562Z","submitted_at":"2020-05-11T13:52:28Z","title":"Whole-grain Petri nets and processes","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2005.05108","snapshot_observed_at":"2026-08-04T14:52:24.875375Z","title":"Kock, Whole-grain Petri nets and processes,J","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:24.875375Z"},"links":{"cited_paper":"/paper/2005.05108","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:2d9de26650226cd05f61dbdcd9a41e3c65c19a5ecefe6d0a8c07577bcf5a1220","observation_id":"8154a597-0864-4040-9e20-e4a27f5dffba","resolution":{"observed_at":"2026-08-04T14:52:24.875375Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:24.994754Z","title":null,"venue":null,"work_id":null,"year":1963},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:24.994754Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:c0219e345f3c5e0df1c36e47ed480527d8bc5316d768a06088a42d0f76bc3ccc","observation_id":"a1962349-7a3a-4803-8fb1-38081330a2be","resolution":{"observed_at":"2026-08-04T14:52:24.994754Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:25.127544Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:25.127544Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:c5372b2ef6dde20a1aba6e885eb5330d0b92623741901d71a04d3b3535fdce7e","observation_id":"5d1ec8fb-1e14-428c-a9a9-55108a42eca0","resolution":{"observed_at":"2026-08-04T14:52:25.127544Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2007.14442","last_updated":"2020-07-28T19:20:36Z","snapshot_observed_at":"2026-08-05T05:05:13.300265Z","submitted_at":"2020-07-28T19:20:36Z","title":"An Algebra of Resource Sharing Machines","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2007.14442","snapshot_observed_at":"2026-08-04T14:52:25.243918Z","title":"Libkind, An algebra of resource sharing machines","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:25.243918Z"},"links":{"cited_paper":"/paper/2007.14442","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:9d475abb5d579c7164c0fc707b5b483328c97aa5e1343a2e887b94b86a7eb075","observation_id":"5fbf2ec9-e36c-4e6e-89f3-1ce06a85fce2","resolution":{"observed_at":"2026-08-04T14:52:25.243918Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.18329","last_updated":"2025-05-28T19:20:26Z","snapshot_observed_at":"2026-08-18T04:12:22.346693Z","submitted_at":"2025-05-23T19:35:57Z","title":"Towards a double operadic theory of systems","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.18329","snapshot_observed_at":"2026-08-04T14:52:25.333811Z","title":"Libkind and D","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:25.333811Z"},"links":{"cited_paper":"/paper/2505.18329","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:502054fe7f15d33d86a965e3ada614a3772feaf9d3d5551f8bf576e0c9a367e5","observation_id":"ddfa3600-2290-4b02-b4b2-7005102b43df","resolution":{"observed_at":"2026-08-04T14:52:25.333811Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2310.06088","last_updated":"2023-04-01T14:50:54Z","snapshot_observed_at":"2026-08-16T15:43:32.231378Z","submitted_at":"2023-04-01T14:50:54Z","title":"Relational Composition of Physical Systems: A Categorical Approach","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2310.06088","snapshot_observed_at":"2026-08-04T14:52:25.424360Z","title":"Lynch,Relational Composition of Physical Systems: A Categorical Approach, M.Sc","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:25.424360Z"},"links":{"cited_paper":"/paper/2310.06088","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:630b3fa5cd5578549b1251c4a9b6f8274c77515a65359614a9ccbf0d0a5544ad","observation_id":"527f3eb5-e13e-4ce3-beec-9fb9b0d4c993","resolution":{"observed_at":"2026-08-04T14:52:25.424360Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1904.09091","last_updated":"2020-10-30T21:52:29Z","snapshot_observed_at":"2026-08-15T06:51:06.207449Z","submitted_at":"2019-04-19T06:29:46Z","title":"Petri Nets Based on Lawvere Theories","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1904.09091","snapshot_observed_at":"2026-08-04T14:52:25.522445Z","title":"Master, Petri nets based on Lawvere theories,Math","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:25.522445Z"},"links":{"cited_paper":"/paper/1904.09091","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:f65f5af6fde3ebf55cf7552d8fd9cef3caf8e4d800a975003b44d8233ada3685","observation_id":"e579c371-5e2e-4a5a-bf7c-28cb2c767393","resolution":{"observed_at":"2026-08-04T14:52:25.522445Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:25.624822Z","title":"McCrudden, Balanced