{"as_of":"2026-08-11T03:37:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:8c79d9bcd59be2dbfe9b7c8ef2751557beb577daf4ad7f6f14d50ac0b69a13d7","coverage":[{"denominator":0,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":5,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":5,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-10T06:31:04.303077+00:00","state":"measured"},{"denominator":5,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":5,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T13:06:16.003692Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":1,"source":"arxiv_reference","source_observed_at":"2026-08-05T02:28:24.338817Z","state":"measured"}],"external_citation_measurements":[{"count":0,"observed_at":"2026-08-05T02:28:24.338817Z","source":"arxiv_reference"}],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2502.15276","last_updated":"2025-07-30T23:31:39Z","snapshot_observed_at":"2026-08-07T17:59:26.155005Z","submitted_at":"2025-02-21T08:04:57Z","title":"Categorical Lyapunov Theory I: Stability of Flows","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.15276","snapshot_observed_at":"2026-08-07T13:06:16.003692Z","title":"Ames, Joe Moeller, and Paulo Tabuada","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.22968","last_updated":"2025-05-29T01:11:38Z","snapshot_observed_at":"2026-08-09T06:36:50.783741Z","submitted_at":"2025-05-29T01:11:38Z","title":"Categorical Lyapunov Theory II: Stability of Systems","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T13:06:16.003692Z"},"links":{"cited_paper":"/paper/2502.15276","citing_paper":"/paper/2505.22968"},"observation_digest":"sha256:93c6a13fc3bd2630ee4120ea9cfd78e49798a37801ef920fc1d0c53d602685c7","observation_id":"cc679914-2107-4b22-96a7-8cd558d45b5d","resolution":{"observed_at":"2026-08-07T13:06:16.003692Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2502.15276","last_updated":"2025-07-30T23:31:39Z","snapshot_observed_at":"2026-08-07T17:59:26.155005Z","submitted_at":"2025-02-21T08:04:57Z","title":"Categorical Lyapunov Theory I: Stability of Flows","version":2},"cited_work":{"arxiv_id":"2502.15276","doi":"10.48550/arxiv.2502.15276","metadata_source":"arxiv_reference","pith_arxiv_id":"2502.15276","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Ames, Joe Moeller & Paulo Tabuada (2025):Categorical Lyapunov Theory I: Stability of Flows","venue":"arXiv (Cornell University)","work_id":"ce7214b3-878a-4f86-a333-aee0e24cc786","year":2025},"citing_paper":{"arxiv_id":"2604.03017","last_updated":"2026-04-03T13:02:04Z","snapshot_observed_at":"2026-07-06T22:52:15.263364Z","submitted_at":"2026-04-03T13:02:04Z","title":"Compositionality of Lyapunov functions via assume-guarantee reasoning","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-05-13T18:35:47.564184Z"},"links":{"cited_paper":"/paper/2502.15276","citing_paper":"/paper/2604.03017"},"observation_digest":"sha256:611a24511f427252525167a479aac8653f4fd117289fc9826a8245a44897e37d","observation_id":"b22ce862-ae2a-4d48-9776-ff40aaa10735","resolution":{"observed_at":"2026-05-13T18:38:07.512410Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2502.15276","last_updated":"2025-07-30T23:31:39Z","snapshot_observed_at":"2026-08-07T17:59:26.155005Z","submitted_at":"2025-02-21T08:04:57Z","title":"Categorical Lyapunov Theory I: Stability of Flows","version":2},"cited_work":{"arxiv_id":"2502.15276","doi":"10.48550/arxiv.2502.15276","metadata_source":"arxiv_reference","pith_arxiv_id":"2502.15276","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Ames, Joe Moeller & Paulo Tabuada (2025):Categorical Lyapunov Theory I: Stability of Flows","venue":"arXiv (Cornell