{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:RKGXQLUHNG3FG6YQHAIVD73SUN","short_pith_number":"pith:RKGXQLUH","canonical_record":{"source":{"id":"1902.09824","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-02-26T09:42:23Z","cross_cats_sorted":[],"title_canon_sha256":"0d2784bffd184557df93ab0311df7c8bac1b81e055fe9182b23d5f4cabc254a0","abstract_canon_sha256":"f0d9967b967d54dc17c2c4c5b555f04beb928e18fc0189dcb2d5cc9070ee01df"},"schema_version":"1.0"},"canonical_sha256":"8a8d782e8769b6537b10381151ff72a367973c32bee8d9e07cd0d6b777bc1af8","source":{"kind":"arxiv","id":"1902.09824","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.09824","created_at":"2026-05-17T23:52:09Z"},{"alias_kind":"arxiv_version","alias_value":"1902.09824v2","created_at":"2026-05-17T23:52:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.09824","created_at":"2026-05-17T23:52:09Z"},{"alias_kind":"pith_short_12","alias_value":"RKGXQLUHNG3F","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"RKGXQLUHNG3FG6YQ","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"RKGXQLUH","created_at":"2026-05-18T12:33:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:RKGXQLUHNG3FG6YQHAIVD73SUN","target":"record","payload":{"canonical_record":{"source":{"id":"1902.09824","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-02-26T09:42:23Z","cross_cats_sorted":[],"title_canon_sha256":"0d2784bffd184557df93ab0311df7c8bac1b81e055fe9182b23d5f4cabc254a0","abstract_canon_sha256":"f0d9967b967d54dc17c2c4c5b555f04beb928e18fc0189dcb2d5cc9070ee01df"},"schema_version":"1.0"},"canonical_sha256":"8a8d782e8769b6537b10381151ff72a367973c32bee8d9e07cd0d6b777bc1af8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:09.213490Z","signature_b64":"KML8kfk5/nWaN1jM2zW64LlBo/SOWDv0XIQAudXfBHlHgWfo0xKahLcfK/gzL9ZHRZrtMBWO6kWU7m2Xfe/1BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a8d782e8769b6537b10381151ff72a367973c32bee8d9e07cd0d6b777bc1af8","last_reissued_at":"2026-05-17T23:52:09.212986Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:09.212986Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.09824","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":"2026-05-17T23:52:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2eWzIjAMTHt+86+nfA1yCCCxxynLMYxPFgUF6hQRfcIBtByMfh/FhTxrem78j68rqPXCBDpcmkNbFo0aackmDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:26:26.282688Z"},"content_sha256":"88c75d2b66d532205a811ebc0b56a98f5f97d649290a9eb5224c5f62aeeef2a1","schema_version":"1.0","event_id":"sha256:88c75d2b66d532205a811ebc0b56a98f5f97d649290a9eb5224c5f62aeeef2a1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:RKGXQLUHNG3FG6YQHAIVD73SUN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Categorical cones and quadratic homological projective duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alexander Kuznetsov, Alexander Perry","submitted_at":"2019-02-26T09:42:23Z","abstract_excerpt":"We introduce the notion of a categorical cone, which provides a categorification of the classical cone over a projective variety, and use our work on categorical joins to describe its behavior under homological projective duality. In particular, our construction provides well-behaved categorical resolutions of singular quadrics, which we use to obtain an explicit quadratic version of the main theorem of homological projective duality. As applications, we prove the duality conjecture for Gushel-Mukai varieties, and produce interesting examples of conifold transitions between noncommutative and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.09824","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":"2026-05-17T23:52:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"94/9aTVbdwC6hH6s/B0rye7wR6MSgth+56sTyo2vnPjHf1ZGccqnfxxEe6iqy+2Tr2cSyP1RT3xGhAeGcO4PCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:26:26.283333Z"},"content_sha256":"dd33a12366c1c72f7cd695df3381d9e9feec30102d3396a1b47f78995ebc4604","schema_version":"1.0","event_id":"sha256:dd33a12366c1c72f7cd695df3381d9e9feec30102d3396a1b47f78995ebc4604"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RKGXQLUHNG3FG6YQHAIVD73SUN/bundle.json","state_url":"https://