coalgebroids,Theory Appl","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:25.624822Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:6858c6aefc0332e7ef058496184e3d26b469b0f8aa42d9a9941f82b21181fac6","observation_id":"ebf3f16a-8952-4992-9ad4-17634b138ae0","resolution":{"observed_at":"2026-08-04T14:52:25.624822Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:25.768972Z","title":"Available at https://modelcollab.usask.ca/","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":68,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:25.768972Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:72269b7bb43554f50c1a1d5bf7db24ac68d88fe516bbde56bdced3bd7de86d48","observation_id":"ef0e4cdf-94a1-45fe-bec7-9c391a26ca12","resolution":{"observed_at":"2026-08-04T14:52:25.768972Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:25.888144Z","title":"Morton, Belief propagation in monoidal categories,Electron","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":69,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:25.888144Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:c38b6a310df0569ec650fd6b180d70bb6403faf14f86babbbba8c968409f94e4","observation_id":"d43be3e9-7fe1-409a-bab9-db274791e05d","resolution":{"observed_at":"2026-08-04T14:52:25.888144Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:25.973047Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":70,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:25.973047Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:56c7b845adaae9c65c0646dda516e6be49d7947a43a70931fa1cb2994c8d2c94","observation_id":"314daff3-c99a-45c9-adc7-b0e90d40472f","resolution":{"observed_at":"2026-08-04T14:52:25.973047Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:26.195589Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":71,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:26.195589Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:f23b83489f779d0dd03d37198da78af249c1fd9b59ed30497e80da8f00c689a7","observation_id":"101a82dc-c187-4391-b475-0c523b1a0beb","resolution":{"observed_at":"2026-08-04T14:52:26.195589Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1201.3789","last_updated":"2012-01-18T14:04:57Z","snapshot_observed_at":"2026-08-20T03:46:28.027748Z","submitted_at":"2012-01-18T14:04:57Z","title":"Span, Cospan, and Other Double Categories","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1201.3789","snapshot_observed_at":"2026-08-04T14:52:26.279762Z","title":"Niefield, Span, cospan, and other double categories,Theory Appl","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":72,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:26.279762Z"},"links":{"cited_paper":"/paper/1201.3789","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:b3754542bd893c0738adaed0cb6b8b4735e15dd8cfd9a3337a72b7cc9758aa0d","observation_id":"f262fb4d-d14d-486b-bb7c-6655f7b14d65","resolution":{"observed_at":"2026-08-04T14:52:26.279762Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:26.437251Z","title":"Par ´e, Superspans, talk at the Octoberfest, Ottawa, 2015","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":73,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:26.437251Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:53545a18d8642a6983862c7d5d54e2b728c974d636b4b7611c3d1e2cd4325424","observation_id":"d27001d0-feae-45c4-885e-5c24494c0423","resolution":{"observed_at":"2026-08-04T14:52:26.437251Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2304.00447","last_updated":"2023-12-14T12:44:17Z","snapshot_observed_at":"2026-08-20T15:38:33.599863Z","submitted_at":"2023-04-02T04:36:49Z","title":"Structured and Decorated Cospans from the Viewpoint of Double Category Theory","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2304.00447","snapshot_observed_at":"2026-08-04T14:52:26.615006Z","title":"Patterson, Structured and decorated cospans from the viewpoint of double category