{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:F4NEZLYFTJHP4EQ2VGTC4DDZN4","short_pith_number":"pith:F4NEZLYF","schema_version":"1.0","canonical_sha256":"2f1a4caf059a4efe121aa9a62e0c796f3660ec0ea2e95222e3e788a1c8a629b9","source":{"kind":"arxiv","id":"2202.06833","version":2},"attestation_state":"computed","paper":{"title":"Perverse schobers and 3d mirror symmetry","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th","math.AG","math.AT"],"primary_cat":"math.RT","authors_text":"Aaron Mazel-Gee, Benjamin Gammage, Justin Hilburn","submitted_at":"2022-02-14T16:12:20Z","abstract_excerpt":"The proposed physical duality known as 3d mirror symmetry relates the geometries of dual pairs of holomorphic symplectic stacks. It has served in recent years as a guiding principle for developments in representation theory. However, due to the lack of definitions, thus far only small pieces of the subject have been mathematically accessible.\n  In this paper, we formulate abelian 3d mirror symmetry as an equivalence between a pair of 2-categories constructed from the algebraic and symplectic geometry, respectively, of Gale dual toric cotangent stacks. In the simplest case, our theorem provides"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2202.06833","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2022-02-14T16:12:20Z","cross_cats_sorted":["hep-th","math.AG","math.AT"],"title_canon_sha256":"7364c0a74a4937a60e49927523b903d71f50d9be9224c254bf7ea9c8bd04f56e","abstract_canon_sha256":"18522b0ee4118a0d1e63eae6dc0cdd592ba47a4d8dd4d636a092b234795b2963"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:14:33.973272Z","signature_b64":"vFjm6Oc9KSwPibTH2nf1X0UXgdYauqHJvbb9BLH/IzJW2dZU4z8k3BT+K/V9jBUSlHOIkvgwT74DIcQfk8sDDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f1a4caf059a4efe121aa9a62e0c796f3660ec0ea2e95222e3e788a1c8a629b9","last_reissued_at":"2026-07-05T06:14:33.972926Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:14:33.972926Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Perverse schobers and 3d mirror symmetry","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th","math.AG","math.AT"],"primary_cat":"math.RT","authors_text":"Aaron Mazel-Gee, Benjamin Gammage, Justin Hilburn","submitted_at":"2022-02-14T16:12:20Z","abstract_excerpt":"The proposed physical duality known as 3d mirror symmetry relates the geometries of dual pairs of holomorphic symplectic stacks. It has served in recent years as a guiding principle for developments in representation theory. However, due to the lack of definitions, thus far only small pieces of the subject have been mathematically accessible.\n  In this paper, we formulate abelian 3d mirror symmetry as an equivalence between a pair of 2-categories constructed from the algebraic and symplectic geometry, respectively, of Gale dual toric cotangent stacks. In the simplest case, our theorem provides"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.06833","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2202.06833/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2202.06833","created_at":"2026-07-05T06:14:33.972979+00:00"},{"alias_kind":"arxiv_version","alias_value":"2202.06833v2","created_at":"2026-07-05T06:14:33.972979+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.06833","created_at":"2026-07-05T06:14:33.972979+00:00"},{"alias_kind":"pith_short_12","alias_value":"F4NEZLYFTJHP","created_at":"2026-07-05T06:14:33.972979+00:00"},{"alias_kind":"pith_short_16","alias_value":"F4NEZLYFTJHP4EQ2","created_at":"2026-07-05T06:14:33.972979+00:00"},{"alias_kind":"pith_short_8","alias_value":"F4NEZLYF","created_at":"2026-07-05T06:14:33.972979+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2412.17906","citing_title":"Nonabelian shift operators and shifted Yangians","ref_index":22,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/F4NEZLYFTJHP4EQ2VGTC4DDZN4","json":"https://pith.science/pith/F4NEZLYFTJHP4EQ2VGTC4DDZN4.json","graph_json":"https://pith.science/api/pith-number/F4NEZLYFTJHP4EQ2VGTC4DDZN4/graph.json","events_json":"https://pith.science/api/pith-number/F4NEZLYFTJHP4EQ2VGTC4DDZN4/events.json","paper":"https://pith.science/paper/F4NEZLYF"},"agent_actions":{"view_html":"https://pith.science/pith/F4NEZLYFTJHP4EQ2VGTC4DDZN4","download_json":"https://pith.science/pith/F4NEZLYFTJHP4EQ2VGTC4DDZN4.json","view_paper":"https://pith.science/paper/F4NEZLYF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2202.06833&json=true","fetch_graph":"https://pith.science/api/pith-number/F4NEZLYFTJHP4EQ2VGTC4DDZN4/graph.json","fetch_events":"https://pith.science/api/pith-number/F4NEZLYFTJHP4EQ2VGTC4DDZN4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F4NEZLYFTJHP4EQ2VGTC4DDZN4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F4NEZLYFTJHP4EQ2VGTC4DDZN4/action/storage_attestation","attest_author":"https://pith.science/pith/F4NEZLYFTJHP4EQ2VGTC4DDZN4/action/author_attestation","sign_citation":"https://pith.science/pith/F4NEZLYFTJHP4EQ2VGTC4DDZN4/action/citation_signature","submit_replication":"https://pith.science/pith/F4NEZLYFTJHP4EQ2VGTC4DDZN4/action/replication_record"}},"created_at":"2026-07-05T06:14:33.972979+00:00","updated_at":"2026-07-05T06:14:33.972979+00:00"}