{"as_of":"2026-08-21T09:57:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:ee90c6a4efc42126a5f230f78e811be95ab2db2e174e548c0f62c376e033b2c2","coverage":[{"denominator":25,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":25,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-30T08:36:10.004000Z","state":"measured"},{"denominator":27,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":27,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-21T06:32:19.484+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":"2026-08-15T14:48:56.556882Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-15T14:48:56.660801Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2606.28869","last_updated":"2026-06-27T11:22:53Z","snapshot_observed_at":"2026-08-09T16:07:45.606559Z","submitted_at":"2026-06-27T11:22:53Z","title":"A General Theory of Paths: Signatures, Jump Lifts, and Expected Signatures of Self-Exciting Processes","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2606.28869","snapshot_observed_at":"2026-08-04T08:57:26.947725Z","title":"A general theory of paths: Signatures, jump lifts, and expected signatures of self-exciting processes.arXiv:2606.28869 [math.PR], 2026","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2608.02355","last_updated":"2026-08-03T15:06:00Z","snapshot_observed_at":"2026-08-21T04:50:42.375035Z","submitted_at":"2026-08-03T15:06:00Z","title":"Path Portfolio Optimization: Defect, Lift, and the Price of Path Complexity","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-04T08:57:26.947725Z"},"links":{"cited_paper":"/paper/2606.28869","citing_paper":"/paper/2608.02355"},"observation_digest":"sha256:4f1d472e7e5cf8909eeb2e9c875948b516921a56ef8fa8f359c08b3ae3a8cfe5","observation_id":"7e6a7b01-dc93-491c-aef1-966e8bf6ce8f","resolution":{"observed_at":"2026-08-04T08:57:26.947725Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2606.28869","last_updated":"2026-06-27T11:22:53Z","snapshot_observed_at":"2026-08-09T16:07:45.606559Z","submitted_at":"2026-06-27T11:22:53Z","title":"A General Theory of Paths: Signatures, Jump Lifts, and Expected Signatures of Self-Exciting Processes","version":1},"cited_work":{"arxiv_id":"2606.28869","doi":null,"metadata_source":"pith","pith_arxiv_id":"2606.28869","snapshot_observed_at":"2026-08-15T14:48:56.660801Z","title":"A General Theory of Paths: Signatures, Jump Lifts, and Expected Signatures of Self-Exciting Processes","venue":"math.PR","work_id":"bfb850c9-2919-4ae2-a77b-85149c25005e","year":2026},"citing_paper":{"arxiv_id":"2608.05198","last_updated":"2026-08-04T20:19:53Z","snapshot_observed_at":"2026-08-19T05:21:10.817927Z","submitted_at":"2026-08-04T20:19:53Z","title":"The Mathematics of Volatility Surfaces","version":1},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-15T14:48:56.556882Z"},"links":{"cited_paper":"/paper/2606.28869","citing_paper":"/paper/2608.05198"},"observation_digest":"sha256:8aee5d6d8d0104eaf907f0593dc23ab9382d1e2a49edf467b19b2ea32394a11f","observation_id":"5790719f-a439-4e44-8bfa-3830c917116e","resolution":{"observed_at":"2026-08-15T14:48:56.667900Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2606.28869/citation-record","integrity":"/paper/2606.28869/integrity","json":"/paper/2606.28869/citation-record.json","paper":"/paper/2606.28869"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T16:57:25.455474Z","title":"Annals of Mathematics , volume =","venue":null,"work_id":"c38ca44b-bd0f-4e0a-b695-5b3a367582ec","year":null},"citing_paper":{"arxiv_id":"2606.28869","last_updated":"2026-06-27T11:22:53Z","snapshot_observed_at":"2026-08-09T16:07:45.606559Z","submitted_at":"2026-06-27T11:22:53Z","title":"A General Theory of Paths: Signatures, Jump Lifts, and Expected Signatures of Self-Exciting Processes","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-06-30T08:36:10.004000Z"},"links":{"citing_paper":"/paper/2606.28869"},"observation_digest":"sha256:24c17df92d6606651d8c5b6b66aaea2c32a0f8296780a61014b5dc21d42e287c","observation_id":"00cc8d10-72b8-48b2-a502-4a477587781e","resolution":{"observed_at":"2026-07-10T16:57:25.458818Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T16:57:25.451625Z","title":"Annals of Mathematics , volume =","venue":null,"work_id":"00ba593a-b5a8-4481-a807-aaa40ef350cf","year":null},"citing_paper":{"arxiv_id":"2606.28869","last_updated":"2026-06-27T11:22:53Z","snapshot_observed_at":"2026-08-09T16:07:45.606559Z","submitted_at":"2026-06-27T11:22:53Z","title":"A General Theory of Paths: Signatures, Jump Lifts, and Expected Signatures of Self-Exciting Processes","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-06-30T08:36:10.004000Z"},"links":{"citing_paper":"/paper/2606.28869"},"observation_digest":"sha256:1bc4217da5fd84c69b31134186a55f1e347ab03ffcca0dfaa2b57011cdd87cc3","observation_id":"061b41e7-342f-47d9-81a2-1d8e4318e2b9","resolution":{"observed_at":"2026-07-10T16:57:25.452772Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T16:57:25.453474Z","title":null,"venue":null,"work_id":"67b000d3-f8ad-4204-9bb6-4c5feb04ef3c","year":null},"citing_paper":{"arxiv_id":"2606.28869","last_updated":"2026-06-27T11:22:53Z","snapshot_observed_at":"2026-08-09T16:07:45.606559Z","submitted_at":"2026-06-27T11:22:53Z","title":"A General Theory of Paths: Signatures, Jump Lifts, and Expected Signatures of Self-Exciting Processes","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-06-30T08:36:10.004000Z"},"links":{"citing_paper":"/paper/2606.28869"},"observation_digest":"sha256:bf035d696bcea967bce525cd6c81bdca512e2049281d47356c0ad2ae8678b5f0","observation_id":"2feb1531-0548-41fa-b3b5-c373232b8c8e","resolution":{"observed_at":"2026-07-10T16:57:25.454643Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T16:57:25.462855Z","title":", title =","venue":null,"work_id":"5cc78dba-bf6a-42d0-a7c0-65b2b119dca2","year":null},"citing_paper":{"arxiv_id":"2606.28869","last_updated":"2026-06-27T11:22:53Z","snapshot_observed_at":"2026-08-09T16:07:45.606559Z","submitted_at":"2026-06-27T11:22:53Z","title":"A General Theory of Paths: Signatures, Jump Lifts, and Expected Signatures of Self-Exciting Processes","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-06-30T08:36:10.004000Z"},"links":{"citing_paper":"/paper/2606.28869"},"observation_digest":"sha256:7cab64a9cdef0ac806d6c563a5d879795c9b2b3264f6e2b3b1c5819b490992b1","observation_id":"88b55138-3306-419f-b4ec-91f4efc92b60","resolution":{"observed_at":"2026-07-10T16:57:25.463935Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T16:57:25.431530Z","title":"and Caruana, Michael and L\\'evy, Thierry , title =","venue":null,"work_id":"3a5d085c-85f9-4361-86f6-f050ba024412","year":null},"citing_paper":{"arxiv_id":"2606.28869","last_updated":"2026-06-27T11:22:53Z","snapshot_observed_at":"2026-08-09T16:07:45.606559Z","submitted_at":"2026-06-27T11:22:53Z","title":"A General Theory of Paths: Signatures, Jump Lifts, and Expected Signatures of Self-Exciting