{"as_of":"2026-08-08T12:11:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:3e89206d24a2713d22d238ddf18c38cb2e0af61a955ced9d770b448384fe73a7","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":"2026-08-07T13:42:15.859955Z","state":"measured"},{"denominator":39,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":39,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-18T15:36:22.785965Z","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":"2026-05-18T15:36:33.361068Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2505.21763","last_updated":"2026-02-18T02:45:14Z","snapshot_observed_at":"2026-08-07T13:21:19.373546Z","submitted_at":"2025-05-27T20:58:03Z","title":"Bochner-type theorems for distributional category","version":2},"cited_work":{"arxiv_id":"2505.21763","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2505.21763","snapshot_observed_at":"2026-07-07T03:18:08.460453Z","title":"Jauhari, J","venue":null,"work_id":"385f4709-f731-49f9-a880-133c654826c6","year":2025},"citing_paper":{"arxiv_id":"2509.16759","last_updated":"2026-04-23T14:54:57Z","snapshot_observed_at":"2026-07-06T22:30:21.881075Z","submitted_at":"2025-09-20T17:51:06Z","title":"On distributional topological complexity of groups and manifolds","version":4},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-05-18T15:36:22.785965Z"},"links":{"cited_paper":"/paper/2505.21763","citing_paper":"/paper/2509.16759"},"observation_digest":"sha256:7cd391f543b6ddbfa62b9a1124eaed527c725787fbba1615219def64a9e6809c","observation_id":"e5733c73-2a56-4e76-a587-36f5c6397435","resolution":{"observed_at":"2026-07-07T03:18:08.460453Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2505.21763/citation-record","integrity":"/paper/2505.21763/integrity","json":"/paper/2505.21763/citation-record.json","paper":"/paper/2505.21763"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:42:21.564452Z","title":"Bazzoni, G","venue":null,"work_id":"8a19f574-0020-4d50-9abd-a37c7c03996a","year":2022},"citing_paper":{"arxiv_id":"2505.21763","last_updated":"2026-02-18T02:45:14Z","snapshot_observed_at":"2026-08-07T13:21:19.373546Z","submitted_at":"2025-05-27T20:58:03Z","title":"Bochner-type theorems for distributional category","version":2},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-07T13:42:11.383086Z"},"links":{"citing_paper":"/paper/2505.21763"},"observation_digest":"sha256:2db7aad7f21d168632557297cf03af9e6a148fffa9fcd6385fd591cd66af399b","observation_id":"07cbd9f1-e0c4-4269-9c60-dac2c5a5518e","resolution":{"observed_at":"2026-08-07T13:42:21.637811Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:42:21.442298Z","title":"Bestvina, N","venue":null,"work_id":"06bfcde8-ede2-4f73-8e95-fe536ec12d6e","year":1997},"citing_paper":{"arxiv_id":"2505.21763","last_updated":"2026-02-18T02:45:14Z","snapshot_observed_at":"2026-08-07T13:21:19.373546Z","submitted_at":"2025-05-27T20:58:03Z","title":"Bochner-type theorems for distributional category","version":2},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-07T13:42:11.448657Z"},"links":{"citing_paper":"/paper/2505.21763"},"observation_digest":"sha256:96ef6b11bc45af915608808a29842a4516b284d759163ce9d9903aa4e6d0b5fd","observation_id":"cac6e104-fa38-404f-9a65-bdeb0fe5d794","resolution":{"observed_at":"2026-08-07T13:42:21.497904Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:42:21.219736Z","title":null,"venue":null,"work_id":"06956ca0-ed42-4b65-b2d9-261ae5ed73a6","year":1982},"citing_paper":{"arxiv_id":"2505.21763","last_updated":"2026-02-18T02:45:14Z","snapshot_observed_at":"2026-08-07T13:21:19.373546Z","submitted_at":"2025-05-27T20:58:03Z","title":"Bochner-type theorems for distributional