{"as_of":"2026-08-09T11:35:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:797d707814d3957150f6e9de86ec8845b0ad8c8a30962c26f0ef7667814966b5","coverage":[{"denominator":38,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":38,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-03T15:40:35.596114Z","state":"measured"},{"denominator":40,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":40,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+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":"2026-06-30T11:33:21.411554Z","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":"2026-07-03T03:47:35.968749Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures","version":2},"cited_work":{"arxiv_id":"2512.16396","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2512.16396","snapshot_observed_at":"2026-07-07T04:17:57.976054Z","title":"Ceylan and D","venue":null,"work_id":"944a0b00-6ad4-4265-8b6f-0b83e6e3ac7c","year":2025},"citing_paper":{"arxiv_id":"2606.09820","last_updated":"2026-06-27T21:12:48Z","snapshot_observed_at":"2026-07-06T23:49:08.412079Z","submitted_at":"2026-06-08T17:57:40Z","title":"Weighted universal approximation of differentiable maps on infinite-dimensional manifolds","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-06-27T14:34:43.143213Z"},"links":{"cited_paper":"/paper/2512.16396","citing_paper":"/paper/2606.09820"},"observation_digest":"sha256:95057cf3498d691d58a302fb01fdd93b4a8b7d06ff3f429e0ddd94669e3a8b1b","observation_id":"8c2e2cd6-35d4-4d5d-bd6b-064587cadec9","resolution":{"observed_at":"2026-07-07T04:17:57.976054Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures","version":2},"cited_work":{"arxiv_id":"2512.16396","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2512.16396","snapshot_observed_at":"2026-07-07T04:17:57.976054Z","title":"Ceylan and D","venue":null,"work_id":"944a0b00-6ad4-4265-8b6f-0b83e6e3ac7c","year":2025},"citing_paper":{"arxiv_id":"2606.09820","last_updated":"2026-06-27T21:12:48Z","snapshot_observed_at":"2026-07-06T23:49:08.412079Z","submitted_at":"2026-06-08T17:57:40Z","title":"Weighted universal approximation of differentiable maps on infinite-dimensional manifolds","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-06-30T11:33:21.411554Z"},"links":{"cited_paper":"/paper/2512.16396","citing_paper":"/paper/2606.09820"},"observation_digest":"sha256:be0d38fa24fe6d3ff37f427d2bc3742101a95d56686fcaa1df5942d76f8e5805","observation_id":"318a4770-e5b0-4884-b7ae-844049045e44","resolution":{"observed_at":"2026-07-07T04:17:57.976054Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2512.16396/citation-record","integrity":"/paper/2512.16396/integrity","json":"/paper/2512.16396/citation-record.json","paper":"/paper/2512.16396"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T15:40:31.517293Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures","version":2},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-03T15:40:31.517293Z"},"links":{"citing_paper":"/paper/2512.16396"},"observation_digest":"sha256:357b0e6da4e3dd197d61ba896a33030eacc84f1d65b4a02b711028dd114c38aa","observation_id":"2f9e099c-59d0-4f5f-bd1d-4a93ed1d5b88","resolution":{"observed_at":"2026-08-03T15:40:31.517293Z","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":"2026-08-03T15:40:31.635582Z","title":"2, Springer, 2011","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures","version":2},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-03T15:40:31.635582Z"},"links":{"citing_paper":"/paper/2512.16396"},"observation_digest":"sha256:c0bbdc83579a0fce93393a2a5193d9eeac5bd918f1accde1f76d7d5f27b81951","observation_id":"c90ee99b-1ba1-4c55-b69c-c2e3ecac8742","resolution":{"observed_at":"2026-08-03T15:40:31.635582Z","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":"2026-08-03T15:40:31.807310Z","title":"Hager, Sebastian Riedel, and Tobias Nauen, Stochastic control with signatures, SIAM