Processes","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-06-30T08:36:10.004000Z"},"links":{"citing_paper":"/paper/2606.28869"},"observation_digest":"sha256:b6c42fd57b50c4ced3b3a6c7016eb1889632f913e5b1977a9c6b922f5da9bd58","observation_id":"0f4d0f5c-749a-4116-97bb-9e1b9fc12ced","resolution":{"observed_at":"2026-07-10T16:57:25.434323Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T16:57:25.434903Z","title":"and Hairer, Martin , title =","venue":null,"work_id":"0e2ea27c-fa00-482a-b677-83bd3329c8a7","year":null},"citing_paper":{"arxiv_id":"2606.28869","last_updated":"2026-06-27T11:22:53Z","snapshot_observed_at":"2026-08-09T16:07:45.606559Z","submitted_at":"2026-06-27T11:22:53Z","title":"A General Theory of Paths: Signatures, Jump Lifts, and Expected Signatures of Self-Exciting Processes","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-06-30T08:36:10.004000Z"},"links":{"citing_paper":"/paper/2606.28869"},"observation_digest":"sha256:6f040872cafb4748f121c852a8772a0e8d8f1a042aca05ae8a22bcaf571a2c9c","observation_id":"0c623211-d8cb-49ba-ae61-ffea6d531b73","resolution":{"observed_at":"2026-07-10T16:57:25.436045Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T16:57:25.437045Z","title":"Annals of Mathematics , volume =","venue":null,"work_id":"846eb436-a9eb-4b03-b9ad-f78261bc8c71","year":null},"citing_paper":{"arxiv_id":"2606.28869","last_updated":"2026-06-27T11:22:53Z","snapshot_observed_at":"2026-08-09T16:07:45.606559Z","submitted_at":"2026-06-27T11:22:53Z","title":"A General Theory of Paths: Signatures, Jump Lifts, and Expected Signatures of Self-Exciting Processes","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-06-30T08:36:10.004000Z"},"links":{"citing_paper":"/paper/2606.28869"},"observation_digest":"sha256:f12d655d59292a9df612ea738d33a59991372bf497213ef58fb4d4bb724bcfa0","observation_id":"009f0d07-e1ae-406f-9427-6ee583369357","resolution":{"observed_at":"2026-07-10T16:57:25.438237Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T16:57:25.438995Z","title":"Advances in Mathematics , volume =","venue":null,"work_id":"e481eb0a-d55e-445b-87e1-93222202c4d4","year":null},"citing_paper":{"arxiv_id":"2606.28869","last_updated":"2026-06-27T11:22:53Z","snapshot_observed_at":"2026-08-09T16:07:45.606559Z","submitted_at":"2026-06-27T11:22:53Z","title":"A General Theory of Paths: Signatures, Jump Lifts, and Expected Signatures of Self-Exciting Processes","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-06-30T08:36:10.004000Z"},"links":{"citing_paper":"/paper/2606.28869"},"observation_digest":"sha256:a059838155052f31b326289f3dd5e3e92255f2c524d97206eacf7d44c3561e57","observation_id":"cef913cc-c2c7-48cb-83f1-0224fb41ed94","resolution":{"observed_at":"2026-07-10T16:57:25.441285Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T16:57:25.441881Z","title":"Annals of Probability , volume =","venue":null,"work_id":"ad7f8063-bbb2-48ad-9e66-f2bfe17c3abd","year":null},"citing_paper":{"arxiv_id":"2606.28869","last_updated":"2026-06-27T11:22:53Z","snapshot_observed_at":"2026-08-09T16:07:45.606559Z","submitted_at":"2026-06-27T11:22:53Z","title":"A General Theory of Paths: Signatures, Jump Lifts, and Expected Signatures of Self-Exciting Processes","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-06-30T08:36:10.004000Z"},"links":{"citing_paper":"/paper/2606.28869"},"observation_digest":"sha256:8eef5676b07c3a0984e35e85dd78b0a91d2cfcacb518ac69a790e61c230a2c38","observation_id":"61cc8cbe-b210-4f92-ac17-209ae1503bfd","resolution":{"observed_at":"2026-07-10T16:57:25.442982Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T16:57:25.459400Z","title":"Journal