{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:BJB37W5DXHUVLEZQFOMI4WHSDM","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":"48be3aeea3998a55f1188f8553668ebcbb84aec880c938460b427d148666a6e5","cross_cats_sorted":["math.AT","math.QA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-08-23T16:57:17Z","title_canon_sha256":"1b088df258516503c69b435265084d26704e030aa1e874b3f0c63a0c92f011ad"},"schema_version":"1.0","source":{"id":"2108.10286","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2108.10286","created_at":"2026-07-05T03:54:22Z"},{"alias_kind":"arxiv_version","alias_value":"2108.10286v2","created_at":"2026-07-05T03:54:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.10286","created_at":"2026-07-05T03:54:22Z"},{"alias_kind":"pith_short_12","alias_value":"BJB37W5DXHUV","created_at":"2026-07-05T03:54:22Z"},{"alias_kind":"pith_short_16","alias_value":"BJB37W5DXHUVLEZQ","created_at":"2026-07-05T03:54:22Z"},{"alias_kind":"pith_short_8","alias_value":"BJB37W5D","created_at":"2026-07-05T03:54:22Z"}],"graph_snapshots":[{"event_id":"sha256:fa9161752d1e263d1677774f24c1bdc9fd6bcdb6113d1b3dd4b3df78392b2b47","target":"graph","created_at":"2026-07-05T03:54:22Z","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/2108.10286/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The quiver Yangian, an infinite-dimensional algebra introduced recently in arXiv:2003.08909, is the algebra underlying BPS state counting problems for toric Calabi-Yau three-folds. We introduce trigonometric and elliptic analogues of quiver Yangians, which we call toroidal quiver algebras and elliptic quiver algebras, respectively. We construct the representations of the shifted toroidal and elliptic algebras in terms of the statistical model of crystal melting. We also derive the algebras and their representations from equivariant localization of three-dimensional $\\mathcal{N}=2$ supersymmetr","authors_text":"Dmitry Galakhov, Masahito Yamazaki, Wei Li","cross_cats":["math.AT","math.QA","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-08-23T16:57:17Z","title":"Toroidal and Elliptic Quiver BPS Algebras and Beyond"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.10286","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":"sha256:95a6adb3173b735f435111676b0a298f8a49f75259b89f2a5ffa2f75a2ba108e","target":"record","created_at":"2026-07-05T03:54:22Z","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":"48be3aeea3998a55f1188f8553668ebcbb84aec880c938460b427d148666a6e5","cross_cats_sorted":["math.AT","math.QA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-08-23T16:57:17Z","title_canon_sha256":"1b088df258516503c69b435265084d26704e030aa1e874b3f0c63a0c92f011ad"},"schema_version":"1.0","source":{"id":"2108.10286","kind":"arxiv","version":2}},"canonical_sha256":"0a43bfdba3b9e95593302b988e58f21b2fbb45285b45c522b753662000d6e690","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a43bfdba3b9e95593302b988e58f21b2fbb45285b45c522b753662000d6e690","first_computed_at":"2026-07-05T03:54:22.996991Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:54:22.996991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FN1hvEMwiH5jDMGTQBKpeiLp3qsxJMRHToZsvRJLgjhk1gpeJ2dPSSpEnvljNV2HRhsupikciq1umHfurUwjCA==","signature_status":"signed_v1","signed_at":"2026-07-05T03:54:22.997348Z","signed_message":"canonical_sha256_bytes"},"source_id":"2108.10286","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:95a6adb3173b735f435111676b0a298f8a49f75259b89f2a5ffa2f75a2ba108e","sha256:fa9161752d1e263d1677774f24c1bdc9fd6bcdb6113d1b3dd4b3df78392b2b47"],"state_sha256":"8a04bb2fae5ee515fdcaa8e6c8c7b6bd90d9e5e6d61babbce36afdada289722e"}