{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UDESQKHWXAJWNYWC5AV5GZUA23","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":"45c304b2ec8318dd68f87076eb35ef985dadf2e2e898117b71d6765fd54c47d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-11-14T11:36:13Z","title_canon_sha256":"09c45804256879f9e7adcea37f8421a3a999d76ede0923003ad5721084b3cebc"},"schema_version":"1.0","source":{"id":"1811.05733","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.05733","created_at":"2026-05-17T23:58:13Z"},{"alias_kind":"arxiv_version","alias_value":"1811.05733v4","created_at":"2026-05-17T23:58:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.05733","created_at":"2026-05-17T23:58:13Z"},{"alias_kind":"pith_short_12","alias_value":"UDESQKHWXAJW","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UDESQKHWXAJWNYWC","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UDESQKHW","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:3518815a051b2b27aac0a67804d23f9658e41470786b2835ba6d346bd76631b4","target":"graph","created_at":"2026-05-17T23:58:13Z","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 $V_i$ be a finite dimensional Hermitian vector space of holomorphic sections of a line bundle $L_i$ on a complex $n$-dimensional manifold $X$. We associate to $V_i$ the non-negative Hermitian quadratic form $g_i$ on $X,$ define a Hermitian mixed volume of $X$ for a \"mixing tuple\" of $n$ non-negative Hermitian forms, and prove that the average number of common zeroes of $f_1\\in V_1,\\ldots, f_n\\in V_n$ equals to the mixed volume of $X$ for the \"mixing tuple\" $g_1,\\ldots,g_n$. This note is related to arXiv:1802.02741, where the average number of common zeros for real equations are treated in ","authors_text":"Boris Kazarnovskii","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-11-14T11:36:13Z","title":"Mixed Hermitian volume and number of common zeros of holomorphic functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.05733","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":"sha256:748638c521f676164c957aedba52f995bfd01a1ef1a711d2939953a632d2dad8","target":"record","created_at":"2026-05-17T23:58:13Z","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":"45c304b2ec8318dd68f87076eb35ef985dadf2e2e898117b71d6765fd54c47d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-11-14T11:36:13Z","title_canon_sha256":"09c45804256879f9e7adcea37f8421a3a999d76ede0923003ad5721084b3cebc"},"schema_version":"1.0","source":{"id":"1811.05733","kind":"arxiv","version":4}},"canonical_sha256":"a0c92828f6b81366e2c2e82bd36680d6ff9dc23a1cfb30ea3902d2df094e853d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a0c92828f6b81366e2c2e82bd36680d6ff9dc23a1cfb30ea3902d2df094e853d","first_computed_at":"2026-05-17T23:58:13.458139Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:13.458139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MlaAuwYC8kjIlQcF3+WYPhWIF1W20ga9jZrwnhOBiTuXEQFEH306OC4iEXU+DS/HT33UJI8JzRpiwLuwPLUVBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:13.458638Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.05733","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:748638c521f676164c957aedba52f995bfd01a1ef1a711d2939953a632d2dad8","sha256:3518815a051b2b27aac0a67804d23f9658e41470786b2835ba6d346bd76631b4"],"state_sha256":"d8445c6aa67ae6c4f6ea4557f82b5b8f40776ae0cd9312f0874955f74ae1abda"}