{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:RVPAI7VIEGHSNVSFQOHD66P53A","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":"690659c030a3071ad224fd482c5eaf697c25fc56b2a874429bd72c0787bb9fab","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2019-08-27T17:55:39Z","title_canon_sha256":"dbcb0afc4bb15c1eac95d76b72d6cd4877c4440a45ae339fe3ef707f72a2f27b"},"schema_version":"1.0","source":{"id":"1908.10358","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.10358","created_at":"2026-07-05T05:13:27Z"},{"alias_kind":"arxiv_version","alias_value":"1908.10358v2","created_at":"2026-07-05T05:13:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.10358","created_at":"2026-07-05T05:13:27Z"},{"alias_kind":"pith_short_12","alias_value":"RVPAI7VIEGHS","created_at":"2026-07-05T05:13:27Z"},{"alias_kind":"pith_short_16","alias_value":"RVPAI7VIEGHSNVSF","created_at":"2026-07-05T05:13:27Z"},{"alias_kind":"pith_short_8","alias_value":"RVPAI7VI","created_at":"2026-07-05T05:13:27Z"}],"graph_snapshots":[{"event_id":"sha256:93785262a2190943fc847a15b589ebfc2373d79b3a83360bb7bc8fe728a51b55","target":"graph","created_at":"2026-07-05T05:13:27Z","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/1908.10358/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We compare two associative algebras which encode the \"quantum topology\" of Legendrian curves in contact threefolds of product type $S\\times\\mathbb R$. The first is the skein algebra of graded Legendrian links and the second is the Hall algebra of the Fukaya category of $S$. We construct a natural homomorphism from the former to the latter, which we show is an isomorphism if $S$ is a disk with marked points and injective if $S$ is the annulus.","authors_text":"Fabian Haiden","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2019-08-27T17:55:39Z","title":"Legendrian skein algebras and Hall algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.10358","kind":"arxiv","version":2},"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":"sha256:2438702a636a662357d75dc2a5e377e14e0e0a0ce671c989fc19e696f48fe3ef","target":"record","created_at":"2026-07-05T05:13:27Z","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":"690659c030a3071ad224fd482c5eaf697c25fc56b2a874429bd72c0787bb9fab","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2019-08-27T17:55:39Z","title_canon_sha256":"dbcb0afc4bb15c1eac95d76b72d6cd4877c4440a45ae339fe3ef707f72a2f27b"},"schema_version":"1.0","source":{"id":"1908.10358","kind":"arxiv","version":2}},"canonical_sha256":"8d5e047ea8218f26d645838e3f79fdd820dc6331cd975c8d8de9a67df154785e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d5e047ea8218f26d645838e3f79fdd820dc6331cd975c8d8de9a67df154785e","first_computed_at":"2026-07-05T05:13:27.083542Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:13:27.083542Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6v8G1W2G6gcH9m5qoTe4Retb+8PGiKATLmU637N8bo68Me/0Al6ow+7zjTgINOXOFPSQ/2VYIa+7HTiaXg6+Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:13:27.083950Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.10358","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2438702a636a662357d75dc2a5e377e14e0e0a0ce671c989fc19e696f48fe3ef","sha256:93785262a2190943fc847a15b589ebfc2373d79b3a83360bb7bc8fe728a51b55"],"state_sha256":"e3dd14ac1dc3e7f3cc8b2d7a161a74c2418507b02d441c86cff21975f8e3c48b"}