{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:NUE7DA4Z6WSU4IO3ZWMZE2ZVLX","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":"26936ac8e4d827e751e5598335f700203612072ead95071a9f0a486569147cdd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-11-16T18:23:47Z","title_canon_sha256":"e5800d03fae0643a79e372deacfaedafadfc5355ec82b5cac00303924dad67b3"},"schema_version":"1.0","source":{"id":"1011.3779","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.3779","created_at":"2026-05-18T04:35:48Z"},{"alias_kind":"arxiv_version","alias_value":"1011.3779v1","created_at":"2026-05-18T04:35:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.3779","created_at":"2026-05-18T04:35:48Z"},{"alias_kind":"pith_short_12","alias_value":"NUE7DA4Z6WSU","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"NUE7DA4Z6WSU4IO3","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"NUE7DA4Z","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:b271b65ac8b4f40fc956ee54d6bab43e58b359135a7e5fa41e646429b8ced315","target":"graph","created_at":"2026-05-18T04:35:48Z","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 study the orbits of vector spaces of skew-symmetric matrices of constant rank 2r and type (N+1)x(N+1) under the natural action of SL(N+1), over an algebraically closed field of characteristic zero. We give a complete description of the orbits for vector spaces of dimension 2, relating them to some 1-generic matrices of linear forms. We also show that, for each rank two vector bundle on P^2 defining a triple Veronese embedding of P^2 in G(1,7), there exists a vector space of 8 x 8 skew-symmetric matrices of constant rank 6 whose kernel bundle is the dual of the given rank two vector bundle.","authors_text":"Emilia Mezzetti, Maria Lucia Fania","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-11-16T18:23:47Z","title":"Vector spaces of skew-symmetric matrices of constant rank"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3779","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":"sha256:0fcb23d8292570f39e8e456e46c89d44a3ef2aa88023b78d1754d77c6ebf1a18","target":"record","created_at":"2026-05-18T04:35:48Z","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":"26936ac8e4d827e751e5598335f700203612072ead95071a9f0a486569147cdd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-11-16T18:23:47Z","title_canon_sha256":"e5800d03fae0643a79e372deacfaedafadfc5355ec82b5cac00303924dad67b3"},"schema_version":"1.0","source":{"id":"1011.3779","kind":"arxiv","version":1}},"canonical_sha256":"6d09f18399f5a54e21dbcd99926b355dc60ed3f280caabbfcbab38b8c86be516","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d09f18399f5a54e21dbcd99926b355dc60ed3f280caabbfcbab38b8c86be516","first_computed_at":"2026-05-18T04:35:48.120945Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:35:48.120945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mWOhvpBk19GK+Af9fnQCQu/Itv7YxXExKtXxhtlxFCbfadyn9nNcohnObmJmi3i+YmARIKJ3OWSY9/ew5C0uAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:35:48.121561Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.3779","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0fcb23d8292570f39e8e456e46c89d44a3ef2aa88023b78d1754d77c6ebf1a18","sha256:b271b65ac8b4f40fc956ee54d6bab43e58b359135a7e5fa41e646429b8ced315"],"state_sha256":"3da2d38452c8bb5296b07b6776dca0c5e7d37441d4fb3cb7b776aab8d4cd9f7c"}