{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:VSYSLGKF5WIBKJUVMH56IKO5GO","short_pith_number":"pith:VSYSLGKF","canonical_record":{"source":{"id":"1405.3897","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-05-15T16:14:16Z","cross_cats_sorted":[],"title_canon_sha256":"2d6d7be0061473e69d02bae8694b15417db4081bed6221e419aeea535402bc1c","abstract_canon_sha256":"f5ab1ba0251bdafad6042c4261383a0920f5ab13368a735cefb92f2fe2c6ffc9"},"schema_version":"1.0"},"canonical_sha256":"acb1259945ed9015269561fbe429dd33ae81925dbb5f9428b4bbcfb72d8a99bd","source":{"kind":"arxiv","id":"1405.3897","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.3897","created_at":"2026-05-18T01:34:30Z"},{"alias_kind":"arxiv_version","alias_value":"1405.3897v1","created_at":"2026-05-18T01:34:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.3897","created_at":"2026-05-18T01:34:30Z"},{"alias_kind":"pith_short_12","alias_value":"VSYSLGKF5WIB","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"VSYSLGKF5WIBKJUV","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"VSYSLGKF","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:VSYSLGKF5WIBKJUVMH56IKO5GO","target":"record","payload":{"canonical_record":{"source":{"id":"1405.3897","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-05-15T16:14:16Z","cross_cats_sorted":[],"title_canon_sha256":"2d6d7be0061473e69d02bae8694b15417db4081bed6221e419aeea535402bc1c","abstract_canon_sha256":"f5ab1ba0251bdafad6042c4261383a0920f5ab13368a735cefb92f2fe2c6ffc9"},"schema_version":"1.0"},"canonical_sha256":"acb1259945ed9015269561fbe429dd33ae81925dbb5f9428b4bbcfb72d8a99bd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:30.057479Z","signature_b64":"yRhucZuHGyPWuwsalOeBcXgo+5tqbaL2WoErYeiQ4Vp8MlZmAJxx4lIhNivLN5Wlvv04M0mPQcUOCCwYaukdCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"acb1259945ed9015269561fbe429dd33ae81925dbb5f9428b4bbcfb72d8a99bd","last_reissued_at":"2026-05-18T01:34:30.056947Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:30.056947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.3897","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:34:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LXj/RmZLcY682gxuFZXF/e21YPbu+ClqxDM2cE4qeSjYKeGmysGAwrW8IH3lsJGwkGs4ijaoiswbSws6p4BNAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T10:57:13.706854Z"},"content_sha256":"7d0a5e20ba5870a038545208a94d6abd9a4b4b87dd6cbd84515f2ba02e944b9b","schema_version":"1.0","event_id":"sha256:7d0a5e20ba5870a038545208a94d6abd9a4b4b87dd6cbd84515f2ba02e944b9b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:VSYSLGKF5WIBKJUVMH56IKO5GO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Barth-Van de Ven-Tyurin-Sato theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alexander S. Tikhomirov, Ivan Penkov","submitted_at":"2014-05-15T16:14:16Z","abstract_excerpt":"The Barth-Van de Ven-Tyurin-Sato Theorem claims that any finite rank vector bundle on the infinite complex projective space $\\mathbf{P}^\\infty$ is isomorphic to a direct sum of line bundles. We establish sufficient conditions on a locally complete linear ind-variety $\\mathbf{X}$ which ensure that the same result holds on $\\mathbf{X}$. We then exhibit natural classes of locally complete linear ind-varieties which satisfy these sufficient conditions.\n  Keywords: ind-variety, vector bundle"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.3897","kind":"arxiv","version":1},"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":"2026-05-18T01:34:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z86HNOzmZ5OaPb9wDj1UgtAYlbTBCTbXNqAF/+DRL64zfy4vIuyOPWHhboqdOHHYqsaovOzvpOEvrUeQOEJDCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T10:57:13.707548Z"},"content_sha256":"2e4acc86eb55bd3384096c642a75c4e933462c04d14b67cb19225f5266b4d6f3","schema_version":"1.0","event_id":"sha256:2e4acc86eb55bd3384096c642a75c4e933462c04d14b67cb19225f5266b4d6f3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VSYSLGKF5WIBKJUVMH56IKO5GO/bundle.json","state_url":"https://pith.science