category","version":2},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-07T13:42:11.481895Z"},"links":{"citing_paper":"/paper/2505.21763"},"observation_digest":"sha256:c95a16a3e9f375b61b5aeffc84b8891a7c9eae515234aa15031477d2daca7f4e","observation_id":"c4d044e2-34db-4763-9750-9e2b60f8fdd1","resolution":{"observed_at":"2026-08-07T13:42:21.331125Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:42:21.078654Z","title":"Cornea, G","venue":null,"work_id":"9750aed2-2aa6-4b06-9359-846d1095b2e5","year":2003},"citing_paper":{"arxiv_id":"2505.21763","last_updated":"2026-02-18T02:45:14Z","snapshot_observed_at":"2026-08-07T13:21:19.373546Z","submitted_at":"2025-05-27T20:58:03Z","title":"Bochner-type theorems for distributional category","version":2},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-07T13:42:11.524358Z"},"links":{"citing_paper":"/paper/2505.21763"},"observation_digest":"sha256:e3b74dab01f12092f21906a4343bf3679a9e8ecab72b370fb0f9d0ab0df53dcd","observation_id":"ced1f8e8-de31-41d6-8dc6-2d6bdcf08f01","resolution":{"observed_at":"2026-08-07T13:42:21.167027Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:42:20.878051Z","title":"Cheeger, D","venue":null,"work_id":"5297f2e0-5ced-47e7-a276-8364511de9f1","year":1971},"citing_paper":{"arxiv_id":"2505.21763","last_updated":"2026-02-18T02:45:14Z","snapshot_observed_at":"2026-08-07T13:21:19.373546Z","submitted_at":"2025-05-27T20:58:03Z","title":"Bochner-type theorems for distributional category","version":2},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-07T13:42:11.603667Z"},"links":{"citing_paper":"/paper/2505.21763"},"observation_digest":"sha256:be88156471fe13662db504aef2d88ffbbfb7658c0e14e31653c333996477e4e0","observation_id":"6b915bb3-d0dd-4054-aa50-102d72481a8d","resolution":{"observed_at":"2026-08-07T13:42:20.929052Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:42:20.712499Z","title":"Conner, F","venue":null,"work_id":"ef2d02e4-22ce-4e11-a120-5ae18251823a","year":1971},"citing_paper":{"arxiv_id":"2505.21763","last_updated":"2026-02-18T02:45:14Z","snapshot_observed_at":"2026-08-07T13:21:19.373546Z","submitted_at":"2025-05-27T20:58:03Z","title":"Bochner-type theorems for distributional category","version":2},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-07T13:42:11.684399Z"},"links":{"citing_paper":"/paper/2505.21763"},"observation_digest":"sha256:ffb5014354b05d4c653c722066ab8a031a2628537dfc4c82fbf84c284271e0ec","observation_id":"5b7e2b3d-ed59-4135-bfcb-f0edf5bf35bd","resolution":{"observed_at":"2026-08-07T13:42:20.811631Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2503.01779","last_updated":"2026-07-20T13:29:18Z","snapshot_observed_at":"2026-08-07T17:32:52.610021Z","submitted_at":"2025-03-03T18:10:08Z","title":"Curvature, macroscopic dimensions, and symmetric products of surfaces","version":7},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2503.01779","snapshot_observed_at":"2026-08-07T13:42:11.809667Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.21763","last_updated":"2026-02-18T02:45:14Z","snapshot_observed_at":"2026-08-07T13:21:19.373546Z","submitted_at":"2025-05-27T20:58:03Z","title":"Bochner-type theorems for distributional category","version":2},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-07T13:42:11.809667Z"},"links":{"cited_paper":"/paper/2503.01779","citing_paper":"/paper/2505.21763"},"observation_digest":"sha256:c2aed348b823de2cd977f28b424a2502b9c9e765b94d906ab8dcfc3ee6a1eab9","observation_id":"a87f2155-6190-4189-b553-0bfbe16a80e2","resolution":{"observed_at":"2026-08-07T13:42:11.809667Z","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":"2026-08-07T13:42:20.575214Z","title":"Dekimpe, M","venue":null,"work_id":"658d94db-a5de-438e-80f9-8babe4c90c3d","year":2009},"citing_paper":{"arxiv_id":"2505.21763","last_updated":"2026-02-18T02:45:14Z","snapshot_observed_at":"2026-08-07T13:21:19.373546Z","submitted_at":"2025-05-27T20:58:03Z","title":"Bochner-type theorems for distributional