{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:HGMZAHL5ML3V4BBZRMLZQCRMM6","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":"057d9328b6dff83ee4656195cdf92390a6955cfc1e661f7d4bad59587d845405","cross_cats_sorted":["math-ph","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-09-05T11:49:19Z","title_canon_sha256":"33647beee5de069c542ca2d2270dfb02c2d3f912e286ed6761f4212101cccdf9"},"schema_version":"1.0","source":{"id":"2109.02045","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.02045","created_at":"2026-07-05T04:25:45Z"},{"alias_kind":"arxiv_version","alias_value":"2109.02045v4","created_at":"2026-07-05T04:25:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.02045","created_at":"2026-07-05T04:25:45Z"},{"alias_kind":"pith_short_12","alias_value":"HGMZAHL5ML3V","created_at":"2026-07-05T04:25:45Z"},{"alias_kind":"pith_short_16","alias_value":"HGMZAHL5ML3V4BBZ","created_at":"2026-07-05T04:25:45Z"},{"alias_kind":"pith_short_8","alias_value":"HGMZAHL5","created_at":"2026-07-05T04:25:45Z"}],"graph_snapshots":[{"event_id":"sha256:437b1c3a3fec7b87e9e8a6eace557abf6ba57c463d5eb2eae00cc2bbe989863e","target":"graph","created_at":"2026-07-05T04:25:45Z","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/2109.02045/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Recently, new classes of infinite-dimensional algebras, quiver Yangian (QY) and shifted QY, were introduced, and they act on BPS states for non-compact toric Calabi-Yau threefolds. In particular, shifted QY acts on general subcrystals of the original BPS crystal. A trigonometric deformation called quiver quantum toroidal algebra (QQTA) was also proposed and shown to act on the same BPS crystal. Unlike QY, QQTA has a formal Hopf superalgebra structure which is useful in deriving representations.\n  In this paper, we define the shifted QQTA and study a class of their representations. We define 1d","authors_text":"Akimi Watanabe, Go Noshita","cross_cats":["math-ph","math.MP","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-09-05T11:49:19Z","title":"Shifted Quiver Quantum Toroidal Algebra and Subcrystal Representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.02045","kind":"arxiv","version":4},"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":"sha256:14a16e5519a059f64240d65f0d23282b4e12b9df1698b820cec6940aaa0dffae","target":"record","created_at":"2026-07-05T04:25:45Z","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":"057d9328b6dff83ee4656195cdf92390a6955cfc1e661f7d4bad59587d845405","cross_cats_sorted":["math-ph","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-09-05T11:49:19Z","title_canon_sha256":"33647beee5de069c542ca2d2270dfb02c2d3f912e286ed6761f4212101cccdf9"},"schema_version":"1.0","source":{"id":"2109.02045","kind":"arxiv","version":4}},"canonical_sha256":"3999901d7d62f75e04398b17980a2c67bfa93a8b78e19150944f6ba72b796537","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3999901d7d62f75e04398b17980a2c67bfa93a8b78e19150944f6ba72b796537","first_computed_at":"2026-07-05T04:25:45.373217Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:25:45.373217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8aqgBFmX4oCYC7+4ytiXVW87sh95rMloiPRnk+ocQwDgel3JCVVAd2Pmk720OB2gyEnZyjKdkMtO+4k2JM/HCg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:25:45.373761Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.02045","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:14a16e5519a059f64240d65f0d23282b4e12b9df1698b820cec6940aaa0dffae","sha256:437b1c3a3fec7b87e9e8a6eace557abf6ba57c463d5eb2eae00cc2bbe989863e"],"state_sha256":"41a7a84ab2404e5bf7e795b7fcb0e7ee80499fb5043a6c917bade2b07b3cb495"}