University)","work_id":"ce7214b3-878a-4f86-a333-aee0e24cc786","year":2025},"citing_paper":{"arxiv_id":"2604.05255","last_updated":"2026-04-06T23:39:17Z","snapshot_observed_at":"2026-08-06T18:33:34.484769Z","submitted_at":"2026-04-06T23:39:17Z","title":"Hybrid Systems as Coalgebras: Lyapunov Morphisms for Zeno Stability","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-05-10T18:36:08.747669Z"},"links":{"cited_paper":"/paper/2502.15276","citing_paper":"/paper/2604.05255"},"observation_digest":"sha256:7c247246a42fc17639bfbee21afd618cb4fdd693251c5949245d48c6d77cde67","observation_id":"f6c296cf-41c4-43cf-9f90-f197d3605058","resolution":{"observed_at":"2026-05-11T00:20:52.209424Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2502.15276","last_updated":"2025-07-30T23:31:39Z","snapshot_observed_at":"2026-08-07T17:59:26.155005Z","submitted_at":"2025-02-21T08:04:57Z","title":"Categorical Lyapunov Theory I: Stability of Flows","version":2},"cited_work":{"arxiv_id":"2502.15276","doi":"10.48550/arxiv.2502.15276","metadata_source":"arxiv_reference","pith_arxiv_id":"2502.15276","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Ames, Joe Moeller & Paulo Tabuada (2025):Categorical Lyapunov Theory I: Stability of Flows","venue":"arXiv (Cornell University)","work_id":"ce7214b3-878a-4f86-a333-aee0e24cc786","year":2025},"citing_paper":{"arxiv_id":"2607.00034","last_updated":"2026-06-24T11:49:30Z","snapshot_observed_at":"2026-08-05T11:11:17.135472Z","submitted_at":"2026-06-24T11:49:30Z","title":"Bayesian updates from coalgebraic determinisation","version":1},"reference_index":75,"source":"arxiv_source","source_observed_at":"2026-07-02T21:20:58.414608Z"},"links":{"cited_paper":"/paper/2502.15276","citing_paper":"/paper/2607.00034"},"observation_digest":"sha256:e77c352924a086dfef7d01667cba191900bea2d5863406008585cd0f2fa0b426","observation_id":"c76b6f22-2e19-4da5-9853-c04377634342","resolution":{"observed_at":"2026-07-02T21:27:23.673492Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2502.15276","last_updated":"2025-07-30T23:31:39Z","snapshot_observed_at":"2026-08-07T17:59:26.155005Z","submitted_at":"2025-02-21T08:04:57Z","title":"Categorical Lyapunov Theory I: Stability of Flows","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.15276","snapshot_observed_at":"2026-08-01T18:00:33.016809Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.17455","last_updated":"2026-07-20T01:06:04Z","snapshot_observed_at":"2026-08-10T09:00:06.390364Z","submitted_at":"2026-07-20T01:06:04Z","title":"Dynamical Systems as Functorial Realisations of Abstract Evolution Shapes","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-01T18:00:33.016809Z"},"links":{"cited_paper":"/paper/2502.15276","citing_paper":"/paper/2607.17455"},"observation_digest":"sha256:fc10f0d64b9f74a67543996ff60c88cc9cea089ed4ff42cda1445222ee51f626","observation_id":"a557d8c9-77ac-42e7-96ca-62e6e4a20930","resolution":{"observed_at":"2026-08-01T18:00:33.016809Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2502.15276/citation-record","integrity":"/paper/2502.15276/integrity","json":"/paper/2502.15276/citation-record.json","paper":"/paper/2502.15276"},"outbound":[],"paper":{"arxiv_id":"2502.15276","last_updated":"2025-07-30T23:31:39Z","latest_version":2,"primary_category":"math.DS","snapshot_observed_at":"2026-08-07T17:59:26.155005Z","submitted_at":"2025-02-21T08:04:57Z","title":"Categorical Lyapunov Theory I: Stability of Flows"},"reference_resolution":{"displayed":0,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":0},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"thesis":"As of 11 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 5 inbound Pith citation observations for arXiv:2502.15276."}