{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:URBMVWOMLUMAIXV5FTWQRUJBVH","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":"9bb90fddeb645c087fabe8c8863235a5b8f3a26a667e6f391ef6ebd598257e79","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"1998-03-25T19:28:35Z","title_canon_sha256":"3eaaa546820dd22b6d818e15b1dee4bafc615bf53c93c01f30b32d7b606a0582"},"schema_version":"1.0","source":{"id":"math/9803124","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9803124","created_at":"2026-05-18T02:20:20Z"},{"alias_kind":"arxiv_version","alias_value":"math/9803124v6","created_at":"2026-05-18T02:20:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9803124","created_at":"2026-05-18T02:20:20Z"},{"alias_kind":"pith_short_12","alias_value":"URBMVWOMLUMA","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"URBMVWOMLUMAIXV5","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"URBMVWOM","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:5a162a3df7db80a6893569d9ac2cf94fa943e882f99fd3e56263f10d0d9300a1","target":"graph","created_at":"2026-05-18T02:20:20Z","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":"Let $G$ be a semisimple complex Lie group with a Borel subgroup $B$. Let $X=G/B$ be the flag manifold of $G$. Let $C=P^1\\ni\\infty$ be the projective line. Let $\\alpha\\in H_2(X,{\\Bbb Z})$. The moduli space of $G$-monopoles of topological charge $\\alpha$ (see e.g. [Jarvis]) is naturally identified with the space $M_b(X,\\alpha)$ of based maps from $(C,\\infty)$ to $(X,B)$ of degree $\\alpha$. The moduli space of $G$-monopoles carries a natural hyperk\\\"ahler structure, and hence a holomorphic symplectic structure. We propose a simple explicit formula for the symplectic structure on $M_b(X,\\alpha)$. ","authors_text":"Alexander Kuznetsov, Ivan Mirkovi\\'c, Michael Finkelberg, Nikita Markarian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"1998-03-25T19:28:35Z","title":"A note on the symplectic structure on the space of G-monopoles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9803124","kind":"arxiv","version":6},"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":"sha256:32aa0f1ac73b88d6ce3c74fb90e21affc175a9a754871af2d2407ba79650a269","target":"record","created_at":"2026-05-18T02:20:20Z","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":"9bb90fddeb645c087fabe8c8863235a5b8f3a26a667e6f391ef6ebd598257e79","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"1998-03-25T19:28:35Z","title_canon_sha256":"3eaaa546820dd22b6d818e15b1dee4bafc615bf53c93c01f30b32d7b606a0582"},"schema_version":"1.0","source":{"id":"math/9803124","kind":"arxiv","version":6}},"canonical_sha256":"a442cad9cc5d18045ebd2ced08d121a9c4bacf429301b3b745fce4d9756b73d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a442cad9cc5d18045ebd2ced08d121a9c4bacf429301b3b745fce4d9756b73d8","first_computed_at":"2026-05-18T02:20:20.821515Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:20.821515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dq4/u3zzGaJMkea66T/JtUlMbFF8u2I9t8SNYywn+3BUQ+JV0Jgeqrjx+7+YbJcWiEWcn02mtgATYpM3ADcjAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:20.822200Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9803124","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32aa0f1ac73b88d6ce3c74fb90e21affc175a9a754871af2d2407ba79650a269","sha256:5a162a3df7db80a6893569d9ac2cf94fa943e882f99fd3e56263f10d0d9300a1"],"state_sha256":"130d048907b1a6d8f91f8719af0149197fdab761b0ae7da1a81899abe1892208"}