{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:GFWZKAZS7NMXDK3BIRDHBTPRZB","short_pith_number":"pith:GFWZKAZS","canonical_record":{"source":{"id":"1009.5238","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-09-27T12:17:58Z","cross_cats_sorted":[],"title_canon_sha256":"3a4066e663075ed469f061313b7e07f4620ce19e4127a142cce3816b0ca187b3","abstract_canon_sha256":"f2a82f48e6f58ffd0b6c1f9b1382aa62261eea0953e24f0911111e7277ae4a50"},"schema_version":"1.0"},"canonical_sha256":"316d950332fb5971ab61444670cdf1c86c88c831cf2008894c52bc6a4aa83a16","source":{"kind":"arxiv","id":"1009.5238","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.5238","created_at":"2026-05-18T03:48:34Z"},{"alias_kind":"arxiv_version","alias_value":"1009.5238v2","created_at":"2026-05-18T03:48:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.5238","created_at":"2026-05-18T03:48:34Z"},{"alias_kind":"pith_short_12","alias_value":"GFWZKAZS7NMX","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GFWZKAZS7NMXDK3B","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GFWZKAZS","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:GFWZKAZS7NMXDK3BIRDHBTPRZB","target":"record","payload":{"canonical_record":{"source":{"id":"1009.5238","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-09-27T12:17:58Z","cross_cats_sorted":[],"title_canon_sha256":"3a4066e663075ed469f061313b7e07f4620ce19e4127a142cce3816b0ca187b3","abstract_canon_sha256":"f2a82f48e6f58ffd0b6c1f9b1382aa62261eea0953e24f0911111e7277ae4a50"},"schema_version":"1.0"},"canonical_sha256":"316d950332fb5971ab61444670cdf1c86c88c831cf2008894c52bc6a4aa83a16","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:34.413717Z","signature_b64":"cUUz9kXPqm8eydUzvq1fs7/moHiR894Bf855acabt7iKccqJKHZWeF5n7KacZ0DQOfK+3Xi3rAz/wN1k3s+yDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"316d950332fb5971ab61444670cdf1c86c88c831cf2008894c52bc6a4aa83a16","last_reissued_at":"2026-05-18T03:48:34.412955Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:34.412955Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.5238","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:48:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xzU1RiwPObfRXE/P+eP4e2Plc52WPvn/Lsi4FloN1ID88xRCagrVC3QVXET9fG4b4qpE30DbTjSZYiFNMpfNCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T15:07:26.610572Z"},"content_sha256":"ffd821fbbad274927aaf37d15349823ce59a85d41aaf8809d079bf96b037e0cd","schema_version":"1.0","event_id":"sha256:ffd821fbbad274927aaf37d15349823ce59a85d41aaf8809d079bf96b037e0cd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:GFWZKAZS7NMXDK3BIRDHBTPRZB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cox rings and pseudoeffective cones of projectivized toric vector bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Hendrik S\\\"u{\\ss}, Jose Gonzalez, Milena Hering, Sam Payne","submitted_at":"2010-09-27T12:17:58Z","abstract_excerpt":"We study projectivizations of a special class of toric vector bundles that includes cotangent bundles, whose associated Klyachko filtrations are particularly simple. For these projectivized bundles, we give generators for the cone of effective divisors and a presentation of the Cox ring as a polynomial algebra over the Cox ring of a blowup of a projective space along a sequence of linear subspaces. As applications, we show that the projectivized cotangent bundles of some toric varieties are not Mori dream spaces and give examples of projectivized toric vector bundles whose Cox rings are isomor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.5238","kind":"arxiv","version":2},"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":"2026-05-18T03:48:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cx24tP7ZnK5PQStKxvNvl5ISPP05sg9bjLoFJMet4Lf/dIYF0sbFCCSsSqyZBPjVsu2V5UKdBVYfNxx8ckJxCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T15:07:26.611284Z"},"content_sha256":"3f07241af22eb117d0edd01c8ab78f751113033391ea21e6955b02cf702be111","schema_version":"1.0","event_id":"sha256:3f07241af22eb117d0edd01c8ab78f751113033391ea21e6955b02cf702be111"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GFWZKAZS7NMXDK3BIRDHBTPRZB/bundle.json","state_url":"https://pith.science/pith/GFWZKAZS7NMXDK3BIRDHBTPRZB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GFWZKAZS7NMXDK3BIRDHBTPRZB/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":"2026-05-30T15:07:26Z","links":{"resolver":"https://pith.science/pith/GFWZKAZS7NMXDK3BIRDHBTPRZB","bundle":"https://pith.science/pith/GFWZKAZS7NMXDK3BIRDHBTPRZB/bundle.json","state":"https://pith.science/pith/GFWZKAZS7NMXDK3BIRDHBTPRZB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GFWZKAZS7NMXDK3BIRDHBTPRZB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:GFWZKAZS7NMXDK3BIRDHBTPRZB","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":"f2a82f48e6f58ffd0b6c1f9b1382aa62261eea0953e24f0911111e7277ae4a50","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-09-27T12:17:58Z","title_canon_sha256":"3a4066e663075ed469f061313b7e07f4620ce19e4127a142cce3816b0ca187b3"},"schema_version":"1.0","source":{"id":"1009.5238","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.5238","created_at":"2026-05-18T03:48:34Z"},{"alias_kind":"arxiv_version","alias_value":"1009.5238v2","created_at":"2026-05-18T03:48:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.5238","created_at":"2026-05-18T03:48:34Z"},{"alias_kind":"pith_short_12","alias_value":"GFWZKAZS7NMX","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GFWZKAZS7NMXDK3B","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GFWZKAZS","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:3f07241af22eb117d0edd01c8ab78f751113033391ea21e6955b02cf702be111","target":"graph","created_at":"2026-05-18T03:48:34Z","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 study projectivizations of a special class of toric vector bundles that includes cotangent bundles, whose associated Klyachko filtrations are particularly simple. For these projectivized bundles, we give generators for the cone of effective divisors and a presentation of the Cox ring as a polynomial algebra over the Cox ring of a blowup of a projective space along a sequence of linear subspaces. As applications, we show that the projectivized cotangent bundles of some toric varieties are not Mori dream spaces and give examples of projectivized toric vector bundles whose Cox rings are isomor","authors_text":"Hendrik S\\\"u{\\ss}, Jose Gonzalez, Milena Hering, Sam Payne","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-09-27T12:17:58Z","title":"Cox rings and pseudoeffective cones of projectivized toric vector bundles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.5238","kind":"arxiv","version":2},"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:ffd821fbbad274927aaf37d15349823ce59a85d41aaf8809d079bf96b037e0cd","target":"record","created_at":"2026-05-18T03:48:34Z","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":"f2a82f48e6f58ffd0b6c1f9b1382aa62261eea0953e24f0911111e7277ae4a50","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-09-27T12:17:58Z","title_canon_sha256":"3a4066e663075ed469f061313b7e07f4620ce19e4127a142cce3816b0ca187b3"},"schema_version":"1.0","source":{"id":"1009.5238","kind":"arxiv","version":2}},"canonical_sha256":"316d950332fb5971ab61444670cdf1c86c88c831cf2008894c52bc6a4aa83a16","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"316d950332fb5971ab61444670cdf1c86c88c831cf2008894c52bc6a4aa83a16","first_computed_at":"2026-05-18T03:48:34.412955Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:48:34.412955Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cUUz9kXPqm8eydUzvq1fs7/moHiR894Bf855acabt7iKccqJKHZWeF5n7KacZ0DQOfK+3Xi3rAz/wN1k3s+yDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:48:34.413717Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.5238","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ffd821fbbad274927aaf37d15349823ce59a85d41aaf8809d079bf96b037e0cd","sha256:3f07241af22eb117d0edd01c8ab78f751113033391ea21e6955b02cf702be111"],"state_sha256":"22e06f3a1bff60974d007e7148ab2a403393f5ced2549a2ee1f817ffbd4ff77d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d29l7j9gR7lU6mGSDIHdM756ODKKgLgmXf3Kw0YqGEdSfNlTW9cUWthvdxA/vIvWCW6/neuDqbwAWZfOQ/AUAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T15:07:26.615072Z","bundle_sha256":"acbd8bd5c3db350cb2723a12f2511b2a0e028e57cb3a914097b8c8e41d704a9d"}}