category","version":2},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-07T13:42:11.914002Z"},"links":{"citing_paper":"/paper/2505.21763"},"observation_digest":"sha256:810ecce0cd748b7c5f9efa3d4b67d7db3af7db0526f65db05e48367bbe8d9a98","observation_id":"8f06f900-b4fc-467d-a5b3-8c0a68bba216","resolution":{"observed_at":"2026-08-07T13:42:20.630706Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:42:12.005822Z","title":"Dranishnikov, On macroscopic dimension of rationally essential manifolds","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2505.21763","last_updated":"2026-02-18T02:45:14Z","snapshot_observed_at":"2026-08-07T13:21:19.373546Z","submitted_at":"2025-05-27T20:58:03Z","title":"Bochner-type theorems for distributional category","version":2},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-07T13:42:12.005822Z"},"links":{"citing_paper":"/paper/2505.21763"},"observation_digest":"sha256:4db8e68f81612f6429dfbeddd600baf4cf98dfd2f522e8403eb2f4728363a905","observation_id":"99b7490d-209a-4249-ba53-af155d34ce48","resolution":{"observed_at":"2026-08-07T13:42:12.005822Z","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":"2026-08-07T13:42:12.147796Z","title":"Dranishnikov, On macroscopic dimension of universal coverings of closed manifolds","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2505.21763","last_updated":"2026-02-18T02:45:14Z","snapshot_observed_at":"2026-08-07T13:21:19.373546Z","submitted_at":"2025-05-27T20:58:03Z","title":"Bochner-type theorems for distributional category","version":2},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-07T13:42:12.147796Z"},"links":{"citing_paper":"/paper/2505.21763"},"observation_digest":"sha256:e10629bd5a88b418090a74434bd24221f2370f810a16dfa15f211d303119a23c","observation_id":"91d4fdc2-4de9-492a-a014-17a3f7a29cc9","resolution":{"observed_at":"2026-08-07T13:42:12.147796Z","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":"2026-08-07T13:42:20.437001Z","title":"Dranishnikov, An upper bound on the LS category in presence of the fundamental group","venue":null,"work_id":"a731bd4a-7c07-4088-9a28-0fe9fe68f862","year":2019},"citing_paper":{"arxiv_id":"2505.21763","last_updated":"2026-02-18T02:45:14Z","snapshot_observed_at":"2026-08-07T13:21:19.373546Z","submitted_at":"2025-05-27T20:58:03Z","title":"Bochner-type theorems for distributional category","version":2},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-07T13:42:12.241652Z"},"links":{"citing_paper":"/paper/2505.21763"},"observation_digest":"sha256:e95d529a0ead14de30af7f95397e59815c3b0109e678612385bfe025a962e3fa","observation_id":"ed448793-2521-46a0-a1ce-3f9a44a496ef","resolution":{"observed_at":"2026-08-07T13:42:20.503569Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2404.03041","last_updated":"2025-08-11T21:19:40Z","snapshot_observed_at":"2026-07-06T17:55:21.083912Z","submitted_at":"2024-04-03T20:04:22Z","title":"Distributional Topological Complexity of groups","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2404.03041","snapshot_observed_at":"2026-08-07T13:42:12.394140Z","title":"Dranishnikov, Distributional topological complexity of groups","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.21763","last_updated":"2026-02-18T02:45:14Z","snapshot_observed_at":"2026-08-07T13:21:19.373546Z","submitted_at":"2025-05-27T20:58:03Z","title":"Bochner-type theorems for distributional category","version":2},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-07T13:42:12.394140Z"},"links":{"cited_paper":"/paper/2404.03041","citing_paper":"/paper/2505.21763"},"observation_digest":"sha256:08d64cf96f63edab867d0ec0f4c6fbfa98344980eb5c2868bdd01223c3c9fd40","observation_id":"7105632a-6126-429e-bfc2-bfab8b7a2d91","resolution":{"observed_at":"2026-08-07T13:42:12.394140Z","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":"2026-08-07T13:42:20.264607Z","title":"Dranishnikov, E","venue":null,"work_id":"befd0a71-359a-495d-809c-9e55cf31b2ae","year":2024},"citing_paper":{"arxiv_id":"2505.21763","last_updated":"2026-02-18T02:45:14Z","snapshot_observed_at":"2026-08-07T13:21:19.373546Z","submitted_at":"2025-05-27T20:58:03Z","title":"Bochner-type