{"as_of":"2026-08-18T05:13:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:768dd993fdf9c394a71ab85fe00af21258bdc02ac3f20987df20447c44de30ed","coverage":[{"denominator":9,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":9,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-16T00:50:46.532390Z","state":"measured"},{"denominator":9,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":9,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-17T06:30:58.91139+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2505.02800/citation-record","integrity":"/paper/2505.02800/integrity","json":"/paper/2505.02800/citation-record.json","paper":"/paper/2505.02800"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:50:46.742474Z","title":"A survey of vectorization methods in topological data analysis","venue":null,"work_id":"cc00f33a-19d4-4c26-ab4d-1606d352bf9d","year":2023},"citing_paper":{"arxiv_id":"2505.02800","last_updated":"2026-05-29T10:14:13Z","snapshot_observed_at":"2026-08-17T06:12:08.165558Z","submitted_at":"2025-05-05T17:21:41Z","title":"Discrete signature tensors for persistence landscapes","version":3},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-16T00:50:46.496574Z"},"links":{"citing_paper":"/paper/2505.02800"},"observation_digest":"sha256:dcd3250013fa1df4cca80fca1aab677a442a1abb0061c5ef7ed5950a59f767c2","observation_id":"ca7b889c-b11c-47fb-acb1-85f22b10263f","resolution":{"observed_at":"2026-08-16T00:50:46.747419Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:50:46.505806Z","title":"Decomposing Tensor Spaces via Path Signatures","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.02800","last_updated":"2026-05-29T10:14:13Z","snapshot_observed_at":"2026-08-17T06:12:08.165558Z","submitted_at":"2025-05-05T17:21:41Z","title":"Discrete signature tensors for persistence landscapes","version":3},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-16T00:50:46.505806Z"},"links":{"citing_paper":"/paper/2505.02800"},"observation_digest":"sha256:684b3ebb089c1013a16496f6cbe3b3b62a618486e2dc7129f9f1e6009ce778f3","observation_id":"e2a534ad-95d1-4931-81e9-66310f39dab9","resolution":{"observed_at":"2026-08-16T00:50:46.505806Z","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":"2026-08-16T00:50:46.532390Z","title":"[RB19] R","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.02800","last_updated":"2026-05-29T10:14:13Z","snapshot_observed_at":"2026-08-17T06:12:08.165558Z","submitted_at":"2025-05-05T17:21:41Z","title":"Discrete signature tensors for persistence landscapes","version":3},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-16T00:50:46.532390Z"},"links":{"citing_paper":"/paper/2505.02800"},"observation_digest":"sha256:6d93f0aebf8d255e4d01d51ac8c28f12b1e41558d404804c39078bf0efed9ae4","observation_id":"e3545b14-d0c7-4e17-903c-b2904951c1b3","resolution":{"observed_at":"2026-08-16T00:50:46.532390Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:50:46.728131Z","title":null,"venue":null,"work_id":"9ddf876b-4dca-4631-859e-c8c9b9106d93","year":null},"citing_paper":{"arxiv_id":"2505.02800","last_updated":"2026-05-29T10:14:13Z","snapshot_observed_at":"2026-08-17T06:12:08.165558Z","submitted_at":"2025-05-05T17:21:41Z","title":"Discrete signature tensors for persistence landscapes","version":3},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-16T00:50:46.501501Z"},"links":{"citing_paper":"/paper/2505.02800"},"observation_digest":"sha256:7c09908743fa59b9ae5588bb3a9c1263945588e5c9b164d66a180dc9f2d8b6db","observation_id":"286acd5c-a2bd-401a-8f42-ceeabefea4b6","resolution":{"observed_at":"2026-08-16T00:50:46.733048Z","resolver_source":"raw_fallback","status":"parse_uncertain"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:50:46.510206Z","title":"A persistence landscapes toolbox for topological statistics","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2505.02800","last_updated":"2026-05-29T10:14:13Z","snapshot_observed_at":"2026-08-17T06:12:08.165558Z","submitted_at":"2025-05-05T17:21:41Z","title":"Discrete signature tensors for persistence landscapes","version":3},"reference_index":117,"source":"pdf_text","source_observed_at":"2026-08-16T00:50:46.510206Z"},"links":{"citing_paper":"/paper/2505.02800"},"observation_digest":"sha256:e520e82dfcc9d1cd649fff6cd2720dcd268d4b0c1c29fbba32d28c54faa08177","observation_id":"278238f0-4c39-4ff1-ab5d-2ae79c84ec08","resolution":{"observed_at":"2026-08-16T00:50:46.510206Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1601.08169","last_updated":"2016-01-29T16:06:36Z","snapshot_observed_at":"2026-08-14T22:12:32.442534Z","submitted_at":"2016-01-29T16:06:36Z","title":"Kernels for sequentially ordered