{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:QTTBGZVQKAFWKMGOR42SSRLPD5","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":"7d827a78e0ee74f7262edfd6f6c1a2e9ae69c2139304f0dc331a882d7d8ccea9","cross_cats_sorted":["math.AG","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2021-11-22T07:23:56Z","title_canon_sha256":"f4dfdfc4731f9a005f95a3a1b536788a4e305010def747e94877cdca868b81ed"},"schema_version":"1.0","source":{"id":"2111.11024","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.11024","created_at":"2026-07-05T04:27:29Z"},{"alias_kind":"arxiv_version","alias_value":"2111.11024v2","created_at":"2026-07-05T04:27:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.11024","created_at":"2026-07-05T04:27:29Z"},{"alias_kind":"pith_short_12","alias_value":"QTTBGZVQKAFW","created_at":"2026-07-05T04:27:29Z"},{"alias_kind":"pith_short_16","alias_value":"QTTBGZVQKAFWKMGO","created_at":"2026-07-05T04:27:29Z"},{"alias_kind":"pith_short_8","alias_value":"QTTBGZVQ","created_at":"2026-07-05T04:27:29Z"}],"graph_snapshots":[{"event_id":"sha256:f0c666b9835ecdc573aa4dd4d706570d68fe66d9d03f3b8a4bb147c3029d0b82","target":"graph","created_at":"2026-07-05T04:27:29Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2111.11024/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Dinh--Sibony theory of tangent and density currents is a recent but powerful tool to study positive closed currents. Over twenty years ago, Alessandrini and Bassanelli initiated the theory of the Lelong number of a positive plurisubharmonic current in $\\mathbb{C}^k$ along a linear subspace. Although the latter theory is intriguing, it has not yet been explored in-depth since then. Introducing the concept of the generalized Lelong numbers and studying these new numerical values, we extend both theories to a more general class of positive plurisubharmonic currents and in a more general context o","authors_text":"Vi\\^et-Anh Nguy\\^en","cross_cats":["math.AG","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2021-11-22T07:23:56Z","title":"Positive plurisubharmonic currents: Generalized Lelong numbers and Tangent theorems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.11024","kind":"arxiv","version":2},"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":"sha256:04c0c1a7db8cde3761e8452e89658b3e5a4de2a68c457c0ce32e14d114ad5209","target":"record","created_at":"2026-07-05T04:27:29Z","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":"7d827a78e0ee74f7262edfd6f6c1a2e9ae69c2139304f0dc331a882d7d8ccea9","cross_cats_sorted":["math.AG","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2021-11-22T07:23:56Z","title_canon_sha256":"f4dfdfc4731f9a005f95a3a1b536788a4e305010def747e94877cdca868b81ed"},"schema_version":"1.0","source":{"id":"2111.11024","kind":"arxiv","version":2}},"canonical_sha256":"84e61366b0500b6530ce8f3529456f1f50eff10a5d12e2c01030e65b323de6e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"84e61366b0500b6530ce8f3529456f1f50eff10a5d12e2c01030e65b323de6e9","first_computed_at":"2026-07-05T04:27:29.315388Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:27:29.315388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G/CgzKclQQtNAsrm8MIZmJ/v+WqxUaopzfE8IKZqQcQmIYmLzCFQXEraaupI6QrJtIyYs77FhJVtvqf3zOw8Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:27:29.315834Z","signed_message":"canonical_sha256_bytes"},"source_id":"2111.11024","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04c0c1a7db8cde3761e8452e89658b3e5a4de2a68c457c0ce32e14d114ad5209","sha256:f0c666b9835ecdc573aa4dd4d706570d68fe66d9d03f3b8a4bb147c3029d0b82"],"state_sha256":"04c9dd4e301d8b14dd34a7efef791a7bfb6f8e7cdd81c49a3798e1271c3bf470"}