theorems for distributional category","version":2},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-07T13:42:12.534798Z"},"links":{"citing_paper":"/paper/2505.21763"},"observation_digest":"sha256:cd0d3294372db8e4ec0737e3c8428fe9770349624fbf700a47648f542c5879ba","observation_id":"93aa335d-3430-4ddc-b0db-02d4e4d3438b","resolution":{"observed_at":"2026-08-07T13:42:20.339856Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:42:20.153759Z","title":"Farber, Invitation to topological robotics","venue":null,"work_id":"c1f10f72-2dcc-4858-846d-a7ffda13fb72","year":2008},"citing_paper":{"arxiv_id":"2505.21763","last_updated":"2026-02-18T02:45:14Z","snapshot_observed_at":"2026-08-07T13:21:19.373546Z","submitted_at":"2025-05-27T20:58:03Z","title":"Bochner-type theorems for distributional category","version":2},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-07T13:42:12.627715Z"},"links":{"citing_paper":"/paper/2505.21763"},"observation_digest":"sha256:57e76e0567983deba672c25f43de19ca6fe760562b4315b3a1a357c6c1a2bf7b","observation_id":"8f8f52b2-1f83-4b57-8c75-3bcb04d60978","resolution":{"observed_at":"2026-08-07T13:42:20.207631Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:42:19.992408Z","title":null,"venue":null,"work_id":"963c0cf0-a7cb-45fe-878c-965f0a1ae316","year":1983},"citing_paper":{"arxiv_id":"2505.21763","last_updated":"2026-02-18T02:45:14Z","snapshot_observed_at":"2026-08-07T13:21:19.373546Z","submitted_at":"2025-05-27T20:58:03Z","title":"Bochner-type theorems for distributional category","version":2},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-07T13:42:12.705866Z"},"links":{"citing_paper":"/paper/2505.21763"},"observation_digest":"sha256:2328ce3674beaa903977553eaeae94b6064d12032a50601f64c48a76b2e73174","observation_id":"9e60fdfa-2535-4769-acdc-183c06851785","resolution":{"observed_at":"2026-08-07T13:42:20.052981Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:42:19.840354Z","title":"Felix, S","venue":null,"work_id":"19076893-353d-4592-acc4-760bf28b672d","year":1982},"citing_paper":{"arxiv_id":"2505.21763","last_updated":"2026-02-18T02:45:14Z","snapshot_observed_at":"2026-08-07T13:21:19.373546Z","submitted_at":"2025-05-27T20:58:03Z","title":"Bochner-type theorems for distributional category","version":2},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-07T13:42:12.770983Z"},"links":{"citing_paper":"/paper/2505.21763"},"observation_digest":"sha256:dc82d5a2d0685cd0fbb047dbff374f4e8da147fcab8b7678313c1e5f5d148042","observation_id":"b96ba236-30d9-4ef1-8dd3-d94dac8cdbad","resolution":{"observed_at":"2026-08-07T13:42:19.927067Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:42:19.691538Z","title":null,"venue":null,"work_id":"1524cc91-cb8f-4cf7-95de-651e7cc88538","year":1995},"citing_paper":{"arxiv_id":"2505.21763","last_updated":"2026-02-18T02:45:14Z","snapshot_observed_at":"2026-08-07T13:21:19.373546Z","submitted_at":"2025-05-27T20:58:03Z","title":"Bochner-type theorems for distributional category","version":2},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-07T13:42:12.846598Z"},"links":{"citing_paper":"/paper/2505.21763"},"observation_digest":"sha256:7d7c7634e91d96aea573e6d8a1403c4abb62d20f057cdd0872ec23867e72a2d4","observation_id":"02913c62-7174-49c2-932a-deaffc716020","resolution":{"observed_at":"2026-08-07T13:42:19.760790Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:42:19.476471Z","title":null,"venue":null,"work_id":"2c4c089e-294c-4b55-a553-85106f973219","year":1969},"citing_paper":{"arxiv_id":"2505.21763","last_updated":"2026-02-18T02:45:14Z","snapshot_observed_at":"2026-08-07T13:21:19.373546Z","submitted_at":"2025-05-27T20:58:03Z","title":"Bochner-type theorems for distributional