data","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1601.08169","snapshot_observed_at":"2026-08-16T00:50:46.519278Z","title":"[LO23] D","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.02800","last_updated":"2026-05-29T10:14:13Z","snapshot_observed_at":"2026-08-17T06:12:08.165558Z","submitted_at":"2025-05-05T17:21:41Z","title":"Discrete signature tensors for persistence landscapes","version":3},"reference_index":2016,"source":"pdf_text","source_observed_at":"2026-08-16T00:50:46.519278Z"},"links":{"cited_paper":"/paper/1601.08169","citing_paper":"/paper/2505.02800"},"observation_digest":"sha256:7fb2b12bf8b89495c1751dbe44034c812f73d7755ee82765da3a52e9c689085d","observation_id":"012c2ef0-081b-4669-8136-ce379f91abb3","resolution":{"observed_at":"2026-08-16T00:50:46.519278Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2305.04625","last_updated":"2023-05-08T11:05:44Z","snapshot_observed_at":"2026-08-16T15:34:49.587060Z","submitted_at":"2023-05-08T11:05:44Z","title":"The Signature Kernel","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2305.04625","snapshot_observed_at":"2026-08-16T00:50:46.523670Z","title":"Quan- tifying similarity of pore-geometry in nanoporous materials","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2505.02800","last_updated":"2026-05-29T10:14:13Z","snapshot_observed_at":"2026-08-17T06:12:08.165558Z","submitted_at":"2025-05-05T17:21:41Z","title":"Discrete signature tensors for persistence landscapes","version":3},"reference_index":2023,"source":"pdf_text","source_observed_at":"2026-08-16T00:50:46.523670Z"},"links":{"cited_paper":"/paper/2305.04625","citing_paper":"/paper/2505.02800"},"observation_digest":"sha256:39dbf10d3cc86ba2c37c9a84bd8927ae2781998e73e6dde432619e5dd5d692a2","observation_id":"4f76b5c8-c848-45c3-af7a-e7151072f069","resolution":{"observed_at":"2026-08-16T00:50:46.523670Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2407.20405","last_updated":"2024-07-29T20:17:01Z","snapshot_observed_at":"2026-08-16T14:59:26.238630Z","submitted_at":"2024-07-29T20:17:01Z","title":"Rank and symmetries of signature tensors","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.20405","snapshot_observed_at":"2026-08-16T00:50:46.514427Z","title":"Toroidal topology of population activity in grid cells","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2505.02800","last_updated":"2026-05-29T10:14:13Z","snapshot_observed_at":"2026-08-17T06:12:08.165558Z","submitted_at":"2025-05-05T17:21:41Z","title":"Discrete signature tensors for persistence landscapes","version":3},"reference_index":2024,"source":"pdf_text","source_observed_at":"2026-08-16T00:50:46.514427Z"},"links":{"cited_paper":"/paper/2407.20405","citing_paper":"/paper/2505.02800"},"observation_digest":"sha256:c9b3789a084cb47d8c2321d8bf71e33664579b88c8ac737c94646e269abc3c17","observation_id":"9bfff646-af45-4959-afd0-cc561549059d","resolution":{"observed_at":"2026-08-16T00:50:46.514427Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2206.14674","last_updated":"2025-02-20T12:44:23Z","snapshot_observed_at":"2026-08-16T16:49:30.898575Z","submitted_at":"2022-06-29T14:23:28Z","title":"Signature Methods in Machine Learning","version":7},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2206.14674","snapshot_observed_at":"2026-08-16T00:50:46.527914Z","title":"Fruit flies and moduli: interactions between biology and mathemat- ics","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2505.02800","last_updated":"2026-05-29T10:14:13Z","snapshot_observed_at":"2026-08-17T06:12:08.165558Z","submitted_at":"2025-05-05T17:21:41Z","title":"Discrete signature tensors for persistence landscapes","version":3},"reference_index":2025,"source":"pdf_text","source_observed_at":"2026-08-16T00:50:46.527914Z"},"links":{"cited_paper":"/paper/2206.14674","citing_paper":"/paper/2505.02800"},"observation_digest":"sha256:52671fbc49b2c15389d6cc64f4591265df24c49898553d96e64a8cd0c1623e1f","observation_id":"1229c206-c1e4-4390-b5be-ffa18c1c41f3","resolution":{"observed_at":"2026-08-16T00:50:46.527914Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2505.02800","last_updated":"2026-05-29T10:14:13Z","latest_version":3,"primary_category":"math.AT","snapshot_observed_at":"2026-08-17T06:12:08.165558Z","submitted_at":"2025-05-05T17:21:41Z","title":"Discrete signature tensors for persistence landscapes"},"reference_resolution":{"displayed":9,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":1,"unresolved":7,"verified_exact":0,"verified_fuzzy":1},"total_outbound_references":9},"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":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"thesis":"As of 18 August 2026, this Paper Citation Record lists 9 of 9 outbound references and 0 inbound Pith citation observations for arXiv:2505.02800."}