{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:4KE3WQAKLLIIMGCAVRZGM5YF4H","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":"100b74d948d11ef614e1b1d3361450a06b4fd6f0d0bcd39d37189911d001f512","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-10-30T19:02:22Z","title_canon_sha256":"3b690c99fcf82fd000fdffd031c42f879072985dbc85b228a0cd55dcd3a8de42"},"schema_version":"1.0","source":{"id":"1910.14086","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1910.14086","created_at":"2026-07-05T00:41:45Z"},{"alias_kind":"arxiv_version","alias_value":"1910.14086v1","created_at":"2026-07-05T00:41:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.14086","created_at":"2026-07-05T00:41:45Z"},{"alias_kind":"pith_short_12","alias_value":"4KE3WQAKLLII","created_at":"2026-07-05T00:41:45Z"},{"alias_kind":"pith_short_16","alias_value":"4KE3WQAKLLIIMGCA","created_at":"2026-07-05T00:41:45Z"},{"alias_kind":"pith_short_8","alias_value":"4KE3WQAK","created_at":"2026-07-05T00:41:45Z"}],"graph_snapshots":[{"event_id":"sha256:c985f9136fd055579dda446e31360b8b27b5240e130cef2465538ec042a6512d","target":"graph","created_at":"2026-07-05T00:41:45Z","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/1910.14086/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"By incorporating higher-form symmetries, we propose a refined definition of the theories obtained by compactification of the 6d $(2,0)$ theory on a three-manifold $M_3$. This generalization is applicable to both the 3d $\\mathcal{N}=2$ and $\\mathcal{N}=1$ supersymmetric reductions. An observable that is sensitive to the higher-form symmetries is the Witten index, which can be computed by counting solutions to a set of Bethe equations that are determined by $M_3$. This is carried out in detail for $M_3$ a Seifert manifold, where we compute a refined version of the Witten index. In the context of","authors_text":"Brian Willett, Heeyeon Kim, Julius Eckhard, Sakura Schafer-Nameki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-10-30T19:02:22Z","title":"Higher-Form Symmetries, Bethe Vacua, and the 3d-3d Correspondence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.14086","kind":"arxiv","version":1},"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:c12cd6da7261714dcd764cd6a387432d9990ced2a959f38afd2256b7b59f385a","target":"record","created_at":"2026-07-05T00:41:45Z","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":"100b74d948d11ef614e1b1d3361450a06b4fd6f0d0bcd39d37189911d001f512","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-10-30T19:02:22Z","title_canon_sha256":"3b690c99fcf82fd000fdffd031c42f879072985dbc85b228a0cd55dcd3a8de42"},"schema_version":"1.0","source":{"id":"1910.14086","kind":"arxiv","version":1}},"canonical_sha256":"e289bb400a5ad0861840ac72667705e1e5d29da3e4520a8eba4338006112e110","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e289bb400a5ad0861840ac72667705e1e5d29da3e4520a8eba4338006112e110","first_computed_at":"2026-07-05T00:41:45.220973Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:41:45.220973Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RvQbwDHi9a2mtMsSyTDw+VTDx5bbU/7NAmRt/vNF6E+Rai2OW9/Azy114Nt2SRujapv/lAmWq+g0xFaa9Q1cDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:41:45.221493Z","signed_message":"canonical_sha256_bytes"},"source_id":"1910.14086","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c12cd6da7261714dcd764cd6a387432d9990ced2a959f38afd2256b7b59f385a","sha256:c985f9136fd055579dda446e31360b8b27b5240e130cef2465538ec042a6512d"],"state_sha256":"4b1ff8e317111480788039e075d300cf590da85739fb2bc70ac8102caa44625c"}