{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:7QTDOIECJKYAD2N2BXRRVWGN5C","short_pith_number":"pith:7QTDOIEC","canonical_record":{"source":{"id":"1102.1956","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-02-09T20:18:05Z","cross_cats_sorted":[],"title_canon_sha256":"b79bf7a38a4e854dba66ec6bd0bf369989f87532cbe627d970bf28a6e6c454ba","abstract_canon_sha256":"273a26e14a8f8907daf2d0e57bdd12fe69a494d65403b754956b1df781140475"},"schema_version":"1.0"},"canonical_sha256":"fc263720824ab001e9ba0de31ad8cde8ae5b9470cbb248003c56da4b9ab050d3","source":{"kind":"arxiv","id":"1102.1956","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.1956","created_at":"2026-05-18T04:29:43Z"},{"alias_kind":"arxiv_version","alias_value":"1102.1956v1","created_at":"2026-05-18T04:29:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.1956","created_at":"2026-05-18T04:29:43Z"},{"alias_kind":"pith_short_12","alias_value":"7QTDOIECJKYA","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7QTDOIECJKYAD2N2","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7QTDOIEC","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:7QTDOIECJKYAD2N2BXRRVWGN5C","target":"record","payload":{"canonical_record":{"source":{"id":"1102.1956","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-02-09T20:18:05Z","cross_cats_sorted":[],"title_canon_sha256":"b79bf7a38a4e854dba66ec6bd0bf369989f87532cbe627d970bf28a6e6c454ba","abstract_canon_sha256":"273a26e14a8f8907daf2d0e57bdd12fe69a494d65403b754956b1df781140475"},"schema_version":"1.0"},"canonical_sha256":"fc263720824ab001e9ba0de31ad8cde8ae5b9470cbb248003c56da4b9ab050d3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:29:43.958573Z","signature_b64":"Ft2gYGlqbfQLSUrT1iri8i1aqDIGhBUZgq0VUwfvMsyxyBRSIsE1L0YzBJlMl2YKGqZuovzPLYj0gH0e63GLBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc263720824ab001e9ba0de31ad8cde8ae5b9470cbb248003c56da4b9ab050d3","last_reissued_at":"2026-05-18T04:29:43.957881Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:29:43.957881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.1956","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":"2026-05-18T04:29:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hUWOoT5Y7SPCll12qCYKyq+x7qDmdqhxKmiq7l4cZu5uFgeHZsGVmWpaMmMhLbGuylN3S3JWvxU9wM8rCcDxCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T10:06:39.509494Z"},"content_sha256":"df4a941bb6fd689883a2a37683f7a097ea8a1da959152f3f30d459290ea83baa","schema_version":"1.0","event_id":"sha256:df4a941bb6fd689883a2a37683f7a097ea8a1da959152f3f30d459290ea83baa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:7QTDOIECJKYAD2N2BXRRVWGN5C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Derived Category of Fibrations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"L. Costa, R.M. Mir\\'o-Roig, S. Di Rocco","submitted_at":"2011-02-09T20:18:05Z","abstract_excerpt":"Let X ->Y be a Zariski locally trivial fibration of smooth complex projective varieties, with fiber F. We give a structure theorem for the derived category of X provided both F and Z have a full strongly exceptional collection of line bundles."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1956","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":"2026-05-18T04:29:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gmZLt/jB2MoZ/nTyiZyZFjlBVwnszIMNkz4j0DEMahjrY1iW2BQEIFdMz02vxLlDMZdu+16CR9sjog/ia1QkAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T10:06:39.509831Z"},"content_sha256":"685b0136df6e102a633624a6bee7d07830cd1968300cda61aff65984b159a32e","schema_version":"1.0","event_id":"sha256:685b0136df6e102a633624a6bee7d07830cd1968300cda61aff65984b159a32e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7QTDOIECJKYAD2N2BXRRVWGN5C/bundle.json","state_url":"https://pith.science/pith/7QTDOIECJKYAD2N2BXRRVWGN5C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7QTDOIECJKYAD2N2BXRRVWGN5C/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":"2026-06-02T10:06:39Z","links":{"resolver":"https://pith.science/pith/7QTDOIECJKYAD2N2BXRRVWGN5C","bundle":"https://pith.science/pith/7QTDOIECJKYAD2N2BXRRVWGN5C/bundle.json","state":"https://pith.science/pith/7QTDOIECJKYAD2N2BXRRVWGN5C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7QTDOIECJKYAD2N2BXRRVWGN5C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7QTDOIECJKYAD2N2BXRRVWGN5C","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":"273a26e14a8f8907daf2d0e57bdd12fe69a494d65403b754956b1df781140475","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-02-09T20:18:05Z","title_canon_sha256":"b79bf7a38a4e854dba66ec6bd0bf369989f87532cbe627d970bf28a6e6c454ba"},"schema_version":"1.0","source":{"id":"1102.1956","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.1956","created_at":"2026-05-18T04:29:43Z"},{"alias_kind":"arxiv_version","alias_value":"1102.1956v1","created_at":"2026-05-18T04:29:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.1956","created_at":"2026-05-18T04:29:43Z"},{"alias_kind":"pith_short_12","alias_value":"7QTDOIECJKYA","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7QTDOIECJKYAD2N2","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7QTDOIEC","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:685b0136df6e102a633624a6bee7d07830cd1968300cda61aff65984b159a32e","target":"graph","created_at":"2026-05-18T04:29:43Z","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 X ->Y be a Zariski locally trivial fibration of smooth complex projective varieties, with fiber F. We give a structure theorem for the derived category of X provided both F and Z have a full strongly exceptional collection of line bundles.","authors_text":"L. Costa, R.M. Mir\\'o-Roig, S. Di Rocco","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-02-09T20:18:05Z","title":"Derived Category of Fibrations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1956","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:df4a941bb6fd689883a2a37683f7a097ea8a1da959152f3f30d459290ea83baa","target":"record","created_at":"2026-05-18T04:29:43Z","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":"273a26e14a8f8907daf2d0e57bdd12fe69a494d65403b754956b1df781140475","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-02-09T20:18:05Z","title_canon_sha256":"b79bf7a38a4e854dba66ec6bd0bf369989f87532cbe627d970bf28a6e6c454ba"},"schema_version":"1.0","source":{"id":"1102.1956","kind":"arxiv","version":1}},"canonical_sha256":"fc263720824ab001e9ba0de31ad8cde8ae5b9470cbb248003c56da4b9ab050d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc263720824ab001e9ba0de31ad8cde8ae5b9470cbb248003c56da4b9ab050d3","first_computed_at":"2026-05-18T04:29:43.957881Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:29:43.957881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ft2gYGlqbfQLSUrT1iri8i1aqDIGhBUZgq0VUwfvMsyxyBRSIsE1L0YzBJlMl2YKGqZuovzPLYj0gH0e63GLBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:29:43.958573Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.1956","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:df4a941bb6fd689883a2a37683f7a097ea8a1da959152f3f30d459290ea83baa","sha256:685b0136df6e102a633624a6bee7d07830cd1968300cda61aff65984b159a32e"],"state_sha256":"c8b7a518736a99bc4c377fe64a22cf22824fdc9f02ac8a80b778d66ff9392b62"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QtYJwGGspEyXv4zOkRMLG0GHqQXfgYMLDAWRqv6tV2MotatA1xUzQiQL120VtKXi3/AIpVDq+IXDAoK+Ah0aAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T10:06:39.512093Z","bundle_sha256":"dacf2628fe9826a70506501a85742b3ee7bbb60d7d64472e1722922411ceb0a3"}}