{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:BRXTY3FRBVZVU5AW35A6TMV4C2","short_pith_number":"pith:BRXTY3FR","canonical_record":{"source":{"id":"1509.09115","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-09-30T10:42:05Z","cross_cats_sorted":[],"title_canon_sha256":"406889b530ebc50b4e0a192579ef856e8732d556e63555b98427fa53690a9431","abstract_canon_sha256":"c0ec16e656a5dcc5cd5d1ee2563517e9d7b9a170488eafac2f7d2db70d191455"},"schema_version":"1.0"},"canonical_sha256":"0c6f3c6cb10d735a7416df41e9b2bc16b4bc5afd62c1eb17295f454db59a1696","source":{"kind":"arxiv","id":"1509.09115","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.09115","created_at":"2026-05-18T00:06:44Z"},{"alias_kind":"arxiv_version","alias_value":"1509.09115v1","created_at":"2026-05-18T00:06:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.09115","created_at":"2026-05-18T00:06:44Z"},{"alias_kind":"pith_short_12","alias_value":"BRXTY3FRBVZV","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BRXTY3FRBVZVU5AW","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BRXTY3FR","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:BRXTY3FRBVZVU5AW35A6TMV4C2","target":"record","payload":{"canonical_record":{"source":{"id":"1509.09115","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-09-30T10:42:05Z","cross_cats_sorted":[],"title_canon_sha256":"406889b530ebc50b4e0a192579ef856e8732d556e63555b98427fa53690a9431","abstract_canon_sha256":"c0ec16e656a5dcc5cd5d1ee2563517e9d7b9a170488eafac2f7d2db70d191455"},"schema_version":"1.0"},"canonical_sha256":"0c6f3c6cb10d735a7416df41e9b2bc16b4bc5afd62c1eb17295f454db59a1696","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:44.117756Z","signature_b64":"sCNVyVvIdqWpYWrnlPmEpFaJBfrpMR1+YQEpGZnXoDJ2d9i/6zs7o6eSn8JWEmRzvLLqmYEcso+OHKu9S29xDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c6f3c6cb10d735a7416df41e9b2bc16b4bc5afd62c1eb17295f454db59a1696","last_reissued_at":"2026-05-18T00:06:44.117231Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:44.117231Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.09115","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":"2026-05-18T00:06:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tKXJsMMZL/8OnHNmsW3QZ+JOSaf6ZMjyup8VSNVmXVkG0xL4bkyVk764Y5/tLy+cBqzGuGMMN9RwYVpOtEezDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T00:43:25.266795Z"},"content_sha256":"4c0cc30d32fa19961b712e3a5bf85370c5502b0920e76ebedb5fb21fd2344257","schema_version":"1.0","event_id":"sha256:4c0cc30d32fa19961b712e3a5bf85370c5502b0920e76ebedb5fb21fd2344257"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:BRXTY3FRBVZVU5AW35A6TMV4C2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Derived categories view on rationality problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alexander Kuznetsov","submitted_at":"2015-09-30T10:42:05Z","abstract_excerpt":"We discuss a relation between the structure of derived categories of smooth projective varieties and their birational properties. We suggest a possible definition of a birational invariant, the derived category analogue of the intermediate Jacobian, and discuss its possible applications to the geometry of prime Fano threefolds and cubic fourfolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.09115","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":"2026-05-18T00:06:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f9ZVlgjl3rB74ftzekRsUpYgsvJiF4gGXFxZVmMyDtjvceWgtFwn+aSWgr6jBSTgfmw6RkROC0wI4pt2D8ATAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T00:43:25.267465Z"},"content_sha256":"89d2c7b0998485260b1d4745e805086d68a224085f70f3032a86b02700f6e17b","schema_version":"1.0","event_id":"sha256:89d2c7b0998485260b1d4745e805086d68a224085f70f3032a86b02700f6e17b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BRXTY3FRBVZVU5AW35A6TMV4C2/bundle.json","state_url":"https://pith.science