theory,Electron","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":74,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:26.615006Z"},"links":{"cited_paper":"/paper/2304.00447","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:7089f1d77916818da56b1baa304a04327f521f25412809a2fb63e6ed8f023c91","observation_id":"8f02f9ca-1606-43bc-9b14-e8ee1d1e1287","resolution":{"observed_at":"2026-08-04T14:52:26.615006Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:26.811688Z","title":"Patterson and M","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":75,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:26.811688Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:b5e83172a02c864bfed4c179609ce9be46a0c041de5b2a52f723af56f207f451","observation_id":"898d8f93-47b9-4ebb-b7a9-d7378a527d3e","resolution":{"observed_at":"2026-08-04T14:52:26.811688Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:27.016265Z","title":null,"venue":null,"work_id":null,"year":1981},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":76,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:27.016265Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:3b93917542663b47c572d8f204d871c2f3af922e04a8c54b8f2181c8aaba2fa6","observation_id":"42bbc65c-ad60-40c1-a706-5675cb462e48","resolution":{"observed_at":"2026-08-04T14:52:27.016265Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1709.09743","last_updated":"2017-09-29T19:35:18Z","snapshot_observed_at":"2026-08-21T12:20:05.877288Z","submitted_at":"2017-09-27T21:46:15Z","title":"Open Markov Processes and Reaction Networks","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1709.09743","snapshot_observed_at":"2026-08-04T14:52:27.114214Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":77,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:27.114214Z"},"links":{"cited_paper":"/paper/1709.09743","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:bd80087bbb829d7b6de1a43b9cf4a21a4522cab72039c80e758ce15cb8b18f25","observation_id":"18743bbd-cd37-40b6-b8f5-7389a0598a4a","resolution":{"observed_at":"2026-08-04T14:52:27.114214Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1411.6691","last_updated":"2014-11-25T00:24:06Z","snapshot_observed_at":"2026-08-16T18:54:10.317160Z","submitted_at":"2014-11-25T00:24:06Z","title":"On dualizable objects in monoidal bicategories, framed surfaces and the Cobordism Hypothesis","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1411.6691","snapshot_observed_at":"2026-08-04T14:52:27.253659Z","title":"Pstra ¸gowski, On dualizable objects in monoidal bicategories","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":78,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:27.253659Z"},"links":{"cited_paper":"/paper/1411.6691","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:21d9ff443e6faafdf0e8a5cbfec8a5515438ecdce91a1c8d6f223f0fd6c0b695","observation_id":"a99896bc-200f-41e1-9949-72f29887c80b","resolution":{"observed_at":"2026-08-04T14:52:27.253659Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:27.392089Z","title":"Rosebrugh, N","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":79,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:27.392089Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:7a25356c47fe072f54252a275f1a155bba2620e3a678bb4440ace04304cbe7d6","observation_id":"dd40dabf-3112-49e5-b783-a9787074f988","resolution":{"observed_at":"2026-08-04T14:52:27.392089Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:27.542298Z","title":"Selinger, Autonomous categories in whichA A ∗ (extended abstract), talk at QPL 2010","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":80,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:27.542298Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:97f76ec77d64ee8aa3a3f2cbc4b4fb718072bd2a25a32ce12a81d251e09cddfe","observation_id":"d014718a-4fde-4c0a-9d31-f6a086e816e6","resolution":{"observed_at":"2026-08-04T14:52:27.542298Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"0908.3347","last_updated":"2009-08-23T23:53:43Z","snapshot_observed_at":"2026-08-15T05:40:46.262096Z","submitted_at":"2009-08-23T23:53:43Z","title":"A survey of graphical languages for monoidal categories","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0908.3347","snapshot_observed_at":"2026-08-04T14:52:27.675018Z","title":"Selinger, A survey of graphical languages for monoidal categories, inNew Structures for