{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:2DTJ7K7AVRIAMIK2YTGQDYFOSU","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":"e143e7bb12e18f5ef950152bf22bedcee75fb6f894a72fb7a62075e62ea0b99a","cross_cats_sorted":["math.RT"],"license":"","primary_cat":"math.AG","submitted_at":"2001-07-13T10:01:35Z","title_canon_sha256":"d1aa99ab926d807b9c004138d417213520e09b000cc26e97cd68030da2ee9726"},"schema_version":"1.0","source":{"id":"math/0107103","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0107103","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"arxiv_version","alias_value":"math/0107103v1","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0107103","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"pith_short_12","alias_value":"2DTJ7K7AVRIA","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"2DTJ7K7AVRIAMIK2","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"2DTJ7K7A","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:096b746f625ced3714a3328e8a79243f1ef35cb6ff395e4bf7d1b08ad7238045","target":"graph","created_at":"2026-05-18T01:38:29Z","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 count the connected components in the moduli space of PU(p,q)-representations of the fundamental group for a closed oriented surface. The components are labelled by pairs of integers which arise as topological invariants of the flat bundles associated to the representations. Our results show that for each allowed value of these invariants, which are bounded by a Milnor-Wood type inequality, there is a unique non-empty connected component. Interpreting the moduli space of representations as a moduli space of Higgs bundles, we take a Morse theoretic approach using a certain smooth proper func","authors_text":"(2) Universidad Autonoma de Madrid, (3) Universidade do Porto), Oscar Garcia-Prada (2), Peter B. Gothen (3) ((1) University of Illinois, Steven B. Bradlow (1)","cross_cats":["math.RT"],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2001-07-13T10:01:35Z","title":"Representations of the fundamental group of a surface in PU(p,q) and holomorphic triples"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0107103","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:a2a5575788685cebd840aed3f56b4389febbe6a747a40482afb758af8999a864","target":"record","created_at":"2026-05-18T01:38:29Z","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":"e143e7bb12e18f5ef950152bf22bedcee75fb6f894a72fb7a62075e62ea0b99a","cross_cats_sorted":["math.RT"],"license":"","primary_cat":"math.AG","submitted_at":"2001-07-13T10:01:35Z","title_canon_sha256":"d1aa99ab926d807b9c004138d417213520e09b000cc26e97cd68030da2ee9726"},"schema_version":"1.0","source":{"id":"math/0107103","kind":"arxiv","version":1}},"canonical_sha256":"d0e69fabe0ac5006215ac4cd01e0ae950a7baaa2f17b125d92539684ef7b4dca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d0e69fabe0ac5006215ac4cd01e0ae950a7baaa2f17b125d92539684ef7b4dca","first_computed_at":"2026-05-18T01:38:29.882172Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:29.882172Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3VekDcytXZLGapqk4s7zLdIzem6WRw6b/OoTV0RqRGPexAJ+jgGDfYL9ICyUsVdZHZHMjpBqxnBqw9SmSy5rAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:29.882612Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0107103","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2a5575788685cebd840aed3f56b4389febbe6a747a40482afb758af8999a864","sha256:096b746f625ced3714a3328e8a79243f1ef35cb6ff395e4bf7d1b08ad7238045"],"state_sha256":"9b792f00170b612be209f442d2a29c0c448978ed79d448ec073bb6761f4296d5"}