of Machine Learning Research , volume =","venue":null,"work_id":"3fecfbe4-8fcb-4cd0-b79a-f4617fa91b29","year":null},"citing_paper":{"arxiv_id":"2606.28869","last_updated":"2026-06-27T11:22:53Z","snapshot_observed_at":"2026-08-09T16:07:45.606559Z","submitted_at":"2026-06-27T11:22:53Z","title":"A General Theory of Paths: Signatures, Jump Lifts, and Expected Signatures of Self-Exciting Processes","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-06-30T08:36:10.004000Z"},"links":{"citing_paper":"/paper/2606.28869"},"observation_digest":"sha256:7de1350b39d2953de356f16fe173af7c0d9c2fe99f9c25654d87508a99e60b84","observation_id":"089d9f06-f3de-4244-90a3-4e2a832057db","resolution":{"observed_at":"2026-07-10T16:57:25.460500Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T16:57:25.424015Z","title":", title =","venue":null,"work_id":"579ef3a8-4ac9-4bc4-bcc2-237789390ba0","year":null},"citing_paper":{"arxiv_id":"2606.28869","last_updated":"2026-06-27T11:22:53Z","snapshot_observed_at":"2026-08-09T16:07:45.606559Z","submitted_at":"2026-06-27T11:22:53Z","title":"A General Theory of Paths: Signatures, Jump Lifts, and Expected Signatures of Self-Exciting Processes","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-06-30T08:36:10.004000Z"},"links":{"citing_paper":"/paper/2606.28869"},"observation_digest":"sha256:cf4acb8f4aaee57f6eedbaf4824a21528682ca7c2876e6c5b53037b9c28d1b65","observation_id":"fa116d27-eb93-4568-9084-903e3449299a","resolution":{"observed_at":"2026-07-10T16:57:25.425259Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T16:57:25.464454Z","title":"and Shekhar, Atul , title =","venue":null,"work_id":"4dcfb81f-afb7-4f31-b827-3ebae15a0a2e","year":null},"citing_paper":{"arxiv_id":"2606.28869","last_updated":"2026-06-27T11:22:53Z","snapshot_observed_at":"2026-08-09T16:07:45.606559Z","submitted_at":"2026-06-27T11:22:53Z","title":"A General Theory of Paths: Signatures, Jump Lifts, and Expected Signatures of Self-Exciting Processes","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-06-30T08:36:10.004000Z"},"links":{"citing_paper":"/paper/2606.28869"},"observation_digest":"sha256:b097552b5bfc304d92ee494dfcb1d34f8958da62240e21cfa3d1d836ffdeb12e","observation_id":"15dd65ef-4b41-438d-b239-dbbab30b4fce","resolution":{"observed_at":"2026-07-10T16:57:25.465486Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T16:57:25.466120Z","title":", title =","venue":null,"work_id":"3abf18a2-3ee4-46b4-ae64-25d073dbf81b","year":null},"citing_paper":{"arxiv_id":"2606.28869","last_updated":"2026-06-27T11:22:53Z","snapshot_observed_at":"2026-08-09T16:07:45.606559Z","submitted_at":"2026-06-27T11:22:53Z","title":"A General Theory of Paths: Signatures, Jump Lifts, and Expected Signatures of Self-Exciting Processes","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-06-30T08:36:10.004000Z"},"links":{"citing_paper":"/paper/2606.28869"},"observation_digest":"sha256:bb848d0c829a953f0d7a6e80a4e2c2d0fc7a4168ab61699d86bfb269ae02a663","observation_id":"ad51dd18-9e60-48e6-994d-cac0a42a12d0","resolution":{"observed_at":"2026-07-10T16:57:25.475792Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T16:57:25.431367Z","title":"Acta Applicandae Mathematicae , volume =","venue":null,"work_id":"a5716853-2255-444d-9797-d7ade537f2d9","year":null},"citing_paper":{"arxiv_id":"2606.28869","last_updated":"2026-06-27T11:22:53Z","snapshot_observed_at":"2026-08-09T16:07:45.606559Z","submitted_at":"2026-06-27T11:22:53Z","title":"A