J","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures","version":2},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-03T15:40:31.807310Z"},"links":{"citing_paper":"/paper/2512.16396"},"observation_digest":"sha256:2c48ad3270e4a74077830035cef2967a6516d66a2bb1812f51191be2e25e6e96","observation_id":"ac33e1de-7183-432f-9003-4e432fc4170c","resolution":{"observed_at":"2026-08-03T15:40:31.807310Z","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":"2026-08-03T15:40:31.932873Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures","version":2},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-03T15:40:31.932873Z"},"links":{"citing_paper":"/paper/2512.16396"},"observation_digest":"sha256:1cac60ed00408d74fccaaae11f8ce0b4efafdad5d8369a5f3c2dab22467c7c9a","observation_id":"74b7aa8e-74b6-48e2-9fe4-466ac903729e","resolution":{"observed_at":"2026-08-03T15:40:31.932873Z","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":"2026-08-03T15:40:32.107704Z","title":"Financial Math","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures","version":2},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-03T15:40:32.107704Z"},"links":{"citing_paper":"/paper/2512.16396"},"observation_digest":"sha256:7b0001d16f128c9bb5efb2682f395de4673306d39cc8eb110ded077918b5f9cd","observation_id":"e7e4e7cb-eac1-4c34-b322-59da371143ee","resolution":{"observed_at":"2026-08-03T15:40:32.107704Z","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":"2026-08-03T15:40:32.279360Z","title":null,"venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures","version":2},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-03T15:40:32.279360Z"},"links":{"citing_paper":"/paper/2512.16396"},"observation_digest":"sha256:81579cb0d56cec61265037d3c805d7480603615512f9fde70c16c7a0f74ef584","observation_id":"ac5b0868-9a1d-4679-afac-8af03809adfa","resolution":{"observed_at":"2026-08-03T15:40:32.279360Z","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":"2026-08-03T15:40:32.453755Z","title":"Hager, Sebastian Riedel, and John Schoenmakers, Optimal stopping with signatures , The Annals of Applied Probability 33 (2023), no","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures","version":2},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-03T15:40:32.453755Z"},"links":{"citing_paper":"/paper/2512.16396"},"observation_digest":"sha256:f542f2d051e4841fc8568ee0b306e6d4e61145e7773a61607a90df65b3772f6d","observation_id":"54be562d-c3e4-4cf0-a6f0-9856fbe2ea56","resolution":{"observed_at":"2026-08-03T15:40:32.453755Z","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":"2026-08-03T15:40:32.572869Z","title":"29 (2025), no","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures","version":2},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-03T15:40:32.572869Z"},"links":{"citing_paper":"/paper/2512.16396"},"observation_digest":"sha256:12ba05a414e5be48af902afd016dd02c2870f1a3cf07cf9190ca3c8e51c15c70","observation_id":"a903559b-c3d3-46df-b4bd-f9f61affb5bf","resolution":{"observed_at":"2026-08-03T15:40:32.572869Z","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":"2026-08-03T15:40:32.740730Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures","version":2},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-03T15:40:32.740730Z"},"links":{"citing_paper":"/paper/2512.16396"},"observation_digest":"sha256:d6badab2f80475b2c603fe854fe8de9b20c5166d089d91d43c954e8ec07fbea3","observation_id":"bca71f14-3bc2-405e-93ef-8da01a2f2ad2","resolution":{"observed_at":"2026-08-03T15:40:32.740730Z","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":"2026-08-03T15:40:32.893050Z","title":"Finance 35 (2025), no","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures","version":2},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-03T15:40:32.893050Z"},"links":{"citing_paper":"/paper/2512.16396"},"observation_digest":"sha256:308ee6a48c8fc8f5681ad9208a4ec0fc5550253d4fadd70ff30b09b3b184d6dd","observation_id":"69097169-90f3-461a-8cc7-41d3f4d2cd38","resolution":{"observed_at":"2026-08-03T15:40:32.893050Z","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":"2026-08-03T15:40:32.983578Z","title":"3, 