{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:BALVYF3DQ6YQINVOPOYR2N7YNE","short_pith_number":"pith:BALVYF3D","canonical_record":{"source":{"id":"1302.0292","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-02-01T21:12:30Z","cross_cats_sorted":["math.AG","math.DG"],"title_canon_sha256":"7bb2013e8103a0aca00fd8feaca568c33e23f4a4979a99ce7759ae7f8b696bcb","abstract_canon_sha256":"9b7e5d965b66ca406c99fc338f41d482056b9095f271dc1fdb3e2a8334207db5"},"schema_version":"1.0"},"canonical_sha256":"08175c176387b10436ae7bb11d37f86918f7d3d9c4614912e269ccfdda066097","source":{"kind":"arxiv","id":"1302.0292","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.0292","created_at":"2026-05-18T03:01:46Z"},{"alias_kind":"arxiv_version","alias_value":"1302.0292v2","created_at":"2026-05-18T03:01:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.0292","created_at":"2026-05-18T03:01:46Z"},{"alias_kind":"pith_short_12","alias_value":"BALVYF3DQ6YQ","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"BALVYF3DQ6YQINVO","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"BALVYF3D","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:BALVYF3DQ6YQINVOPOYR2N7YNE","target":"record","payload":{"canonical_record":{"source":{"id":"1302.0292","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-02-01T21:12:30Z","cross_cats_sorted":["math.AG","math.DG"],"title_canon_sha256":"7bb2013e8103a0aca00fd8feaca568c33e23f4a4979a99ce7759ae7f8b696bcb","abstract_canon_sha256":"9b7e5d965b66ca406c99fc338f41d482056b9095f271dc1fdb3e2a8334207db5"},"schema_version":"1.0"},"canonical_sha256":"08175c176387b10436ae7bb11d37f86918f7d3d9c4614912e269ccfdda066097","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:46.791615Z","signature_b64":"G70nuzM/H3DkVV6+5MtgCqrvXor42ZZVPpnfwsg3sRQNiGKULQS5VHNJo6Y992FvF+O5UVz9mM5hqynN7PsdBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08175c176387b10436ae7bb11d37f86918f7d3d9c4614912e269ccfdda066097","last_reissued_at":"2026-05-18T03:01:46.791065Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:46.791065Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.0292","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:01:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CCrq+BWCZY1rFZv05m0d/mmYIvo9gU1FE2caQrltxfk8Cs3CdxVu2HOAcm7EV+wj5JHBpqFPklJydEtiYaFDBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T22:07:52.180954Z"},"content_sha256":"d120084e7bfbef94b2f3cc909333c370892ed15bb5570aaeae43e0774dbbef10","schema_version":"1.0","event_id":"sha256:d120084e7bfbef94b2f3cc909333c370892ed15bb5570aaeae43e0774dbbef10"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:BALVYF3DQ6YQINVOPOYR2N7YNE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the approximation of positive closed currents on compact Kaehler manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.DG"],"primary_cat":"math.CV","authors_text":"Dan Coman, George Marinescu","submitted_at":"2013-02-01T21:12:30Z","abstract_excerpt":"Let $L$ be a holomorphic line bundle over a compact K\\\"ahler manifold $X$ endowed with a singular Hermitian metric $h$ with curvature current $c_1(L,h)\\geq0$. In certain cases when the wedge product $c_1(L,h)^k$ is a well defined current for some positive integer $k\\leq\\dim X$, we prove that $c_1(L,h)^k$ can be approximated by averages of currents of integration over the common zero sets of $k$-tuples of holomorphic sections over $X$ of the high powers $L^p:=L^{\\otimes p}$.\n  In the second part of the paper we study the convergence of the Fubini-Study currents and the equidistribution of zeros"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0292","kind":"arxiv","version":2},"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":"2026-05-18T03:01:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DBQli8+HY+Cqhv8HEhsNV/CzrHSyM152aVUL0FskekoiYchPlRy/0TYukNCqLuMG6ozr7JPRjvIN5pq4t7lzCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T22:07:52.181515Z"},"content_sha256":"f0f458e8b74a4c282e9ddbf0fd9b80fb23dbf782396954fe1d0bef82c4402063","schema_version":"1.0","event_id":"sha256:f0f458e8b74a4c282e9ddbf0fd9b80fb23dbf782396954fe1d0bef82c4402063"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BALVYF3DQ6YQINVOPOYR2N7YNE/bundle.json","state_url":"https://pith.science/pith/BALVYF3DQ6YQINVOPOYR2N7YNE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BALVYF3DQ6YQINVOPOYR2N7YNE/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":"2026-06-04T22:07:52Z","links":{"resolver":"https://pith.science/pith/BALVYF3DQ6YQINVOPOYR2N7YNE","bundle":"https://pith.science/pith/BALVYF3DQ6YQINVOPOYR2N7YNE/bundle.json","state":"https://pith.science/pith/BALVYF3DQ6YQINVOPOYR2N7YNE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BALVYF3DQ6YQINVOPOYR2N7YNE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BALVYF3DQ6YQINVOPOYR2N7YNE","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":"9b7e5d965b66ca406c99fc338f41d482056b9095f271dc1fdb3e2a8334207db5","cross_cats_sorted":["math.AG","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-02-01T21:12:30Z","title_canon_sha256":"7bb2013e8103a0aca00fd8feaca568c33e23f4a4979a99ce7759ae7f8b696bcb"},"schema_version":"1.0","source":{"id":"1302.0292","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.0292","created_at":"2026-05-18T03:01:46Z"},{"alias_kind":"arxiv_version","alias_value":"1302.0292v2","created_at":"2026-05-18T03:01:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.0292","created_at":"2026-05-18T03:01:46Z"},{"alias_kind":"pith_short_12","alias_value":"BALVYF3DQ6YQ","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"BALVYF3DQ6YQINVO","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"BALVYF3D","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:f0f458e8b74a4c282e9ddbf0fd9b80fb23dbf782396954fe1d0bef82c4402063","target":"graph","created_at":"2026-05-18T03:01:46Z","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 $L$ be a holomorphic line bundle over a compact K\\\"ahler manifold $X$ endowed with a singular Hermitian metric $h$ with curvature current $c_1(L,h)\\geq0$. In certain cases when the wedge product $c_1(L,h)^k$ is a well defined current for some positive integer $k\\leq\\dim X$, we prove that $c_1(L,h)^k$ can be approximated by averages of currents of integration over the common zero sets of $k$-tuples of holomorphic sections over $X$ of the high powers $L^p:=L^{\\otimes p}$.\n  In the second part of the paper we study the convergence of the Fubini-Study currents and the equidistribution of zeros","authors_text":"Dan Coman, George Marinescu","cross_cats":["math.AG","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-02-01T21:12:30Z","title":"On the approximation of positive closed currents on compact Kaehler manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0292","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:d120084e7bfbef94b2f3cc909333c370892ed15bb5570aaeae43e0774dbbef10","target":"record","created_at":"2026-05-18T03:01:46Z","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":"9b7e5d965b66ca406c99fc338f41d482056b9095f271dc1fdb3e2a8334207db5","cross_cats_sorted":["math.AG","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-02-01T21:12:30Z","title_canon_sha256":"7bb2013e8103a0aca00fd8feaca568c33e23f4a4979a99ce7759ae7f8b696bcb"},"schema_version":"1.0","source":{"id":"1302.0292","kind":"arxiv","version":2}},"canonical_sha256":"08175c176387b10436ae7bb11d37f86918f7d3d9c4614912e269ccfdda066097","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08175c176387b10436ae7bb11d37f86918f7d3d9c4614912e269ccfdda066097","first_computed_at":"2026-05-18T03:01:46.791065Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:46.791065Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G70nuzM/H3DkVV6+5MtgCqrvXor42ZZVPpnfwsg3sRQNiGKULQS5VHNJo6Y992FvF+O5UVz9mM5hqynN7PsdBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:46.791615Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.0292","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d120084e7bfbef94b2f3cc909333c370892ed15bb5570aaeae43e0774dbbef10","sha256:f0f458e8b74a4c282e9ddbf0fd9b80fb23dbf782396954fe1d0bef82c4402063"],"state_sha256":"52f72c92ca7dc29fcd48367d295d961b1f94dc385b0a40fef030a69bf856ea2e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t1nm0/TYJ4po9EnSJRIsoICcVIU5TU15oDqhq7+R1/CgWo+XUT/X9eEKK34tJHBHlB8/2uccvYOWK4QF2XV/Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T22:07:52.184563Z","bundle_sha256":"ee3736a279753e2a3006a1386818cba34a0c2a74c84b45dcfa60894e62eab49c"}}