General Theory of Paths: Signatures, Jump Lifts, and Expected Signatures of Self-Exciting Processes","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-06-30T08:36:10.004000Z"},"links":{"citing_paper":"/paper/2606.28869"},"observation_digest":"sha256:acaa6a9aba372b5464fc76ca67b9119df784803b5b2a59e772721dc24b0cde38","observation_id":"dc422edc-a97d-421c-9cfd-459f3b672d8d","resolution":{"observed_at":"2026-07-10T16:57:25.434041Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T16:57:25.399848Z","title":"title =","venue":null,"work_id":"378201d4-42a1-48ad-b144-a8338174f6f7","year":null},"citing_paper":{"arxiv_id":"2606.28869","last_updated":"2026-06-27T11:22:53Z","snapshot_observed_at":"2026-08-09T16:07:45.606559Z","submitted_at":"2026-06-27T11:22:53Z","title":"A General Theory of Paths: Signatures, Jump Lifts, and Expected Signatures of Self-Exciting Processes","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-06-30T08:36:10.004000Z"},"links":{"citing_paper":"/paper/2606.28869"},"observation_digest":"sha256:35db5929163f50ebb49c3c8635178173e48af0e8e87620627541d70157ee39e1","observation_id":"081f142e-2267-483b-a193-ac5d21e5ae8d","resolution":{"observed_at":"2026-07-10T16:57:25.401296Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T16:57:25.421650Z","title":"and Oakes, David , title =","venue":null,"work_id":"675ca69b-8ebb-4b8e-bcde-7733fadc81f9","year":null},"citing_paper":{"arxiv_id":"2606.28869","last_updated":"2026-06-27T11:22:53Z","snapshot_observed_at":"2026-08-09T16:07:45.606559Z","submitted_at":"2026-06-27T11:22:53Z","title":"A General Theory of Paths: Signatures, Jump Lifts, and Expected Signatures of Self-Exciting Processes","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-06-30T08:36:10.004000Z"},"links":{"citing_paper":"/paper/2606.28869"},"observation_digest":"sha256:4dbf7b8158f054657444e557d3731b53aedf116a3d358a578e0fd12ddb0c722f","observation_id":"fa7bb6ac-0c10-41f1-bf8a-da2fbfbf061e","resolution":{"observed_at":"2026-07-10T16:57:25.423067Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T16:57:25.423877Z","title":", title =","venue":null,"work_id":"5138fc06-e9d1-4827-aebf-7bb51f7dd4cd","year":null},"citing_paper":{"arxiv_id":"2606.28869","last_updated":"2026-06-27T11:22:53Z","snapshot_observed_at":"2026-08-09T16:07:45.606559Z","submitted_at":"2026-06-27T11:22:53Z","title":"A General Theory of Paths: Signatures, Jump Lifts, and Expected Signatures of Self-Exciting Processes","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-06-30T08:36:10.004000Z"},"links":{"citing_paper":"/paper/2606.28869"},"observation_digest":"sha256:0b8eadf9876aecc000f25f124a5be37e0c839d770455049a8942578a508a4733","observation_id":"ac2c0a9c-4098-4198-9bbc-cdb92385f481","resolution":{"observed_at":"2026-07-10T16:57:25.424932Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T16:57:25.416636Z","title":"IEEE Transactions on Information Theory , volume =","venue":null,"work_id":"c95137f3-7feb-4f4d-9eab-a89346b52205","year":null},"citing_paper":{"arxiv_id":"2606.28869","last_updated":"2026-06-27T11:22:53Z","snapshot_observed_at":"2026-08-09T16:07:45.606559Z","submitted_at":"2026-06-27T11:22:53Z","title":"A General Theory of Paths: Signatures, Jump Lifts, and Expected Signatures of Self-Exciting