{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:KTJPJFTR2GH3FTBRDRRZBU4BCB","short_pith_number":"pith:KTJPJFTR","canonical_record":{"source":{"id":"1304.7675","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-04-29T14:41:35Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"8d0ad27ed22f82df582b5de2090915862f8faa30866d2f8f276752b26c8f8852","abstract_canon_sha256":"c229a16d587dee3bfa34dc9f77841deb1b9afec40334399eb9a1f0e9073f3004"},"schema_version":"1.0"},"canonical_sha256":"54d2f49671d18fb2cc311c6390d38110784bb6e7cfb5bea97c005cdf176f9ec0","source":{"kind":"arxiv","id":"1304.7675","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.7675","created_at":"2026-05-18T02:38:53Z"},{"alias_kind":"arxiv_version","alias_value":"1304.7675v3","created_at":"2026-05-18T02:38:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.7675","created_at":"2026-05-18T02:38:53Z"},{"alias_kind":"pith_short_12","alias_value":"KTJPJFTR2GH3","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KTJPJFTR2GH3FTBR","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KTJPJFTR","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:KTJPJFTR2GH3FTBRDRRZBU4BCB","target":"record","payload":{"canonical_record":{"source":{"id":"1304.7675","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-04-29T14:41:35Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"8d0ad27ed22f82df582b5de2090915862f8faa30866d2f8f276752b26c8f8852","abstract_canon_sha256":"c229a16d587dee3bfa34dc9f77841deb1b9afec40334399eb9a1f0e9073f3004"},"schema_version":"1.0"},"canonical_sha256":"54d2f49671d18fb2cc311c6390d38110784bb6e7cfb5bea97c005cdf176f9ec0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:53.230238Z","signature_b64":"547KC86hp4TJv1GfTFkW4COyraXHVVIvhyDPBNlpa9J6jcAt7JPG2IJJ7GPRyBiPg+Bz85N/+PlY3s68xU5LCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"54d2f49671d18fb2cc311c6390d38110784bb6e7cfb5bea97c005cdf176f9ec0","last_reissued_at":"2026-05-18T02:38:53.229876Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:53.229876Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.7675","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":"2026-05-18T02:38:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zuJyDShz+Uc4q+8xXPzEBlecO8o6lFM+1lzIwC95sU0+fKQZlC3LlsZsgvxlNm5xrZDYPnsDLcQoHMGcyuq7Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T22:14:06.903620Z"},"content_sha256":"fcb8fa17afd21021609d03311dc211bee647e4e404823cf9f0816b9092b32aa2","schema_version":"1.0","event_id":"sha256:fcb8fa17afd21021609d03311dc211bee647e4e404823cf9f0816b9092b32aa2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:KTJPJFTR2GH3FTBRDRRZBU4BCB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Green functions, Segre numbers, and King's formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CV","authors_text":"Elizabeth Wulcan, Mats Andersson","submitted_at":"2013-04-29T14:41:35Z","abstract_excerpt":"Let $\\mathcal J$ be a coherent ideal sheaf on a complex manifold $X$ with zero set $Z$, and let $G$ be a plurisubharmonic function such that $G=\\log|f|+\\mathcal O(1)$ locally at $Z$, where $f$ is a tuple of holomorphic functions that defines $\\mathcal J$. We give a meaning to the Monge-Amp\\`{e}re products $(dd^c G)^k$ for $k=0,1,2,...$, and prove that the Lelong numbers of the currents $M_k^{\\mathcal J}:=\\mathbf 1_Z(dd^c G)^k$ at $x$ coincide with the so-called Segre numbers of $\\mathcal J$ at $x$, introduced independently by Tworzewski, Gaffney-Gassler, and Achilles-Manaresi. More generally, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7675","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":""},"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":"2026-05-18T02:38:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3bC6pYUkb09MD2PHMmpV2WCT8wFIwYTkY7q1UfpHWdFCWIQH9B8VjRUL5qV7mFQhOpvIE8i7LQsY80YtM7bxAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T22:14:06.904302Z"},"content_sha256":"0661c030745bdc652a3e76ed23142de61ecc9a2f9a5297acb4fa2cc777290c94","schema_version":"1.0","event_id":"sha256:0661c030745bdc652a3e76ed23142de61ecc9a2f9a5297acb4fa2cc777290c94"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KTJPJFTR2GH3FTBRDRRZBU4BCB/bundle.json","state_url":"https://pith.science/pith/KTJPJFTR2GH3FTBRDRRZBU4BCB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KTJPJFTR2GH3FTBRDRRZBU4BCB/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":"2026-05-27T22:14:06Z","links":{"resolver":"https://pith.science/pith/KTJPJFTR2GH3FTBRDRRZBU4BCB","bundle":"https://pith.science/pith/KTJPJFTR2GH3FTBRDRRZBU4BCB/bundle.json","state":"https://pith.science/pith/KTJPJFTR2GH3FTBRDRRZBU4BCB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KTJPJFTR2GH3FTBRDRRZBU4BCB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:KTJPJFTR2GH3FTBRDRRZBU4BCB","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":"c229a16d587dee3bfa34dc9f77841deb1b9afec40334399eb9a1f0e9073f3004","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-04-29T14:41:35Z","title_canon_sha256":"8d0ad27ed22f82df582b5de2090915862f8faa30866d2f8f276752b26c8f8852"},"schema_version":"1.0","source":{"id":"1304.7675","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.7675","created_at":"2026-05-18T02:38:53Z"},{"alias_kind":"arxiv_version","alias_value":"1304.7675v3","created_at":"2026-05-18T02:38:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.7675","created_at":"2026-05-18T02:38:53Z"},{"alias_kind":"pith_short_12","alias_value":"KTJPJFTR2GH3","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KTJPJFTR2GH3FTBR","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KTJPJFTR","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:0661c030745bdc652a3e76ed23142de61ecc9a2f9a5297acb4fa2cc777290c94","target":"graph","created_at":"2026-05-18T02:38:53Z","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 $\\mathcal J$ be a coherent ideal sheaf on a complex manifold $X$ with zero set $Z$, and let $G$ be a plurisubharmonic function such that $G=\\log|f|+\\mathcal O(1)$ locally at $Z$, where $f$ is a tuple of holomorphic functions that defines $\\mathcal J$. We give a meaning to the Monge-Amp\\`{e}re products $(dd^c G)^k$ for $k=0,1,2,...$, and prove that the Lelong numbers of the currents $M_k^{\\mathcal J}:=\\mathbf 1_Z(dd^c G)^k$ at $x$ coincide with the so-called Segre numbers of $\\mathcal J$ at $x$, introduced independently by Tworzewski, Gaffney-Gassler, and Achilles-Manaresi. More generally, ","authors_text":"Elizabeth Wulcan, Mats Andersson","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-04-29T14:41:35Z","title":"Green functions, Segre numbers, and King's formula"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7675","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:fcb8fa17afd21021609d03311dc211bee647e4e404823cf9f0816b9092b32aa2","target":"record","created_at":"2026-05-18T02:38:53Z","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":"c229a16d587dee3bfa34dc9f77841deb1b9afec40334399eb9a1f0e9073f3004","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-04-29T14:41:35Z","title_canon_sha256":"8d0ad27ed22f82df582b5de2090915862f8faa30866d2f8f276752b26c8f8852"},"schema_version":"1.0","source":{"id":"1304.7675","kind":"arxiv","version":3}},"canonical_sha256":"54d2f49671d18fb2cc311c6390d38110784bb6e7cfb5bea97c005cdf176f9ec0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"54d2f49671d18fb2cc311c6390d38110784bb6e7cfb5bea97c005cdf176f9ec0","first_computed_at":"2026-05-18T02:38:53.229876Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:53.229876Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"547KC86hp4TJv1GfTFkW4COyraXHVVIvhyDPBNlpa9J6jcAt7JPG2IJJ7GPRyBiPg+Bz85N/+PlY3s68xU5LCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:53.230238Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.7675","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fcb8fa17afd21021609d03311dc211bee647e4e404823cf9f0816b9092b32aa2","sha256:0661c030745bdc652a3e76ed23142de61ecc9a2f9a5297acb4fa2cc777290c94"],"state_sha256":"c2632746b1691ef43670e4568ccea13d30efb0c852224ff94665a504f179981f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NSfZVpBaBEaIdDYobyUdxjbPTiTUi/NGYJGf5d1mUBKOFrsfR8WFNDEZDdqzFILcziMRDzjyrEWkvaGhNk7XCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T22:14:06.907992Z","bundle_sha256":"411fbb6b07ed8e429c4346a43d7f96eb5dfd618224db30b9d8e4041bf6f6bcf5"}}