{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:5AAARNA6UJ27C3VTDAJQFL5E65","short_pith_number":"pith:5AAARNA6","canonical_record":{"source":{"id":"2510.27100","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2025-10-31T01:51:46Z","cross_cats_sorted":[],"title_canon_sha256":"0c7d1afe61366ce8716a818efcfb6a7fc6cbc7c6ad7c7dd753d39ff12e370c6e","abstract_canon_sha256":"ce4b6b4f0e6e115586610500b8cfe126ca0451b045d213763761ab7abc64e9b5"},"schema_version":"1.0"},"canonical_sha256":"e80008b41ea275f16eb3181302afa4f7644917c3b29fdb9843b8c70f92096178","source":{"kind":"arxiv","id":"2510.27100","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:5AAARNA6UJ27C3VTDAJQFL5E65","target":"record","payload":{"canonical_record":{"source":{"id":"2510.27100","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2025-10-31T01:51:46Z","cross_cats_sorted":[],"title_canon_sha256":"0c7d1afe61366ce8716a818efcfb6a7fc6cbc7c6ad7c7dd753d39ff12e370c6e","abstract_canon_sha256":"ce4b6b4f0e6e115586610500b8cfe126ca0451b045d213763761ab7abc64e9b5"},"schema_version":"1.0"},"canonical_sha256":"e80008b41ea275f16eb3181302afa4f7644917c3b29fdb9843b8c70f92096178","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:02:57.938799Z","signature_b64":"yaBVcjPnhG1Ma6ZGZKXnBWqMg6sARDCyTsULSK/0g89JHmKyDqTq4nC3qgNeCX38Zyq+bkbCXxXZh6BPOAylCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e80008b41ea275f16eb3181302afa4f7644917c3b29fdb9843b8c70f92096178","last_reissued_at":"2026-05-20T00:02:57.938094Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:02:57.938094Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2510.27100","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-20T00:02:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PNH6I4zIck9+4ejY4blcB31CGP/6So14vZeFfcq6HzI0izbs4jFQhPRWOfwPmD892lmYkWcfRQo3hrU9+slqAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:10:15.455560Z"},"content_sha256":"a15a31fdc98c7911b3ef55a12373824251dab7b0fe96bf069d081646fcc2fff9","schema_version":"1.0","event_id":"sha256:a15a31fdc98c7911b3ef55a12373824251dab7b0fe96bf069d081646fcc2fff9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:5AAARNA6UJ27C3VTDAJQFL5E65","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Meromorphic Convexity on Complex Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Blake J Boudreaux, Rasul Shafikov","submitted_at":"2025-10-31T01:51:46Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.27100","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2510.27100/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-20T00:02:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eEH5bZe0dLz+rQKoOhhbXzY7Tuj6ZksMaUyNeyiKZbK/d2/lSOUG+FpAAwTmUomC7PCqHQKkfIpoGBlpoHjFDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:10:15.455956Z"},"content_sha256":"d638ca826cc8c36f7976890821f4b4353c64b0a9f8e3b813111a96cf5150fc5e","schema_version":"1.0","event_id":"sha256:d638ca826cc8c36f7976890821f4b4353c64b0a9f8e3b813111a96cf5150fc5e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5AAARNA6UJ27C3VTDAJQFL5E65/bundle.json","state_url":"https://pith.science/pith/5AAARNA6UJ27C3VTDAJQFL5E65/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5AAARNA6UJ27C3VTDAJQFL5E65/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-31T06:10:15Z","links":{"resolver":"https://pith.science/pith/5AAARNA6UJ27C3VTDAJQFL5E65","bundle":"https://pith.science/pith/5AAARNA6UJ27C3VTDAJQFL5E65/bundle.json","state":"https://pith.science/pith/5AAARNA6UJ27C3VTDAJQFL5E65/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5AAARNA6UJ27C3VTDAJQFL5E65/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6+6OKF0vSD9BANl7GcF3aXoCLJJ8W53hyWh9Id4oeCu6k7LLh4PKk996rDhR4sgOtUawvb3SeGC1FZ8Y3tY9Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T06:10:15.458807Z","bundle_sha256":"aee0ca6867959681c85e0f9a731f0a040554a466185fd27aaaefed721de01d4b"}}