/pith/VSYSLGKF5WIBKJUVMH56IKO5GO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VSYSLGKF5WIBKJUVMH56IKO5GO/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":"2026-05-27T10:57:13Z","links":{"resolver":"https://pith.science/pith/VSYSLGKF5WIBKJUVMH56IKO5GO","bundle":"https://pith.science/pith/VSYSLGKF5WIBKJUVMH56IKO5GO/bundle.json","state":"https://pith.science/pith/VSYSLGKF5WIBKJUVMH56IKO5GO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VSYSLGKF5WIBKJUVMH56IKO5GO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:VSYSLGKF5WIBKJUVMH56IKO5GO","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":"f5ab1ba0251bdafad6042c4261383a0920f5ab13368a735cefb92f2fe2c6ffc9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-05-15T16:14:16Z","title_canon_sha256":"2d6d7be0061473e69d02bae8694b15417db4081bed6221e419aeea535402bc1c"},"schema_version":"1.0","source":{"id":"1405.3897","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.3897","created_at":"2026-05-18T01:34:30Z"},{"alias_kind":"arxiv_version","alias_value":"1405.3897v1","created_at":"2026-05-18T01:34:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.3897","created_at":"2026-05-18T01:34:30Z"},{"alias_kind":"pith_short_12","alias_value":"VSYSLGKF5WIB","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"VSYSLGKF5WIBKJUV","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"VSYSLGKF","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:2e4acc86eb55bd3384096c642a75c4e933462c04d14b67cb19225f5266b4d6f3","target":"graph","created_at":"2026-05-18T01:34:30Z","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":"The Barth-Van de Ven-Tyurin-Sato Theorem claims that any finite rank vector bundle on the infinite complex projective space $\\mathbf{P}^\\infty$ is isomorphic to a direct sum of line bundles. We establish sufficient conditions on a locally complete linear ind-variety $\\mathbf{X}$ which ensure that the same result holds on $\\mathbf{X}$. We then exhibit natural classes of locally complete linear ind-varieties which satisfy these sufficient conditions.\n  Keywords: ind-variety, vector bundle","authors_text":"Alexander S. Tikhomirov, Ivan Penkov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-05-15T16:14:16Z","title":"On the Barth-Van de Ven-Tyurin-Sato theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.3897","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":"sha256:7d0a5e20ba5870a038545208a94d6abd9a4b4b87dd6cbd84515f2ba02e944b9b","target":"record","created_at":"2026-05-18T01:34:30Z","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":"f5ab1ba0251bdafad6042c4261383a0920f5ab13368a735cefb92f2fe2c6ffc9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-05-15T16:14:16Z","title_canon_sha256":"2d6d7be0061473e69d02bae8694b15417db4081bed6221e419aeea535402bc1c"},"schema_version":"1.0","source":{"id":"1405.3897","kind":"arxiv","version":1}},"canonical_sha256":"acb1259945ed9015269561fbe429dd33ae81925dbb5f9428b4bbcfb72d8a99bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"acb1259945ed9015269561fbe429dd33ae81925dbb5f9428b4bbcfb72d8a99bd","first_computed_at":"2026-05-18T01:34:30.056947Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:30.056947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yRhucZuHGyPWuwsalOeBcXgo+5tqbaL2WoErYeiQ4Vp8MlZmAJxx4lIhNivLN5Wlvv04M0mPQcUOCCwYaukdCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:30.057479Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.3897","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d0a5e20ba5870a038545208a94d6abd9a4b4b87dd6cbd84515f2ba02e944b9b","sha256:2e4acc86eb55bd3384096c642a75c4e933462c04d14b67cb19225f5266b4d6f3"],"state_sha256":"cc13a57380808f503634b441cb0bfec4ba0a382ece4b2f55cb0cc4a290744db3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yNSZRwJdlz0bkJU0+ERqvhL7v0dFsA7Z7XJJedYg9KMqIbH82BnZBrqZrMpwUMc0NHASl5R9trJ4OgdsfzAVAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T10:57:13.711286Z","bundle_sha256":"654e1d1e52c6b7b518121ca0b9fd4844a3dc013460c10d9397427b650fd226a6"}}