Processes","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-06-30T08:36:10.004000Z"},"links":{"citing_paper":"/paper/2606.28869"},"observation_digest":"sha256:85a024db1f21ea38637f7f3d085c0a94c9ebd7288ed11a668ba79d17e78250c7","observation_id":"fdec5001-ace0-46ae-9212-d32fbcbec3ca","resolution":{"observed_at":"2026-07-10T16:57:25.418587Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T16:57:25.438660Z","title":null,"venue":null,"work_id":"13008543-21d6-4f43-a9e4-f353d974c0db","year":null},"citing_paper":{"arxiv_id":"2606.28869","last_updated":"2026-06-27T11:22:53Z","snapshot_observed_at":"2026-08-09T16:07:45.606559Z","submitted_at":"2026-06-27T11:22:53Z","title":"A General Theory of Paths: Signatures, Jump Lifts, and Expected Signatures of Self-Exciting Processes","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-06-30T08:36:10.004000Z"},"links":{"citing_paper":"/paper/2606.28869"},"observation_digest":"sha256:4d072e41013b8ec517d935d31ade7c59800cde6d54c91c5824f0690599bafc3f","observation_id":"d1d116fc-4a0d-47d5-9793-0f6b78f7abb1","resolution":{"observed_at":"2026-07-10T16:57:25.443590Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T16:57:25.426172Z","title":"Electronic Communications in Probability , volume =","venue":null,"work_id":"a2fb2e67-cf98-4b98-adda-94c02971b598","year":null},"citing_paper":{"arxiv_id":"2606.28869","last_updated":"2026-06-27T11:22:53Z","snapshot_observed_at":"2026-08-09T16:07:45.606559Z","submitted_at":"2026-06-27T11:22:53Z","title":"A General Theory of Paths: Signatures, Jump Lifts, and Expected Signatures of Self-Exciting Processes","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-06-30T08:36:10.004000Z"},"links":{"citing_paper":"/paper/2606.28869"},"observation_digest":"sha256:8516a2c36d046be962624fe344622460d4f9bf37f0296a17dc3f5b20c4429095","observation_id":"56517fe7-0990-4b1d-abc9-471d7cda061c","resolution":{"observed_at":"2026-07-10T16:57:25.430824Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T16:57:25.443578Z","title":null,"venue":null,"work_id":"0f1e9f98-c7ab-4781-ba53-aa6882616859","year":null},"citing_paper":{"arxiv_id":"2606.28869","last_updated":"2026-06-27T11:22:53Z","snapshot_observed_at":"2026-08-09T16:07:45.606559Z","submitted_at":"2026-06-27T11:22:53Z","title":"A General Theory of Paths: Signatures, Jump Lifts, and Expected Signatures of Self-Exciting Processes","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-06-30T08:36:10.004000Z"},"links":{"citing_paper":"/paper/2606.28869"},"observation_digest":"sha256:ee2767761b9020e4615e300fa58842df9fe11da4ded8c561497897930f407250","observation_id":"33924121-378f-49ab-ba4b-16a4825dce21","resolution":{"observed_at":"2026-07-10T16:57:25.450779Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2302.01362","last_updated":"2026-07-07T16:35:29Z","snapshot_observed_at":"2026-08-19T23:42:42.355636Z","submitted_at":"2023-02-02T19:01:04Z","title":"Signature SDEs from an affine and polynomial perspective","version":3},"cited_work":{"arxiv_id":"2302.01362","doi":"10.48550/arxiv.2302.01362","metadata_source":"arxiv_reference","pith_arxiv_id":"2302.01362","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Signature SDEs from an affine and polynomial perspective","venue":"arXiv (Cornell University)","work_id":"c839a54f-1bac-4845-8ba8-cf885617f22f","year":2025},"citing_paper":{"arxiv_id":"2606.28869","last_updated":"2026-06-27T11:22:53Z","snapshot_observed_at":"2026-08-09T16:07:45.606559Z","submitted_at":"2026-06-27T11:22:53Z","title":"A General Theory of Paths: Signatures, Jump Lifts, and Expected Signatures of Self-Exciting