910--957","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures","version":2},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-03T15:40:32.983578Z"},"links":{"citing_paper":"/paper/2512.16396"},"observation_digest":"sha256:617e7b12216b2477da2b85e630f7bfc05b359fb485fc29af33c97e113738a8b2","observation_id":"7041fd81-0a51-447c-bde6-c78e5b86610d","resolution":{"observed_at":"2026-08-03T15:40:32.983578Z","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":"2026-08-03T15:40:33.142944Z","title":"London Math","venue":null,"work_id":null,"year":1954},"citing_paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures","version":2},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-03T15:40:33.142944Z"},"links":{"citing_paper":"/paper/2512.16396"},"observation_digest":"sha256:9729bee25ce5d971c6f93f9392bdc7862af39130304540c4b4206f88ed8d3ea6","observation_id":"a1545a36-f26a-4625-82f3-e8f600c0ffd6","resolution":{"observed_at":"2026-08-03T15:40:33.142944Z","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":"2026-08-03T15:40:33.235526Z","title":"4, 1239--1303","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures","version":2},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-03T15:40:33.235526Z"},"links":{"citing_paper":"/paper/2512.16396"},"observation_digest":"sha256:c340157728b3a0ab7742731cca7379cf93dfd43df3ee93eb0027ba9ec13a0420","observation_id":"663ad718-5320-430b-ba1e-765cf1d30ae7","resolution":{"observed_at":"2026-08-03T15:40:33.235526Z","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":"2026-08-03T15:40:33.320702Z","title":"01, 192--202","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures","version":2},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-03T15:40:33.320702Z"},"links":{"citing_paper":"/paper/2512.16396"},"observation_digest":"sha256:563f329865ef93dea3f794614af7f5183238dfc2c25d6fe67632a493ed657a04","observation_id":"444b7d3e-d06a-4ce5-b4dc-d0caab41eec0","resolution":{"observed_at":"2026-08-03T15:40:33.320702Z","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":"2026-08-03T15:40:33.387945Z","title":"176, 1--42","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures","version":2},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-03T15:40:33.387945Z"},"links":{"citing_paper":"/paper/2512.16396"},"observation_digest":"sha256:17554ab65b13efa38968ed7555498eb5b49aba24a9729bd6e374996a06411778","observation_id":"f5894e4a-e148-47c0-8acb-063772b4e855","resolution":{"observed_at":"2026-08-03T15:40:33.387945Z","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":"2026-08-03T15:40:33.468755Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures","version":2},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-03T15:40:33.468755Z"},"links":{"citing_paper":"/paper/2512.16396"},"observation_digest":"sha256:60482db9c596f1afb830b108b57878362f1786a92d2feea9826a8db7df3cff6f","observation_id":"c8b7f145-ca2a-4db9-9649-74d63589c9a4","resolution":{"observed_at":"2026-08-03T15:40:33.468755Z","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":"2026-08-03T15:40:33.559329Z","title":null,"venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures","version":2},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-03T15:40:33.559329Z"},"links":{"citing_paper":"/paper/2512.16396"},"observation_digest":"sha256:530ae38aedbb829d5b967d4178a848bd7a5ed0a240bf46f6c0c9e463822593d4","observation_id":"8e79704f-4273-4cfd-8d3e-9950a6028c14","resolution":{"observed_at":"2026-08-03T15:40:33.559329Z","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":"2026-08-03T15:40:33.622882Z","title":"Finance 19 (2019), no","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures","version":2},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-03T15:40:33.622882Z"},"links":{"citing_paper":"/paper/2512.16396"},"observation_digest":"sha256:711aaf9e2a7960dabf01130578bd6e80ba3f4d4e28f8d0e0bf673848947afc81","observation_id":"13ee0d75-b2e3-4232-9d7d-4a72e758b0d9","resolution":{"observed_at":"2026-08-03T15:40:33.622882Z","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":"2026-08-03T15:40:33.694977Z","title":"Friz