{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QE7UKXE7CZEUZDHZNKRL3KS5T4","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":"bd894742c69b40e5c29454139bad0e1b790d5ce050a38da42673d58a71ffa3f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-07-25T09:57:57Z","title_canon_sha256":"ea6c38d0e627af0a7d9aa67027fa0f29232f3e8ef28515a77933b3d230f17330"},"schema_version":"1.0","source":{"id":"1607.07193","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.07193","created_at":"2026-05-18T01:10:34Z"},{"alias_kind":"arxiv_version","alias_value":"1607.07193v1","created_at":"2026-05-18T01:10:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.07193","created_at":"2026-05-18T01:10:34Z"},{"alias_kind":"pith_short_12","alias_value":"QE7UKXE7CZEU","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QE7UKXE7CZEUZDHZ","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QE7UKXE7","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:df21c82ec1cf3041aaff50f46853c6617bb3a92c888fad6deb840eb584a30719","target":"graph","created_at":"2026-05-18T01:10:34Z","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 show that tensor products of semiample vector bundles are semiample. For k-ampleness in the sens of Sommese, we show that over compact complex manifolds tensor products of semiample and k-ample vector bundles are k-ample, and the sum of k-ample vector bundles is k-ample. In particular results of Sommese on k-ampleness are strenghtened.","authors_text":"F. Laytimi, W. Nahm","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-07-25T09:57:57Z","title":"Semiample and k-ample vector bundles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07193","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":"sha256:5c356ec67d088b802cf05dd032aaadcf97f5afa26fbba62953d2e15192b7a086","target":"record","created_at":"2026-05-18T01:10:34Z","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":"bd894742c69b40e5c29454139bad0e1b790d5ce050a38da42673d58a71ffa3f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-07-25T09:57:57Z","title_canon_sha256":"ea6c38d0e627af0a7d9aa67027fa0f29232f3e8ef28515a77933b3d230f17330"},"schema_version":"1.0","source":{"id":"1607.07193","kind":"arxiv","version":1}},"canonical_sha256":"813f455c9f16494c8cf96aa2bdaa5d9f397ebd7a20f503c59fff4e70dbffea83","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"813f455c9f16494c8cf96aa2bdaa5d9f397ebd7a20f503c59fff4e70dbffea83","first_computed_at":"2026-05-18T01:10:34.540262Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:34.540262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EeAt1tgpAdC+LeyPruqd9coSiJnh3+Ko/zAvWF/0IHMrrZl5jv2HVAg/ksSNFuhdlb9u+G087ktUdFCE+RQnBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:34.540767Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.07193","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c356ec67d088b802cf05dd032aaadcf97f5afa26fbba62953d2e15192b7a086","sha256:df21c82ec1cf3041aaff50f46853c6617bb3a92c888fad6deb840eb584a30719"],"state_sha256":"cdce273f9be565c7857fb3ce916ecfebdebf8dc8130882da0e6967daeb1387f8"}