Physics, ed","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":81,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:27.675018Z"},"links":{"cited_paper":"/paper/0908.3347","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:2cb490ffcca2f76b1c6d40459a8514a7a45c65f80c8dc92ec77d7e96161ae0b2","observation_id":"7054ba8b-fe26-4d62-8279-9eafe2cf7c2b","resolution":{"observed_at":"2026-08-04T14:52:27.675018Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"0706.1286","last_updated":"2009-01-09T19:47:32Z","snapshot_observed_at":"2026-08-17T11:50:37.786063Z","submitted_at":"2007-06-09T04:19:34Z","title":"Framed bicategories and monoidal fibrations","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0706.1286","snapshot_observed_at":"2026-08-04T14:52:27.783194Z","title":"Shulman, Framed bicategories and monoidal fibrations,Theory Appl","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":82,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:27.783194Z"},"links":{"cited_paper":"/paper/0706.1286","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:62000fcb7820f693160ebbad1dfd027c4071eae062ed4b1cbc84ba2749d65ac8","observation_id":"8973c746-70a5-4925-9351-d932b8c91f42","resolution":{"observed_at":"2026-08-04T14:52:27.783194Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1004.0993","last_updated":"2010-04-07T02:06:25Z","snapshot_observed_at":"2026-08-15T12:30:32.976451Z","submitted_at":"2010-04-07T02:06:25Z","title":"Constructing symmetric monoidal bicategories","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1004.0993","snapshot_observed_at":"2026-08-04T14:52:27.865484Z","title":"Shulman, Constructing symmetric monoidal bicategories","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":83,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:27.865484Z"},"links":{"cited_paper":"/paper/1004.0993","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:6e5dddf2d85caecfcbff38d6793a2ed34faf3becd75a7cbc79580b1bd826a317","observation_id":"7602aeba-6338-4727-8c82-708e07e5ef24","resolution":{"observed_at":"2026-08-04T14:52:27.865484Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1301.1053","last_updated":"2016-08-19T15:23:40Z","snapshot_observed_at":"2026-08-18T05:52:11.860371Z","submitted_at":"2013-01-06T20:56:39Z","title":"Compact Closed Bicategories","version":7},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1301.1053","snapshot_observed_at":"2026-08-04T14:52:28.054301Z","title":"Stay, Compact closed bicategories,Theory Appl","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":85,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:28.054301Z"},"links":{"cited_paper":"/paper/1301.1053","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:c8a9046855719a65d7e7c5f1a5219029b91aacee8bc67e9c1fa920743ca403e0","observation_id":"8e26c965-9317-4b60-8951-29cc9ae39d3c","resolution":{"observed_at":"2026-08-04T14:52:28.054301Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:28.168695Z","title":"Available at https://algebraicjulia.github.io/StockFlow.jl/","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":86,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:28.168695Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:75d37e1e4c3feed9c9f659b3920e397dc2fa9d661a99d490cfc9e605e01353fe","observation_id":"0d9eb527-3d3e-4e5e-87f5-8414e01b13f6","resolution":{"observed_at":"2026-08-04T14:52:28.168695Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:28.260667Z","title":"Street, Frobenius monads and pseudomonoids,J","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":87,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:28.260667Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:e0fd2172a1393a296c6191d7b2520243ad2dfd4362fb149ee16c4b8c6978a1d3","observation_id":"5d6a29e2-1d22-478c-b35a-edd3335c2054","resolution":{"observed_at":"2026-08-04T14:52:28.260667Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:28.414134Z","title":null,"venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":88,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:28.414134Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:b5170bf35d4f0ad8d34d77b007a992f79dc48f4158515e9a0adaa25f34251399","observation_id":"e313ee28-831a-4db9-9175-3da2ef56ad5c","resolution":{"observed_at":"2026-08-04T14:52:28.414134Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:28.551100Z","title":null,"venue":null,"work_id":null,"year":1982},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":89,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:28.551100Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:68028089eb63a2cc51dda7f31c788e2523292503996cb35a030f7c4d06846e61","observation_id":"f0b26ead-e01e-46d1-b0b3-13d43160f180","resolution":{"observed_at":"2026-08-04T14:52:28.551100Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:28.697264Z","title":null,"venue":null,"work_id":null,"year":1985},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":90,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:28.697264Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:5cfb3d06512534c0dd9c9fdef87176608c1f9d05e9cf082ea142615c01ad8079","observation_id":"cb78c184-510d-4d8b-9da3-27c3db865cf5","resolution":{"observed_at":"2026-08-04T14:52:28.697264Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1512.01602","last_updated":"2017-02-07T14:53:03Z","snapshot_observed_at":"2026-08-20T17:10:33.459573Z","submitted_at":"2015-12-05T00:39:34Z","title":"Operads of Wiring Diagrams","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1512.01602","snapshot_observed_at":"2026-08-04T14:52:28.806078Z","title":"Yau,Operads of Wiring Diagrams, Lecture Notes in Mathematics2192, Springer, Berlin, 2018","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":91,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:28.806078Z"},"links":{"cited_paper":"/paper/1512.01602","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:bf1bbede4d1841fc8a634f1a2d705596e33de399718f30b2e0c4af4c99c00d31","observation_id":"51e10a0c-67ed-4cac-a00b-f833c3bddb43","resolution":{"observed_at":"2026-08-04T14:52:28.806078Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2005.05956","last_updated":"2021-02-04T02:21:46Z","snapshot_observed_at":"2026-08-13T22:44:31.258036Z","submitted_at":"2020-05-12T17:56:31Z","title":"Double Categories of Open Dynamical Systems (Extended Abstract)","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2005.05956","snapshot_observed_at":"2026-08-04T14:52:26.077377Z","title":"(Referred to on page 2.)","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":167,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:26.077377Z"},"links":{"cited_paper":"/paper/2005.05956","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:9e95fdc17f0086b84da35c4034b1ea8d3fdec30697badfd867496debc17280c7","observation_id":"8ebcecde-9446-4748-9717-ea721f7f985c","resolution":{"observed_at":"2026-08-04T14:52:26.077377Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T14:52:21.980588Z","title":"(Referred to on page 2, 42.)","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":377,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:21.980588Z"},"links":{"citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:f4d6216f8c396c941382d324d0616996c474ad2727cef5e1f109a2aa6f547a70","observation_id":"301871e1-a7e2-4353-a6d0-9fcaabe07458","resolution":{"observed_at":"2026-08-04T14:52:21.980588Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1710.11343","last_updated":"2018-11-21T23:00:36Z","snapshot_observed_at":"2026-08-14T20:18:35.597289Z","submitted_at":"2017-10-31T06:27:25Z","title":"Coarse-Graining Open Markov Processes","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1710.11343","snapshot_observed_at":"2026-08-04T14:52:17.904741Z","title":"(Referred to on page 2.)","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach","version":3},"reference_index":1268,"source":"pdf_text","source_observed_at":"2026-08-04T14:52:17.904741Z"},"links":{"cited_paper":"/paper/1710.11343","citing_paper":"/paper/2509.22584"},"observation_digest":"sha256:2366d8636c48b8691fdcea3fec1b954fb366dbd3e0b71dd07a35b377adb90247","observation_id":"ad90acbe-f421-4a8d-8b0f-59aded5d5ed0","resolution":{"observed_at":"2026-08-04T14:52:17.904741Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2509.22584","last_updated":"2026-07-24T13:29:15Z","latest_version":3,"primary_category":"math.CT","snapshot_observed_at":"2026-08-06T13:56:17.301821Z","submitted_at":"2025-09-26T17:04:14Z","title":"Double Categories of Open Systems: the Cospan Approach"},"reference_resolution":{"displayed":93,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":93,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":93},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"thesis":"As of 22 August 2026, this Paper Citation Record lists 93 of 93 outbound references and 2 inbound Pith citation observations for arXiv:2509.22584."}