and Martin Hairer, A course on rough paths: with an introduction to regularity structures, second edition ed., Universitext, Cham, Switzerland, 2020","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures","version":2},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-03T15:40:33.694977Z"},"links":{"citing_paper":"/paper/2512.16396"},"observation_digest":"sha256:803b066910c31d78732366641300b42f6e3b7fcb208716dea2798ee2289c3c81","observation_id":"159116f2-c8db-4b42-9928-6aa4195acd5b","resolution":{"observed_at":"2026-08-03T15:40:33.694977Z","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":"2026-08-03T15:40:33.750934Z","title":"Folland, Real analysis: modern techniques and their applications, 2","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures","version":2},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-03T15:40:33.750934Z"},"links":{"citing_paper":"/paper/2512.16396"},"observation_digest":"sha256:bddc1fb4eec8eaa86e071fbfad6c468bdc924b03a0311d9eae29e14ca37d7e3f","observation_id":"7d7719d8-b7cb-4e53-b8c8-255a1026aa69","resolution":{"observed_at":"2026-08-03T15:40:33.750934Z","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":"2026-08-03T15:40:33.845021Z","title":null,"venue":null,"work_id":null,"year":1982},"citing_paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures","version":2},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-03T15:40:33.845021Z"},"links":{"citing_paper":"/paper/2512.16396"},"observation_digest":"sha256:eaa38be816995d5ee698b8358a73ac676b821bddcea8c12152b89feec4e5c245","observation_id":"126ec608-fcdf-45f2-acd4-83fa68b4e09f","resolution":{"observed_at":"2026-08-03T15:40:33.845021Z","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":"2026-08-03T15:40:33.920713Z","title":"Theory Related Fields 136 (2006), no","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures","version":2},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-03T15:40:33.920713Z"},"links":{"citing_paper":"/paper/2512.16396"},"observation_digest":"sha256:bc6e86fa59a620abe6ef45c53416bca8b146e83d84d62a69cfc150df0df37415","observation_id":"10934eb3-4f5d-4df6-b354-b3c76d7d05f3","resolution":{"observed_at":"2026-08-03T15:40:33.920713Z","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":"2026-08-03T15:40:34.029566Z","title":"Friz and Nicolas B","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures","version":2},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-03T15:40:34.029566Z"},"links":{"citing_paper":"/paper/2512.16396"},"observation_digest":"sha256:3be05bf9255fd01091a05b0376aa84142d1d52bb1197e087ae9aa09ef824693b","observation_id":"707e1e99-76e4-4fbe-a608-5fb74e54e282","resolution":{"observed_at":"2026-08-03T15:40:34.029566Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1308.0371","last_updated":"2013-12-01T17:17:06Z","snapshot_observed_at":"2026-08-06T17:41:01.024808Z","submitted_at":"2013-08-01T22:29:41Z","title":"Sparse arrays of signatures for online character recognition","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1308.0371","snapshot_observed_at":"2026-08-03T15:40:34.095968Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures","version":2},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-03T15:40:34.095968Z"},"links":{"cited_paper":"/paper/1308.0371","citing_paper":"/paper/2512.16396"},"observation_digest":"sha256:0bc539dbbb06ee321717a9a3c39caa5c41d9e1491a335a141b96336678ad6b5e","observation_id":"b4e9c4bf-4a3f-4745-88db-c584d1f09201","resolution":{"observed_at":"2026-08-03T15:40:34.095968Z","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":"2026-08-03T15:40:34.168376Z","title":null,"venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures","version":2},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-03T15:40:34.168376Z"},"links":{"citing_paper":"/paper/2512.16396"},"observation_digest":"sha256:1cd99684706f12b0bb5691606b76938b6758286774da65dbf32fa8b75fac429a","observation_id":"6ed75188