{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:LL3DFIHL5XCSOGVP4QR5J532BS","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"dd0b36f1cf95eb5df1086804d03a26db896cd04eec1c9e832d8b3fd040473013","cross_cats_sorted":["math.AT","math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2021-09-08T03:15:28Z","title_canon_sha256":"4fd689d693b0f8f6ae9f2d2d40e2fb529b8848a07e5babc7ee0188637cae5739"},"schema_version":"1.0","source":{"id":"2109.03411","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.03411","created_at":"2026-07-05T04:08:58Z"},{"alias_kind":"arxiv_version","alias_value":"2109.03411v3","created_at":"2026-07-05T04:08:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.03411","created_at":"2026-07-05T04:08:58Z"},{"alias_kind":"pith_short_12","alias_value":"LL3DFIHL5XCS","created_at":"2026-07-05T04:08:58Z"},{"alias_kind":"pith_short_16","alias_value":"LL3DFIHL5XCSOGVP","created_at":"2026-07-05T04:08:58Z"},{"alias_kind":"pith_short_8","alias_value":"LL3DFIHL","created_at":"2026-07-05T04:08:58Z"}],"graph_snapshots":[{"event_id":"sha256:f965ed56d98fbb13655fe90bbbb4f7bfc08c9ab8900c5b14bb9467def0cc8a39","target":"graph","created_at":"2026-07-05T04:08:58Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2109.03411/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We construct a new cylinder object for semifree differential graded (dg) categories in the category of dg categories. Using this, we give a practical formula computing homotopy colimits of semifree dg categories. Combining it with the result of Ganatra, Pardon, and Shende, we get a formula computing wrapped Fukaya categories of Weinstein manifolds using their sectorial coverings. This formula has lots of applications including a practical computation of the wrapped Fukaya category of any cotangent bundle or plumbing space. In this paper, we compute wrapped Fukaya categories of cotangent bundle","authors_text":"Dogancan Karabas, Sangjin Lee","cross_cats":["math.AT","math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2021-09-08T03:15:28Z","title":"Homotopy Colimits of DG Categories and Fukaya Categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.03411","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:0c9f55fb8acd2326d24b578906ad720574b63bd976457bb851cdf2482dd7e2e1","target":"record","created_at":"2026-07-05T04:08:58Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"dd0b36f1cf95eb5df1086804d03a26db896cd04eec1c9e832d8b3fd040473013","cross_cats_sorted":["math.AT","math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2021-09-08T03:15:28Z","title_canon_sha256":"4fd689d693b0f8f6ae9f2d2d40e2fb529b8848a07e5babc7ee0188637cae5739"},"schema_version":"1.0","source":{"id":"2109.03411","kind":"arxiv","version":3}},"canonical_sha256":"5af632a0ebedc5271aafe423d4f77a0c8b6c0e23057776b5d055f19706b1abb6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5af632a0ebedc5271aafe423d4f77a0c8b6c0e23057776b5d055f19706b1abb6","first_computed_at":"2026-07-05T04:08:58.579708Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:08:58.579708Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3M/buC+nVySkClSy0KG8hIzTpdifO+n5Gh6FhJHHYatjlqE2XXUCn33wDipxAQXhaNvTUyHCUmYuJFeh19WqDA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:08:58.580137Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.03411","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c9f55fb8acd2326d24b578906ad720574b63bd976457bb851cdf2482dd7e2e1","sha256:f965ed56d98fbb13655fe90bbbb4f7bfc08c9ab8900c5b14bb9467def0cc8a39"],"state_sha256":"dedcabdf607b53a07dc2f94355eecaf880117828d6108f1c14635115c97c211d"}