{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:5AAARNA6UJ27C3VTDAJQFL5E65","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":"ce4b6b4f0e6e115586610500b8cfe126ca0451b045d213763761ab7abc64e9b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2025-10-31T01:51:46Z","title_canon_sha256":"0c7d1afe61366ce8716a818efcfb6a7fc6cbc7c6ad7c7dd753d39ff12e370c6e"},"schema_version":"1.0","source":{"id":"2510.27100","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2510.27100","created_at":"2026-05-20T00:02:57Z"},{"alias_kind":"arxiv_version","alias_value":"2510.27100v3","created_at":"2026-05-20T00:02:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.27100","created_at":"2026-05-20T00:02:57Z"},{"alias_kind":"pith_short_12","alias_value":"5AAARNA6UJ27","created_at":"2026-05-20T00:02:57Z"},{"alias_kind":"pith_short_16","alias_value":"5AAARNA6UJ27C3VT","created_at":"2026-05-20T00:02:57Z"},{"alias_kind":"pith_short_8","alias_value":"5AAARNA6","created_at":"2026-05-20T00:02:57Z"}],"graph_snapshots":[{"event_id":"sha256:d638ca826cc8c36f7976890821f4b4353c64b0a9f8e3b813111a96cf5150fc5e","target":"graph","created_at":"2026-05-20T00:02:57Z","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/2510.27100/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The notion of meromorphic convexity is defined and studied on complex manifolds. Using this notion, in analogy with Stein manifolds, a new class of complex manifolds, called {\\calligra M }-manifolds, is introduced. This is a class of complex manifolds with a good supply of global meromorphic functions, in particular, it includes all Stein manifolds and projective manifolds. It is also shown that there exist noncompact complex manifolds, known as long $\\mathbb C^2$, that are {\\calligra M }-manifolds but do not contain any nonconstant holomorphic functions.","authors_text":"Blake J Boudreaux, Rasul Shafikov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2025-10-31T01:51:46Z","title":"Meromorphic Convexity on Complex Manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.27100","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:a15a31fdc98c7911b3ef55a12373824251dab7b0fe96bf069d081646fcc2fff9","target":"record","created_at":"2026-05-20T00:02:57Z","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":"ce4b6b4f0e6e115586610500b8cfe126ca0451b045d213763761ab7abc64e9b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2025-10-31T01:51:46Z","title_canon_sha256":"0c7d1afe61366ce8716a818efcfb6a7fc6cbc7c6ad7c7dd753d39ff12e370c6e"},"schema_version":"1.0","source":{"id":"2510.27100","kind":"arxiv","version":3}},"canonical_sha256":"e80008b41ea275f16eb3181302afa4f7644917c3b29fdb9843b8c70f92096178","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e80008b41ea275f16eb3181302afa4f7644917c3b29fdb9843b8c70f92096178","first_computed_at":"2026-05-20T00:02:57.938094Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:02:57.938094Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yaBVcjPnhG1Ma6ZGZKXnBWqMg6sARDCyTsULSK/0g89JHmKyDqTq4nC3qgNeCX38Zyq+bkbCXxXZh6BPOAylCg==","signature_status":"signed_v1","signed_at":"2026-05-20T00:02:57.938799Z","signed_message":"canonical_sha256_bytes"},"source_id":"2510.27100","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a15a31fdc98c7911b3ef55a12373824251dab7b0fe96bf069d081646fcc2fff9","sha256:d638ca826cc8c36f7976890821f4b4353c64b0a9f8e3b813111a96cf5150fc5e"],"state_sha256":"f10eed4446830ca8b689b4b23a9c5a96485b269d0440089e6d374b05c9a5cce3"}