{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:25AD3JKIO2DO2KBXBN2BWHQPDO","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":"3ecba7892843a74184aa7ff0feed2ecc679239c08ad6f34961888272c105678b","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-10-29T15:55:56Z","title_canon_sha256":"14f0ecb1157da8e580bb769fb11e10fd1a1dd6fe1ee4cc37c9cb7dc1f805ceb9"},"schema_version":"1.0","source":{"id":"0910.5534","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.5534","created_at":"2026-05-18T04:22:48Z"},{"alias_kind":"arxiv_version","alias_value":"0910.5534v3","created_at":"2026-05-18T04:22:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.5534","created_at":"2026-05-18T04:22:48Z"},{"alias_kind":"pith_short_12","alias_value":"25AD3JKIO2DO","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"25AD3JKIO2DO2KBX","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"25AD3JKI","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:ee889680b5ae8989bcdea90092946cd848c63bdd84020891ec47ff56de0782d0","target":"graph","created_at":"2026-05-18T04:22:48Z","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"},"paper":{"abstract_excerpt":"We define the category of B-branes in a (not necessarily affine) Landau-Ginzburg B-model, incorporating the notion of R-charge. Our definition is a direct generalization of the category of perfect complexes. We then consider pairs of Landau-Ginzburg B-models that arise as different GIT quotients of a vector space by a one-dimensional torus, and show that for each such pair the two categories of B-branes are quasi-equivalent. In fact we produce a whole set of quasi-equivalences indexed by the integers, and show that the resulting auto-equivalences are all spherical twists.","authors_text":"Ed Segal","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-10-29T15:55:56Z","title":"Equivalences between GIT quotients of Landau-Ginzburg B-models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.5534","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":"sha256:9b5ecbd906ca9f91d9dfcd8e3f975801809fe560fade98bb31800898e32a4b3f","target":"record","created_at":"2026-05-18T04:22:48Z","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":"3ecba7892843a74184aa7ff0feed2ecc679239c08ad6f34961888272c105678b","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-10-29T15:55:56Z","title_canon_sha256":"14f0ecb1157da8e580bb769fb11e10fd1a1dd6fe1ee4cc37c9cb7dc1f805ceb9"},"schema_version":"1.0","source":{"id":"0910.5534","kind":"arxiv","version":3}},"canonical_sha256":"d7403da5487686ed28370b741b1e0f1b8661bf86eaf2494d8b29e68f714cd32e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d7403da5487686ed28370b741b1e0f1b8661bf86eaf2494d8b29e68f714cd32e","first_computed_at":"2026-05-18T04:22:48.935260Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:22:48.935260Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nxrK7c3kYdEXrNuLFAbRlD+J4aNTPjVXOPV29BTsNER1LZQF5FnYjMBibrIsL2a7pxdpExR/6xxjrixS9zdFCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:22:48.935877Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.5534","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b5ecbd906ca9f91d9dfcd8e3f975801809fe560fade98bb31800898e32a4b3f","sha256:ee889680b5ae8989bcdea90092946cd848c63bdd84020891ec47ff56de0782d0"],"state_sha256":"32288d571e0d8c066d0ae6cd2dcf7f58e9109d974ea170f7ea2b8e442375a791"}