category","version":2},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-07T13:42:12.931963Z"},"links":{"citing_paper":"/paper/2505.21763"},"observation_digest":"sha256:0add6509fc4a32fa1918b0655f829549949a120c40830e59001a5577ad51fd64","observation_id":"fba24127-a75f-4701-be89-1ed5b0bd5811","resolution":{"observed_at":"2026-08-07T13:42:19.589722Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:42:19.379298Z","title":null,"venue":null,"work_id":"85dfe1e3-0b9f-4d59-9e6f-3aeee0ef8828","year":1989},"citing_paper":{"arxiv_id":"2505.21763","last_updated":"2026-02-18T02:45:14Z","snapshot_observed_at":"2026-08-07T13:21:19.373546Z","submitted_at":"2025-05-27T20:58:03Z","title":"Bochner-type theorems for distributional category","version":2},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-07T13:42:13.055937Z"},"links":{"citing_paper":"/paper/2505.21763"},"observation_digest":"sha256:252fc240150e5198de8ee42a15b3841c9b9b69ee0df83f98df8d5bfa713b3083","observation_id":"f7168042-d8a8-4127-ae0c-acd47dd86523","resolution":{"observed_at":"2026-08-07T13:42:19.418559Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:42:13.147507Z","title":"Gromov, Filling Riemannian manifolds","venue":null,"work_id":null,"year":1983},"citing_paper":{"arxiv_id":"2505.21763","last_updated":"2026-02-18T02:45:14Z","snapshot_observed_at":"2026-08-07T13:21:19.373546Z","submitted_at":"2025-05-27T20:58:03Z","title":"Bochner-type theorems for distributional category","version":2},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-07T13:42:13.147507Z"},"links":{"citing_paper":"/paper/2505.21763"},"observation_digest":"sha256:5e005802c966c8dd2e47abd162e13201d7e45e008477119b9c9f622a274035ac","observation_id":"dc45bc2a-fd7f-4e63-aa7c-223e0a890a92","resolution":{"observed_at":"2026-08-07T13:42:13.147507Z","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":"2026-08-07T13:42:13.246432Z","title":"Gromov, Positive curvature, macroscopic dimension, spectral gaps and higher signatures","venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2505.21763","last_updated":"2026-02-18T02:45:14Z","snapshot_observed_at":"2026-08-07T13:21:19.373546Z","submitted_at":"2025-05-27T20:58:03Z","title":"Bochner-type theorems for distributional category","version":2},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-07T13:42:13.246432Z"},"links":{"citing_paper":"/paper/2505.21763"},"observation_digest":"sha256:b7b2a6d090358f06e5c5d9ca764ca64bbb023a414bcffde1c6f786a3bb84c6d1","observation_id":"daaedf7e-aaae-4fe0-9dc6-9e9a81b90e45","resolution":{"observed_at":"2026-08-07T13:42:13.246432Z","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":"2026-08-07T13:42:19.274094Z","title":"Hiller, C.-H","venue":null,"work_id":"0a56f2f8-9207-4162-a121-2c7b81906df1","year":1986},"citing_paper":{"arxiv_id":"2505.21763","last_updated":"2026-02-18T02:45:14Z","snapshot_observed_at":"2026-08-07T13:21:19.373546Z","submitted_at":"2025-05-27T20:58:03Z","title":"Bochner-type theorems for distributional category","version":2},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-07T13:42:13.334119Z"},"links":{"citing_paper":"/paper/2505.21763"},"observation_digest":"sha256:32f8a9296550e7ef7f55d03c68a1a23f311f664a8c94667f46aebaa339fbbfd6","observation_id":"31f95a2d-b29a-462a-9411-7d02af384667","resolution":{"observed_at":"2026-08-07T13:42:19.336849Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:42:19.084894Z","title":"Gromov, Metric structures for Riemannian and non-Riemannian spaces","venue":null,"work_id":"11eb34d4-9538-4b04-bfe3-94074ae1bf57","year":2007},"citing_paper":{"arxiv_id":"2505.21763","last_updated":"2026-02-18T02:45:14Z","snapshot_observed_at":"2026-08-07T13:21:19.373546Z","submitted_at":"2025-05-27T20:58:03Z","title":"Bochner-type theorems for distributional category","version":2},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-07T13:42:13.482927Z"},"links":{"citing_paper":"/paper/2505.21763"},"observation_digest":"sha256:036577da88d08f2e10eddb21fe6fef59de778254fdc8a62bfcb4b000e5caaf75","observation_id":"db3cf320-0f5f-4f16-9488-539e5962bdb8","resolution":{"observed_at":"2026-08-07T13:42:19.152953Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:42:18.872035Z","title":"Jauhari, Distributional