-fa4c-4add-bd02-b70c584b8100","resolution":{"observed_at":"2026-08-03T15:40:34.168376Z","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":"2026-08-03T15:40:34.272993Z","title":null,"venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures","version":2},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-03T15:40:34.272993Z"},"links":{"citing_paper":"/paper/2512.16396"},"observation_digest":"sha256:abaf1e485894b13cca72088b16b427c6002098faee45ea1cafdf85c16c558ef3","observation_id":"1316cdf3-1af5-439e-8fb8-3750dc4d9e13","resolution":{"observed_at":"2026-08-03T15:40:34.272993Z","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":"2026-08-03T15:40:34.394100Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures","version":2},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-03T15:40:34.394100Z"},"links":{"citing_paper":"/paper/2512.16396"},"observation_digest":"sha256:90cf0fcf9fb2a6377a11c014d10b02aaf0a1a3c3055f0a851e609ffc830e1f9c","observation_id":"b4b27229-ca11-44b8-82e5-bad489864511","resolution":{"observed_at":"2026-08-03T15:40:34.394100Z","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":"2026-08-03T15:40:34.512464Z","title":"Financial Math","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures","version":2},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-03T15:40:34.512464Z"},"links":{"citing_paper":"/paper/2512.16396"},"observation_digest":"sha256:3be507a148446623f58d68cbcf0c28af0d69e0fd28ab7df3f5a4fc538eb07117","observation_id":"f05da04d-70ee-48f6-8442-52dfa895a2e5","resolution":{"observed_at":"2026-08-03T15:40:34.512464Z","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":"2026-08-03T15:40:34.640711Z","title":"Kloeden, Numerical solution of stochastic differential equations, Applications of Mathematics, Stochastic Modelling and Applied Probability; 23, Berlin, Heidelberg, 1992","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures","version":2},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-03T15:40:34.640711Z"},"links":{"citing_paper":"/paper/2512.16396"},"observation_digest":"sha256:b1cbb428264420ce653cd657f99d953a9bb8b96fbb2a4ea3002ef69cfa887753","observation_id":"7b0a78e8-bd50-4ac0-9dc1-b49e9b287941","resolution":{"observed_at":"2026-08-03T15:40:34.640711Z","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":"2026-08-03T15:40:34.756617Z","title":"Kaneko and S","venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures","version":2},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-03T15:40:34.756617Z"},"links":{"citing_paper":"/paper/2512.16396"},"observation_digest":"sha256:31008e68fb38094a3e8bca4b1728ae349a905b6f5be16ae992915d60e699d256","observation_id":"0bd4338a-f1e8-4d62-be55-cc3d2ea2c195","resolution":{"observed_at":"2026-08-03T15:40:34.756617Z","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":"2026-08-03T15:40:34.876147Z","title":"Kir \\'a ly and Harald Oberhauser, Kernels for sequentially ordered data, J","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures","version":2},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-03T15:40:34.876147Z"},"links":{"citing_paper":"/paper/2512.16396"},"observation_digest":"sha256:af380aba0d69e5759effa8ae5a6e899a2a996bddbcdcd95d02ad7827005675e7","observation_id":"4661e3d5-1026-46e9-bbda-897979b89ff0","resolution":{"observed_at":"2026-08-03T15:40:34.876147Z","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":"2026-08-03T15:40:35.006944Z","title":"Shreve, Brownian motion and stochastic calculus, second ed., Graduate Texts in Mathematics, vol","venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures","version":2},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-03T15:40:35.006944Z"},"links":{"citing_paper":"/paper/2512.16396"},"observation_digest":"sha256:999826aba72a5793706f2a6eb1f1f5ef8fbb939c2d99db6347c45f9deaa7eaf9","observation_id":"452d543a-ee96-496c-b004-aba4b2210441","resolution":{"observed_at":"2026-08-03T15:40:35.006944Z","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":"2026-08-03T15:40:35.144033Z","title":"Lyons, Michael