{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QWO5L2WQZPTTBQY7WC2NBWK7IH","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":"fe95ff15a2a1bec378698764e45aac7926c0ba78b7ade639c632d06ff930dd47","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-05-04T01:34:32Z","title_canon_sha256":"a1efa8cbca6445bfcd9bdd21ca3d56c3a72fdc89ac7fb8b3cadd30b41f30f857"},"schema_version":"1.0","source":{"id":"1305.0864","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.0864","created_at":"2026-05-18T03:26:31Z"},{"alias_kind":"arxiv_version","alias_value":"1305.0864v1","created_at":"2026-05-18T03:26:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.0864","created_at":"2026-05-18T03:26:31Z"},{"alias_kind":"pith_short_12","alias_value":"QWO5L2WQZPTT","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QWO5L2WQZPTTBQY7","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QWO5L2WQ","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:4bdeb92454779f64322557f64d577cb647348df990de6315083f51257b2b2a7c","target":"graph","created_at":"2026-05-18T03:26:31Z","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":"Let $T$ be a positive closed current of unit mass on the complex projective space $\\mathbb P^n$. For certain values $\\alpha<1$, we prove geometric properties of the set of points in $\\mathbb P^n$ where the Lelong number of $T$ exceeds $\\alpha$. We also consider the case of positive closed currents of bidimension (1,1) on multiprojective spaces.","authors_text":"Dan Coman, Tuyen Trung Truong","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-05-04T01:34:32Z","title":"Geometric properties of upper level sets of Lelong numbers on projective spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0864","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:ba950979e69f04c25df566f231e8fbfcb4752f78e7c973a8a02b0a664e28a0ef","target":"record","created_at":"2026-05-18T03:26:31Z","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":"fe95ff15a2a1bec378698764e45aac7926c0ba78b7ade639c632d06ff930dd47","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-05-04T01:34:32Z","title_canon_sha256":"a1efa8cbca6445bfcd9bdd21ca3d56c3a72fdc89ac7fb8b3cadd30b41f30f857"},"schema_version":"1.0","source":{"id":"1305.0864","kind":"arxiv","version":1}},"canonical_sha256":"859dd5ead0cbe730c31fb0b4d0d95f41da05e3389d325743fd4bb43c34646d2b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"859dd5ead0cbe730c31fb0b4d0d95f41da05e3389d325743fd4bb43c34646d2b","first_computed_at":"2026-05-18T03:26:31.474984Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:31.474984Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QlxfMvyaZ/Fr0rvDe146r52zQnfZH0+cCbifGSJpETKvT/Jl8dxSFVzS6NEZ4YnSdJTBYZOcLlWLmlOLM01FDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:31.475793Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.0864","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba950979e69f04c25df566f231e8fbfcb4752f78e7c973a8a02b0a664e28a0ef","sha256:4bdeb92454779f64322557f64d577cb647348df990de6315083f51257b2b2a7c"],"state_sha256":"0ca17ae0b3f90c8433cc8d28045d7a15fa7abbf24f256958847530316b86e79f"}