{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:AKVZLZTN5P4CPAL2HPVMVFJ2C6","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":"38bdd15e2c90e32708e9ed336f69e35ae1626bdb97ce26cc0673e108ab49d929","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-24T08:43:25Z","title_canon_sha256":"26497dd9534af7c6a3fe24119918b787829b5cfb53ce5d4437adf06cce1d8914"},"schema_version":"1.0","source":{"id":"2605.24943","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.24943","created_at":"2026-05-26T01:04:06Z"},{"alias_kind":"arxiv_version","alias_value":"2605.24943v1","created_at":"2026-05-26T01:04:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.24943","created_at":"2026-05-26T01:04:06Z"},{"alias_kind":"pith_short_12","alias_value":"AKVZLZTN5P4C","created_at":"2026-05-26T01:04:06Z"},{"alias_kind":"pith_short_16","alias_value":"AKVZLZTN5P4CPAL2","created_at":"2026-05-26T01:04:06Z"},{"alias_kind":"pith_short_8","alias_value":"AKVZLZTN","created_at":"2026-05-26T01:04:06Z"}],"graph_snapshots":[{"event_id":"sha256:22d3ba936612a213f7c431a8c6d1f77830a070ba6a6d1534c765dc853a85a3c2","target":"graph","created_at":"2026-05-26T01:04:06Z","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/2605.24943/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that every discrete faithful representation of the surfcae group into SL(2,C) is the monodromy of a holomorphic connection on the trivial rank-2 vector bundle over a Riemann surface. As an application, we answer the question posed by Ghys and Huckleberry-Winkelmann (known as the Margulis' problem) by proving that every compact quotient of SL(2,C) contains a holomorphic curve of genus at least two. The main tools we use are the Non-Abelian Hodge correspondence, the WKB analysis, and the Morgan-Shalen compactification.","authors_text":"Vladimir Markovic, Yiran Lin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-24T08:43:25Z","title":"Holomorphic curves in compact quotients of SL(2,C)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.24943","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":"sha256:5d56ca99973c87880a485c6f8e4c620f378559cf79d50d82582b77680107548b","target":"record","created_at":"2026-05-26T01:04:06Z","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":"38bdd15e2c90e32708e9ed336f69e35ae1626bdb97ce26cc0673e108ab49d929","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-24T08:43:25Z","title_canon_sha256":"26497dd9534af7c6a3fe24119918b787829b5cfb53ce5d4437adf06cce1d8914"},"schema_version":"1.0","source":{"id":"2605.24943","kind":"arxiv","version":1}},"canonical_sha256":"02ab95e66debf827817a3beaca953a178cb62166932d530c7eafb4c5e302b832","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02ab95e66debf827817a3beaca953a178cb62166932d530c7eafb4c5e302b832","first_computed_at":"2026-05-26T01:04:06.914474Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T01:04:06.914474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pXntx/20vVxa2RZKUXsl6yrmLLupMeB8QVoh+Kwh++jom1nuitaGjkBseqHTCDuT7cm33f4aeOYylDMNcx9jBA==","signature_status":"signed_v1","signed_at":"2026-05-26T01:04:06.915079Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.24943","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d56ca99973c87880a485c6f8e4c620f378559cf79d50d82582b77680107548b","sha256:22d3ba936612a213f7c431a8c6d1f77830a070ba6a6d1534c765dc853a85a3c2"],"state_sha256":"e15aadfa5de9a027c6e4df91ad2d7a6c099af68b9432dc9f6e55478e38940621"}