{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:KXFHJUX57XMG326ZB5MJ5NMT7X","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":"bc6b5849d762682d95338d9a32cb990cdc02185a91d6aab5ae826ea6a7d42d0e","cross_cats_sorted":["math-ph","math.GT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-01-20T18:35:28Z","title_canon_sha256":"34478c18f0dad08200e446019c668393a2f3202f4bae1a9f9e70c575b9047c08"},"schema_version":"1.0","source":{"id":"2201.08351","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2201.08351","created_at":"2026-07-05T05:30:06Z"},{"alias_kind":"arxiv_version","alias_value":"2201.08351v3","created_at":"2026-07-05T05:30:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.08351","created_at":"2026-07-05T05:30:06Z"},{"alias_kind":"pith_short_12","alias_value":"KXFHJUX57XMG","created_at":"2026-07-05T05:30:06Z"},{"alias_kind":"pith_short_16","alias_value":"KXFHJUX57XMG326Z","created_at":"2026-07-05T05:30:06Z"},{"alias_kind":"pith_short_8","alias_value":"KXFHJUX5","created_at":"2026-07-05T05:30:06Z"}],"graph_snapshots":[{"event_id":"sha256:a166120c61f442ac662c1bd8fbb85c22da19e25158a32da8a5099bdbc8e77955","target":"graph","created_at":"2026-07-05T05:30:06Z","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/2201.08351/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We calculate homological blocks for a knot in Seifert manifolds when the gauge group is $SU(N)$. We obtain the homological blocks with a given representation of the gauge group from the expectation value of the Wilson loop operator by analytically continuing the Chern-Simons level. We also obtain homological blocks with the analytically continued level and representation for a knot in the Seifert integer homology spheres.","authors_text":"Hee-Joong Chung","cross_cats":["math-ph","math.GT","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-01-20T18:35:28Z","title":"BPS Invariants for a Knot in Seifert Manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.08351","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":"sha256:0a15c7b2203e19b6dd5389082653bcbf016157f745afb69dfb13bd903da690b7","target":"record","created_at":"2026-07-05T05:30:06Z","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":"bc6b5849d762682d95338d9a32cb990cdc02185a91d6aab5ae826ea6a7d42d0e","cross_cats_sorted":["math-ph","math.GT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-01-20T18:35:28Z","title_canon_sha256":"34478c18f0dad08200e446019c668393a2f3202f4bae1a9f9e70c575b9047c08"},"schema_version":"1.0","source":{"id":"2201.08351","kind":"arxiv","version":3}},"canonical_sha256":"55ca74d2fdfdd86debd90f589eb593fdce2f00e34d9a9ddaa7e8bebff7451905","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"55ca74d2fdfdd86debd90f589eb593fdce2f00e34d9a9ddaa7e8bebff7451905","first_computed_at":"2026-07-05T05:30:06.037280Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:30:06.037280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UZPmaNW/sSWN/1FHTLpE5CZVE6FnVulPzSAadL7ImRHQ7TeU1z7aWgeBV1os5/w++XAWQpb+dEF44BmH+LkKCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:30:06.037774Z","signed_message":"canonical_sha256_bytes"},"source_id":"2201.08351","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a15c7b2203e19b6dd5389082653bcbf016157f745afb69dfb13bd903da690b7","sha256:a166120c61f442ac662c1bd8fbb85c22da19e25158a32da8a5099bdbc8e77955"],"state_sha256":"d0d8c57958b66675a921d37a229b810cfa5ba0091d7782773409ace42ccf0c6a"}