pith.science/pith/RKGXQLUHNG3FG6YQHAIVD73SUN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RKGXQLUHNG3FG6YQHAIVD73SUN/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":"2026-05-26T20:26:26Z","links":{"resolver":"https://pith.science/pith/RKGXQLUHNG3FG6YQHAIVD73SUN","bundle":"https://pith.science/pith/RKGXQLUHNG3FG6YQHAIVD73SUN/bundle.json","state":"https://pith.science/pith/RKGXQLUHNG3FG6YQHAIVD73SUN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RKGXQLUHNG3FG6YQHAIVD73SUN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:RKGXQLUHNG3FG6YQHAIVD73SUN","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":"f0d9967b967d54dc17c2c4c5b555f04beb928e18fc0189dcb2d5cc9070ee01df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-02-26T09:42:23Z","title_canon_sha256":"0d2784bffd184557df93ab0311df7c8bac1b81e055fe9182b23d5f4cabc254a0"},"schema_version":"1.0","source":{"id":"1902.09824","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.09824","created_at":"2026-05-17T23:52:09Z"},{"alias_kind":"arxiv_version","alias_value":"1902.09824v2","created_at":"2026-05-17T23:52:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.09824","created_at":"2026-05-17T23:52:09Z"},{"alias_kind":"pith_short_12","alias_value":"RKGXQLUHNG3F","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"RKGXQLUHNG3FG6YQ","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"RKGXQLUH","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:dd33a12366c1c72f7cd695df3381d9e9feec30102d3396a1b47f78995ebc4604","target":"graph","created_at":"2026-05-17T23:52:09Z","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 introduce the notion of a categorical cone, which provides a categorification of the classical cone over a projective variety, and use our work on categorical joins to describe its behavior under homological projective duality. In particular, our construction provides well-behaved categorical resolutions of singular quadrics, which we use to obtain an explicit quadratic version of the main theorem of homological projective duality. As applications, we prove the duality conjecture for Gushel-Mukai varieties, and produce interesting examples of conifold transitions between noncommutative and ","authors_text":"Alexander Kuznetsov, Alexander Perry","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-02-26T09:42:23Z","title":"Categorical cones and quadratic homological projective duality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.09824","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":"sha256:88c75d2b66d532205a811ebc0b56a98f5f97d649290a9eb5224c5f62aeeef2a1","target":"record","created_at":"2026-05-17T23:52:09Z","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":"f0d9967b967d54dc17c2c4c5b555f04beb928e18fc0189dcb2d5cc9070ee01df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-02-26T09:42:23Z","title_canon_sha256":"0d2784bffd184557df93ab0311df7c8bac1b81e055fe9182b23d5f4cabc254a0"},"schema_version":"1.0","source":{"id":"1902.09824","kind":"arxiv","version":2}},"canonical_sha256":"8a8d782e8769b6537b10381151ff72a367973c32bee8d9e07cd0d6b777bc1af8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a8d782e8769b6537b10381151ff72a367973c32bee8d9e07cd0d6b777bc1af8","first_computed_at":"2026-05-17T23:52:09.212986Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:09.212986Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KML8kfk5/nWaN1jM2zW64LlBo/SOWDv0XIQAudXfBHlHgWfo0xKahLcfK/gzL9ZHRZrtMBWO6kWU7m2Xfe/1BQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:09.213490Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.09824","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88c75d2b66d532205a811ebc0b56a98f5f97d649290a9eb5224c5f62aeeef2a1","sha256:dd33a12366c1c72f7cd695df3381d9e9feec30102d3396a1b47f78995ebc4604"],"state_sha256":"962e6c394ae8f818b1a063bd27048847e19b8b997db7a7c1ce227383256e13fd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i1LJPJ4nfYTS0OgXgnbbrOCG59aSCvqrJySqq5Ba7MIyr9sv26ly4GaVzgPe6VSHQKY0x7LSFTw9j3quzhdlDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T20:26:26.286659Z","bundle_sha256":"3330cafc7cadd9408bf21ec9d58fc52aa3d5d1ee692a28f1357122fac520dff7"}}