category of manifolds","venue":null,"work_id":"e9e88e88-3295-44d0-86fb-3cfc8e0ee09c","year":2025},"citing_paper":{"arxiv_id":"2505.21763","last_updated":"2026-02-18T02:45:14Z","snapshot_observed_at":"2026-08-07T13:21:19.373546Z","submitted_at":"2025-05-27T20:58:03Z","title":"Bochner-type theorems for distributional category","version":2},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-07T13:42:13.635275Z"},"links":{"citing_paper":"/paper/2505.21763"},"observation_digest":"sha256:63d8304229a47c9c9946d35453552f7697204ce0cb2e3f1ee204a2bb2ec92450","observation_id":"1246357b-c519-45e8-9929-71db98380fe1","resolution":{"observed_at":"2026-08-07T13:42:19.014034Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:42:13.797952Z","title":null,"venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2505.21763","last_updated":"2026-02-18T02:45:14Z","snapshot_observed_at":"2026-08-07T13:21:19.373546Z","submitted_at":"2025-05-27T20:58:03Z","title":"Bochner-type theorems for distributional category","version":2},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-07T13:42:13.797952Z"},"links":{"citing_paper":"/paper/2505.21763"},"observation_digest":"sha256:8b7e721adb0f6ec7bf9569746fa0962e2846cd0821df6ac2735a22691c776a1f","observation_id":"24e8b856-67c6-4eed-bb43-02e2cbe3b96c","resolution":{"observed_at":"2026-08-07T13:42:13.797952Z","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":"2026-08-07T13:42:18.743538Z","title":"Knudsen, S","venue":null,"work_id":"5247d35c-1edf-476b-810c-ab749a0c40ef","year":2024},"citing_paper":{"arxiv_id":"2505.21763","last_updated":"2026-02-18T02:45:14Z","snapshot_observed_at":"2026-08-07T13:21:19.373546Z","submitted_at":"2025-05-27T20:58:03Z","title":"Bochner-type theorems for distributional category","version":2},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-07T13:42:13.959911Z"},"links":{"citing_paper":"/paper/2505.21763"},"observation_digest":"sha256:873f3a326b71079b07593a2c4575892094a77eb062f8fb2ae1f28d6dacf2886f","observation_id":"a26a797a-be96-4792-9338-2405d631f710","resolution":{"observed_at":"2026-08-07T13:42:18.814059Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:42:18.552677Z","title":"Kreck, W","venue":null,"work_id":"41604010-de1d-4781-951e-59a4eff0cbfd","year":2009},"citing_paper":{"arxiv_id":"2505.21763","last_updated":"2026-02-18T02:45:14Z","snapshot_observed_at":"2026-08-07T13:21:19.373546Z","submitted_at":"2025-05-27T20:58:03Z","title":"Bochner-type theorems for distributional category","version":2},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-07T13:42:14.104634Z"},"links":{"citing_paper":"/paper/2505.21763"},"observation_digest":"sha256:e6aae7b3d2bc3174c25184006ee4e346dea112f855a5f393d134e41943500df4","observation_id":"4bd126ff-d4c6-4dbd-8650-7dade6ec1553","resolution":{"observed_at":"2026-08-07T13:42:18.666435Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:42:18.402045Z","title":null,"venue":null,"work_id":"0dc2270c-38d9-4d1f-aa46-5f2e5aa3fa4e","year":1989},"citing_paper":{"arxiv_id":"2505.21763","last_updated":"2026-02-18T02:45:14Z","snapshot_observed_at":"2026-08-07T13:21:19.373546Z","submitted_at":"2025-05-27T20:58:03Z","title":"Bochner-type theorems for distributional category","version":2},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-07T13:42:14.252324Z"},"links":{"citing_paper":"/paper/2505.21763"},"observation_digest":"sha256:ff4fd498fe7061f0484da736a1567b5c7216c7a74e510c6503a2720606f46656","observation_id":"df4a6a04-7e57-4981-8369-0d372eb378de","resolution":{"observed_at":"2026-08-07T13:42:18.475405Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:42:18.237058Z","title":"Lusternik, L","venue":null,"work_id":"208e1559-3f45-47a4-9436-bede9ca4829b","year":1934},"citing_paper":{"arxiv_id":"2505.21763","last_updated":"2026-02-18T02:45:14Z","snapshot_observed_at":"2026-08-07T13:21:19.373546Z","submitted_at":"2025-05-27T20:58:03Z","title":"Bochner-type