Processes","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-06-30T08:36:10.004000Z"},"links":{"cited_paper":"/paper/2302.01362","citing_paper":"/paper/2606.28869"},"observation_digest":"sha256:9d150c9b99933bb840f9d451ed9a77582249d06e60ad35599ad1d10822184cc1","observation_id":"8421432a-1d70-4936-9094-5f21439d25c7","resolution":{"observed_at":"2026-07-08T01:19:03.887976Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T16:57:25.461150Z","title":null,"venue":null,"work_id":"53619f24-4732-442a-9f07-146008f08e3a","year":null},"citing_paper":{"arxiv_id":"2606.28869","last_updated":"2026-06-27T11:22:53Z","snapshot_observed_at":"2026-08-09T16:07:45.606559Z","submitted_at":"2026-06-27T11:22:53Z","title":"A General Theory of Paths: Signatures, Jump Lifts, and Expected Signatures of Self-Exciting Processes","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-06-30T08:36:10.004000Z"},"links":{"citing_paper":"/paper/2606.28869"},"observation_digest":"sha256:29800de9fed6d1c1e7c8420292a5c22104e2ec712bd3de67c2b29bda7a5acc92","observation_id":"572b43f9-70e8-488b-8b95-5f581c60948b","resolution":{"observed_at":"2026-07-10T16:57:25.462206Z","resolver_source":"raw_fallback","status":"parse_uncertain"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T16:57:25.476486Z","title":"and Victoir, Nicolas B","venue":null,"work_id":"c6f2826e-4f99-4624-978b-cacc7c76916d","year":null},"citing_paper":{"arxiv_id":"2606.28869","last_updated":"2026-06-27T11:22:53Z","snapshot_observed_at":"2026-08-09T16:07:45.606559Z","submitted_at":"2026-06-27T11:22:53Z","title":"A General Theory of Paths: Signatures, Jump Lifts, and Expected Signatures of Self-Exciting Processes","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-06-30T08:36:10.004000Z"},"links":{"citing_paper":"/paper/2606.28869"},"observation_digest":"sha256:09ddc723971e7d46e28bccae1ecb2c759dc5e112b997ec2517cf50751e61bc68","observation_id":"d8a5cf26-b635-4201-9bf3-1b3cbb7e6278","resolution":{"observed_at":"2026-07-10T16:57:25.478387Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T16:57:25.426168Z","title":"Bernoulli , volume =","venue":null,"work_id":"925f3d67-7298-48d9-abda-201bab807b35","year":null},"citing_paper":{"arxiv_id":"2606.28869","last_updated":"2026-06-27T11:22:53Z","snapshot_observed_at":"2026-08-09T16:07:45.606559Z","submitted_at":"2026-06-27T11:22:53Z","title":"A General Theory of Paths: Signatures, Jump Lifts, and Expected Signatures of Self-Exciting Processes","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-06-30T08:36:10.004000Z"},"links":{"citing_paper":"/paper/2606.28869"},"observation_digest":"sha256:2166a35cd007f72eb4e62a1ac16c30399dfd1739d528da5e9f2be4f99d0eef84","observation_id":"b2e939ff-5be5-4854-8886-8a47470762c8","resolution":{"observed_at":"2026-07-10T16:57:25.427752Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2606.28869","last_updated":"2026-06-27T11:22:53Z","latest_version":1,"primary_category":"math.PR","snapshot_observed_at":"2026-08-09T16:07:45.606559Z","submitted_at":"2026-06-27T11:22:53Z","title":"A General Theory of Paths: Signatures, Jump Lifts, and Expected Signatures of Self-Exciting Processes"},"reference_resolution":{"displayed":25,"state_counts":{"malformed_identifier":0,"metadata_mismatch":1,"parse_uncertain":1,"unresolved":3,"verified_exact":0,"verified_fuzzy":20},"total_outbound_references":25},"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":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"thesis":"As of 21 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 2 inbound Pith citation observations for arXiv:2606.28869."}