{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:QWO5L2WQZPTTBQY7WC2NBWK7IH","short_pith_number":"pith:QWO5L2WQ","canonical_record":{"source":{"id":"1305.0864","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-05-04T01:34:32Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"a1efa8cbca6445bfcd9bdd21ca3d56c3a72fdc89ac7fb8b3cadd30b41f30f857","abstract_canon_sha256":"fe95ff15a2a1bec378698764e45aac7926c0ba78b7ade639c632d06ff930dd47"},"schema_version":"1.0"},"canonical_sha256":"859dd5ead0cbe730c31fb0b4d0d95f41da05e3389d325743fd4bb43c34646d2b","source":{"kind":"arxiv","id":"1305.0864","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:QWO5L2WQZPTTBQY7WC2NBWK7IH","target":"record","payload":{"canonical_record":{"source":{"id":"1305.0864","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-05-04T01:34:32Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"a1efa8cbca6445bfcd9bdd21ca3d56c3a72fdc89ac7fb8b3cadd30b41f30f857","abstract_canon_sha256":"fe95ff15a2a1bec378698764e45aac7926c0ba78b7ade639c632d06ff930dd47"},"schema_version":"1.0"},"canonical_sha256":"859dd5ead0cbe730c31fb0b4d0d95f41da05e3389d325743fd4bb43c34646d2b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:31.475793Z","signature_b64":"QlxfMvyaZ/Fr0rvDe146r52zQnfZH0+cCbifGSJpETKvT/Jl8dxSFVzS6NEZ4YnSdJTBYZOcLlWLmlOLM01FDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"859dd5ead0cbe730c31fb0b4d0d95f41da05e3389d325743fd4bb43c34646d2b","last_reissued_at":"2026-05-18T03:26:31.474984Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:31.474984Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.0864","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:26:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VLOcaVoWVH2wqyz52zysUfaabb0WzcjrdPsZGB4ngmW6oXb2AVbUCIrqhGxPhp7V9O38nAqMIERpNBhDTIWsDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T03:13:07.071995Z"},"content_sha256":"ba950979e69f04c25df566f231e8fbfcb4752f78e7c973a8a02b0a664e28a0ef","schema_version":"1.0","event_id":"sha256:ba950979e69f04c25df566f231e8fbfcb4752f78e7c973a8a02b0a664e28a0ef"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:QWO5L2WQZPTTBQY7WC2NBWK7IH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometric properties of upper level sets of Lelong numbers on projective spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CV","authors_text":"Dan Coman, Tuyen Trung Truong","submitted_at":"2013-05-04T01:34:32Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0864","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T03:26:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sURqV9+34X2zVod01YZC8nEhrANLblHGX4MoSBQPNcEbBUbdG096wZ9BtmnyzL0RGAMb8CQE9o4YyGpwebqkAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T03:13:07.072640Z"},"content_sha256":"4bdeb92454779f64322557f64d577cb647348df990de6315083f51257b2b2a7c","schema_version":"1.0","event_id":"sha256:4bdeb92454779f64322557f64d577cb647348df990de6315083f51257b2b2a7c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QWO5L2WQZPTTBQY7WC2NBWK7IH/bundle.json","state_url":"https://pith.science/pith/QWO5L2WQZPTTBQY7WC2NBWK7IH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QWO5L2WQZPTTBQY7WC2NBWK7IH/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":"2026-06-05T03:13:07Z","links":{"resolver":"https://pith.science/pith/QWO5L2WQZPTTBQY7WC2NBWK7IH","bundle":"https://pith.science/pith/QWO5L2WQZPTTBQY7WC2NBWK7IH/bundle.json","state":"https://pith.science/pith/QWO5L2WQZPTTBQY7WC2NBWK7IH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QWO5L2WQZPTTBQY7WC2NBWK7IH/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YVoI3THi29s1kdrZctYrg/09qYYA4IBPL2EMHfDyWgqO1g2NXkvTnEHGudvNpAD/4brtT3LNwAqdayVxW9+5Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T03:13:07.075818Z","bundle_sha256":"d1707b6221d8ae862310b31b62ea8e401ded09e4baab670d7ecec534409d86bb"}}