theorems for distributional category","version":2},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-07T13:42:14.417336Z"},"links":{"citing_paper":"/paper/2505.21763"},"observation_digest":"sha256:d6052e4a15106139a0942664330ad4c224dfe550bbe81302761ff87597c7aec7","observation_id":"f7929f17-e1ef-4ba7-8646-cf6060811893","resolution":{"observed_at":"2026-08-07T13:42:18.309118Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:42:18.095486Z","title":"Lupton, J","venue":null,"work_id":"1107d381-61d2-4783-b707-fc10a57f32ea","year":1995},"citing_paper":{"arxiv_id":"2505.21763","last_updated":"2026-02-18T02:45:14Z","snapshot_observed_at":"2026-08-07T13:21:19.373546Z","submitted_at":"2025-05-27T20:58:03Z","title":"Bochner-type theorems for distributional category","version":2},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-07T13:42:14.557867Z"},"links":{"citing_paper":"/paper/2505.21763"},"observation_digest":"sha256:5e366aaf982d25581ecb839dfa1021e631eed7fd352d13b7bb42db9c33d3987e","observation_id":"270359ea-f2bc-433d-a0b1-cbc387c6ab8d","resolution":{"observed_at":"2026-08-07T13:42:18.157185Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:42:14.697534Z","title":null,"venue":null,"work_id":null,"year":1962},"citing_paper":{"arxiv_id":"2505.21763","last_updated":"2026-02-18T02:45:14Z","snapshot_observed_at":"2026-08-07T13:21:19.373546Z","submitted_at":"2025-05-27T20:58:03Z","title":"Bochner-type theorems for distributional category","version":2},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-07T13:42:14.697534Z"},"links":{"citing_paper":"/paper/2505.21763"},"observation_digest":"sha256:ff9c00c16adb6bf77dbb8c3839958b242c73d244a30c27452633bc617c560cb5","observation_id":"baf83696-8ce4-42d4-853d-9380624b8c81","resolution":{"observed_at":"2026-08-07T13:42:14.697534Z","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":"2026-08-07T13:42:17.711372Z","title":"Oprea, Category bounds for nonnegative Ricci curvature manifolds with infinite fundamental group","venue":null,"work_id":"64316ce3-f2a4-411e-a533-0e8eff966a56","year":2002},"citing_paper":{"arxiv_id":"2505.21763","last_updated":"2026-02-18T02:45:14Z","snapshot_observed_at":"2026-08-07T13:21:19.373546Z","submitted_at":"2025-05-27T20:58:03Z","title":"Bochner-type theorems for distributional category","version":2},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-07T13:42:14.880016Z"},"links":{"citing_paper":"/paper/2505.21763"},"observation_digest":"sha256:0575d7b27608652cff87d3afffd8ec81a52fe4d5c515ff7cbd05390e2a1c338f","observation_id":"c95a5bb7-a594-4cb4-a212-99929044da96","resolution":{"observed_at":"2026-08-07T13:42:17.927944Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:42:17.310320Z","title":"Oprea, Bochner-type theorems for the Gottlieb group and injective toral actions","venue":null,"work_id":"13d6b48a-d690-40e9-9ac7-2f5f31ff05ee","year":2001},"citing_paper":{"arxiv_id":"2505.21763","last_updated":"2026-02-18T02:45:14Z","snapshot_observed_at":"2026-08-07T13:21:19.373546Z","submitted_at":"2025-05-27T20:58:03Z","title":"Bochner-type theorems for distributional category","version":2},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-07T13:42:15.044975Z"},"links":{"citing_paper":"/paper/2505.21763"},"observation_digest":"sha256:cc28b234ec7812013672f27e80561d506785c917dcfb5898e3f2781bc5986655","observation_id":"052ccc9b-4647-48de-bc99-201257116105","resolution":{"observed_at":"2026-08-07T13:42:17.478080Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:42:16.919277Z","title":"Oprea, J","venue":null,"work_id":"38d06d89-b2c7-4c41-b085-ca5a621abadb","year":2010},"citing_paper":{"arxiv_id":"2505.21763","last_updated":"2026-02-18T02:45:14Z","snapshot_observed_at":"2026-08-07T13:21:19.373546Z","submitted_at":"2025-05-27T20:58:03Z","title":"Bochner-type