/pith/BRXTY3FRBVZVU5AW35A6TMV4C2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BRXTY3FRBVZVU5AW35A6TMV4C2/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":"2026-05-27T00:43:25Z","links":{"resolver":"https://pith.science/pith/BRXTY3FRBVZVU5AW35A6TMV4C2","bundle":"https://pith.science/pith/BRXTY3FRBVZVU5AW35A6TMV4C2/bundle.json","state":"https://pith.science/pith/BRXTY3FRBVZVU5AW35A6TMV4C2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BRXTY3FRBVZVU5AW35A6TMV4C2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:BRXTY3FRBVZVU5AW35A6TMV4C2","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":"c0ec16e656a5dcc5cd5d1ee2563517e9d7b9a170488eafac2f7d2db70d191455","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-09-30T10:42:05Z","title_canon_sha256":"406889b530ebc50b4e0a192579ef856e8732d556e63555b98427fa53690a9431"},"schema_version":"1.0","source":{"id":"1509.09115","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.09115","created_at":"2026-05-18T00:06:44Z"},{"alias_kind":"arxiv_version","alias_value":"1509.09115v1","created_at":"2026-05-18T00:06:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.09115","created_at":"2026-05-18T00:06:44Z"},{"alias_kind":"pith_short_12","alias_value":"BRXTY3FRBVZV","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BRXTY3FRBVZVU5AW","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BRXTY3FR","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:89d2c7b0998485260b1d4745e805086d68a224085f70f3032a86b02700f6e17b","target":"graph","created_at":"2026-05-18T00:06:44Z","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 discuss a relation between the structure of derived categories of smooth projective varieties and their birational properties. We suggest a possible definition of a birational invariant, the derived category analogue of the intermediate Jacobian, and discuss its possible applications to the geometry of prime Fano threefolds and cubic fourfolds.","authors_text":"Alexander Kuznetsov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-09-30T10:42:05Z","title":"Derived categories view on rationality problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.09115","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":"sha256:4c0cc30d32fa19961b712e3a5bf85370c5502b0920e76ebedb5fb21fd2344257","target":"record","created_at":"2026-05-18T00:06:44Z","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":"c0ec16e656a5dcc5cd5d1ee2563517e9d7b9a170488eafac2f7d2db70d191455","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-09-30T10:42:05Z","title_canon_sha256":"406889b530ebc50b4e0a192579ef856e8732d556e63555b98427fa53690a9431"},"schema_version":"1.0","source":{"id":"1509.09115","kind":"arxiv","version":1}},"canonical_sha256":"0c6f3c6cb10d735a7416df41e9b2bc16b4bc5afd62c1eb17295f454db59a1696","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c6f3c6cb10d735a7416df41e9b2bc16b4bc5afd62c1eb17295f454db59a1696","first_computed_at":"2026-05-18T00:06:44.117231Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:44.117231Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sCNVyVvIdqWpYWrnlPmEpFaJBfrpMR1+YQEpGZnXoDJ2d9i/6zs7o6eSn8JWEmRzvLLqmYEcso+OHKu9S29xDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:44.117756Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.09115","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c0cc30d32fa19961b712e3a5bf85370c5502b0920e76ebedb5fb21fd2344257","sha256:89d2c7b0998485260b1d4745e805086d68a224085f70f3032a86b02700f6e17b"],"state_sha256":"d59b680babd6e014dd93b7db7512c1ce874b985bdffd9ab88b0d99494a4f0f17"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PAA6jcoEmp1nGRrDfJaGSu/WSQFRRSlIkpnA/R13F4euGqgiybGEYd+8Y9rh8vCY/yaLVDdl6RwmDDupfpVxBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T00:43:25.270923Z","bundle_sha256":"0ed146000b5cf62be655f1844ce04eb72139ae362aa40b469789371b49254a63"}}