{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:WEYJHZDSOEQFQZGFKTPC3UA2XN","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":"082f52f2ad3ddc1732a618b44975c06e651e0c06d88b3202c057602abfe02b61","cross_cats_sorted":["math.DG"],"license":"","primary_cat":"math.CV","submitted_at":"2005-12-15T21:25:59Z","title_canon_sha256":"d7d324c31688242d21ee1561132c9eb1b3779db7f75730b86b06e53e7a30a958"},"schema_version":"1.0","source":{"id":"math/0512379","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0512379","created_at":"2026-05-18T00:22:49Z"},{"alias_kind":"arxiv_version","alias_value":"math/0512379v4","created_at":"2026-05-18T00:22:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0512379","created_at":"2026-05-18T00:22:49Z"},{"alias_kind":"pith_short_12","alias_value":"WEYJHZDSOEQF","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"WEYJHZDSOEQFQZGF","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"WEYJHZDS","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:8ba0a9d5545390cf6502352dc52b7d7bede9cf15201d6ad5870afa9d24ef45a2","target":"graph","created_at":"2026-05-18T00:22:49Z","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":"We introduce the notion of the projective linking number Link(M,Z) of a compact oriented real submanifold M of dimension 2p-1 in complex projective n-space P^n with an algebraic subvariety Z in P^n - M of codimension p. This notion is related to projective winding numbers and quasi-plurisubharmonic functions, and it generalizes directly from P^n to any projective manifold. Part 1 of this paper establishes the following result for the case p=1. Let M be an oriented, stable, real analytic curve in P^n. Then M is the boundary of a positive holomorphic 1-chain T with Mass(T) < K in P^n if and only","authors_text":"F. Reese Harvey, H. Blaine Lawson Jr","cross_cats":["math.DG"],"headline":"","license":"","primary_cat":"math.CV","submitted_at":"2005-12-15T21:25:59Z","title":"Projective Linking and Boundaries of Positive Holomorphic Chains in Projective Manifolds, Part I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0512379","kind":"arxiv","version":4},"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:b5b4735a30ea45f3314433ed169a936d1d9a0235f5942f758afd5f5d1cf5f45b","target":"record","created_at":"2026-05-18T00:22:49Z","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":"082f52f2ad3ddc1732a618b44975c06e651e0c06d88b3202c057602abfe02b61","cross_cats_sorted":["math.DG"],"license":"","primary_cat":"math.CV","submitted_at":"2005-12-15T21:25:59Z","title_canon_sha256":"d7d324c31688242d21ee1561132c9eb1b3779db7f75730b86b06e53e7a30a958"},"schema_version":"1.0","source":{"id":"math/0512379","kind":"arxiv","version":4}},"canonical_sha256":"b13093e47271205864c554de2dd01abb72f01f520386ea1636b4746b82be653e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b13093e47271205864c554de2dd01abb72f01f520386ea1636b4746b82be653e","first_computed_at":"2026-05-18T00:22:49.552383Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:49.552383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t3hlq+q6R+BL/nlBRAYI41PeRi4PbrVggD004Bq+Z2tkoAS3XEQUezyTKbnTTCRlSJ/rjdjuJ+aCssuQ3qI3AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:49.552842Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0512379","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5b4735a30ea45f3314433ed169a936d1d9a0235f5942f758afd5f5d1cf5f45b","sha256:8ba0a9d5545390cf6502352dc52b7d7bede9cf15201d6ad5870afa9d24ef45a2"],"state_sha256":"b5460e1c68e6f8428ddec370bb49556a419827637ab8a1200b240f7af31cc459"}