theorems for distributional category","version":2},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-07T13:42:15.195879Z"},"links":{"citing_paper":"/paper/2505.21763"},"observation_digest":"sha256:ae87598bb430386e3a7b7e01a6819d06d098c989274a597da91673910334131e","observation_id":"700668c9-02b5-4b4c-94d9-aef876de6341","resolution":{"observed_at":"2026-08-07T13:42:17.140864Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:42:16.621759Z","title":null,"venue":null,"work_id":"31b773e4-5770-4a7a-84d2-7069ac0ffba3","year":1956},"citing_paper":{"arxiv_id":"2505.21763","last_updated":"2026-02-18T02:45:14Z","snapshot_observed_at":"2026-08-07T13:21:19.373546Z","submitted_at":"2025-05-27T20:58:03Z","title":"Bochner-type theorems for distributional category","version":2},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-07T13:42:15.361214Z"},"links":{"citing_paper":"/paper/2505.21763"},"observation_digest":"sha256:fb31cc9d21d61c1c179b56a80c443708dbca2865dcfabe5e77b459e54d037512","observation_id":"acc0cb3e-5000-4eef-86a9-2eeae6066ada","resolution":{"observed_at":"2026-08-07T13:42:16.758180Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:42:15.541901Z","title":null,"venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2505.21763","last_updated":"2026-02-18T02:45:14Z","snapshot_observed_at":"2026-08-07T13:21:19.373546Z","submitted_at":"2025-05-27T20:58:03Z","title":"Bochner-type theorems for distributional category","version":2},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-07T13:42:15.541901Z"},"links":{"citing_paper":"/paper/2505.21763"},"observation_digest":"sha256:26b1d70d78c2129f1e0b109f1fc8f28bdd4ef30af7614b731bd1c855d71b2113","observation_id":"7a054169-dc78-4bc9-bbc6-68337e273bc8","resolution":{"observed_at":"2026-08-07T13:42:15.541901Z","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":"2026-08-07T13:42:16.320603Z","title":"Vasquez, Flat Riemannian manifolds","venue":null,"work_id":"c86611f7-7c68-44a0-bbf8-702eb302e3e0","year":1970},"citing_paper":{"arxiv_id":"2505.21763","last_updated":"2026-02-18T02:45:14Z","snapshot_observed_at":"2026-08-07T13:21:19.373546Z","submitted_at":"2025-05-27T20:58:03Z","title":"Bochner-type theorems for distributional category","version":2},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-08-07T13:42:15.730187Z"},"links":{"citing_paper":"/paper/2505.21763"},"observation_digest":"sha256:a7db46ac512c7e0cdb7af2f08c1aed089d7f3525f8b38ded21d8fbf67b9cbd61","observation_id":"5c59a592-87be-45d6-912f-413587215362","resolution":{"observed_at":"2026-08-07T13:42:16.470708Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T13:42:16.021230Z","title":"Yau, Calabi's conjecture and some new results in algebraic geometry","venue":null,"work_id":"8b28a2c4-c644-4c49-8dfe-31f271227626","year":1977},"citing_paper":{"arxiv_id":"2505.21763","last_updated":"2026-02-18T02:45:14Z","snapshot_observed_at":"2026-08-07T13:21:19.373546Z","submitted_at":"2025-05-27T20:58:03Z","title":"Bochner-type theorems for distributional category","version":2},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-07T13:42:15.859955Z"},"links":{"citing_paper":"/paper/2505.21763"},"observation_digest":"sha256:a245ff3914b3720f12ba3f0bbcb351111396403ba3da03cec06673d3a5c07d1d","observation_id":"2745942f-137a-4e2b-8816-1def70cfd4c3","resolution":{"observed_at":"2026-08-07T13:42:16.131713Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2505.21763","last_updated":"2026-02-18T02:45:14Z","latest_version":2,"primary_category":"math.AT","snapshot_observed_at":"2026-08-07T13:21:19.373546Z","submitted_at":"2025-05-27T20:58:03Z","title":"Bochner-type theorems for distributional category"},"reference_resolution":{"displayed":38,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":16,"verified_exact":0,"verified_fuzzy":22},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 1 inbound Pith citation observation for arXiv:2505.21763."}