Caruana, and Thierry L\\' e vy, Differential equations driven by rough paths, Lecture Notes in Mathematics, vol","venue":null,"work_id":null,"year":1908},"citing_paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures","version":2},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-03T15:40:35.144033Z"},"links":{"citing_paper":"/paper/2512.16396"},"observation_digest":"sha256:072026cf1e6de1841cedcec99f10fb1f72fbf43c04cca97871628d772e46321f","observation_id":"ea2c9bdf-886c-4c22-88fe-13d56d34bfff","resolution":{"observed_at":"2026-08-03T15:40:35.144033Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1309.0260","last_updated":"2016-03-22T14:54:05Z","snapshot_observed_at":"2026-07-31T15:38:04.263962Z","submitted_at":"2013-09-01T20:34:55Z","title":"Learning from the past, predicting the statistics for the future, learning an evolving system","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1309.0260","snapshot_observed_at":"2026-08-03T15:40:35.252879Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures","version":2},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-03T15:40:35.252879Z"},"links":{"cited_paper":"/paper/1309.0260","citing_paper":"/paper/2512.16396"},"observation_digest":"sha256:561f03a097439f43db6a2344aad9a1f29a9208f12422fc7b3db75723a5a51ec8","observation_id":"ecb68c71-f7fe-40bb-a5b0-7c3312ca37e1","resolution":{"observed_at":"2026-08-03T15:40:35.252879Z","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":"2026-08-03T15:40:35.353266Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures","version":2},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-03T15:40:35.353266Z"},"links":{"citing_paper":"/paper/2512.16396"},"observation_digest":"sha256:7c9db599782115069fc65f79dccef2b61776bd7a571df2fb39e5dc74801c6c78","observation_id":"65b647e1-52ac-4fad-a4f8-722278e2e6d6","resolution":{"observed_at":"2026-08-03T15:40:35.353266Z","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":"2026-08-03T15:40:35.426024Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures","version":2},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-03T15:40:35.426024Z"},"links":{"citing_paper":"/paper/2512.16396"},"observation_digest":"sha256:0a5ce013f8b099768bb1129c2fbebe9f2ef9de14a846f756b5ab2919529e0558","observation_id":"42eb5a77-7c87-454f-b017-c5a53e0b6c0e","resolution":{"observed_at":"2026-08-03T15:40:35.426024Z","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":"2026-08-03T15:40:35.491571Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures","version":2},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-08-03T15:40:35.491571Z"},"links":{"citing_paper":"/paper/2512.16396"},"observation_digest":"sha256:e99c6d1f4b1d1529842519bda76d8e1a9eb1f0aa0c53f1f3b63d68938c9718e7","observation_id":"9a89abcb-fe23-41b9-ac69-a3b673c9c936","resolution":{"observed_at":"2026-08-03T15:40:35.491571Z","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":"2026-08-03T15:40:35.596114Z","title":"Schell and R","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures","version":2},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-03T15:40:35.596114Z"},"links":{"citing_paper":"/paper/2512.16396"},"observation_digest":"sha256:75d9902bc495ebe0c095a3b1e4fc79589b41b4c7f43fdb8f8e634a4ede7b9386","observation_id":"fdc53e00-0b39-4603-8f1e-7ec689ec4fd3","resolution":{"observed_at":"2026-08-03T15:40:35.596114Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2512.16396","last_updated":"2026-07-06T13:31:36Z","latest_version":2,"primary_category":"math.PR","snapshot_observed_at":"2026-08-09T08:39:36.693755Z","submitted_at":"2025-12-18T10:49:20Z","title":"Global universal approximation with Brownian signatures"},"reference_resolution":{"displayed":38,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":38,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":38},"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":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 2 inbound Pith citation observations for arXiv:2512.16396."}