{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:63G3EIG4GUCBVEPHPVEJIHB3K2","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":"13303d2caa44cbf1cacfa7a2ed693849d8ee8f43d823a2560c2ca187c3d1f996","cross_cats_sorted":["math.CT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-19T09:32:26Z","title_canon_sha256":"dcb052b8a0d7b9b20975063d6ac9688e2fc7ae812ea185516e5b557cbbdf7290"},"schema_version":"1.0","source":{"id":"1409.5568","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.5568","created_at":"2026-05-18T02:42:27Z"},{"alias_kind":"arxiv_version","alias_value":"1409.5568v1","created_at":"2026-05-18T02:42:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.5568","created_at":"2026-05-18T02:42:27Z"},{"alias_kind":"pith_short_12","alias_value":"63G3EIG4GUCB","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"63G3EIG4GUCBVEPH","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"63G3EIG4","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:e2fc35c3e465c36a29946d446e684725b47190405e058da80674ea5e780f9e26","target":"graph","created_at":"2026-05-18T02:42:27Z","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 provide descriptions of the derived categories of degree $d$ hypersurface fibrations which generalize a result of Kuznetsov for quadric fibrations and give a relative version of a well-known theorem of Orlov. Using a local generator and Morita theory, we re-interpret the resulting matrix factorization category as a derived-equivalent sheaf of dg-algebras on the base. Then, applying homological perturbation methods, we obtain a sheaf of $A_\\infty$-algebras which gives a new description of homological projective duals for (relative) $d$-Veronese embeddings, recovering the sheaf of Clifford al","authors_text":"David Favero, Dragos Deliu, Ludmil Katzarkov, Matthew Ballard, M. Umut Isik","cross_cats":["math.CT","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-19T09:32:26Z","title":"On the Derived Categories of Degree d Hypersurface Fibrations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5568","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:dd8f1488b88620e99724741a8ef54e58531f8deb1a2e2655635d8c20da7e5fef","target":"record","created_at":"2026-05-18T02:42:27Z","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":"13303d2caa44cbf1cacfa7a2ed693849d8ee8f43d823a2560c2ca187c3d1f996","cross_cats_sorted":["math.CT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-19T09:32:26Z","title_canon_sha256":"dcb052b8a0d7b9b20975063d6ac9688e2fc7ae812ea185516e5b557cbbdf7290"},"schema_version":"1.0","source":{"id":"1409.5568","kind":"arxiv","version":1}},"canonical_sha256":"f6cdb220dc35041a91e77d48941c3b56984d6e661423999a2fb9d0e1f86d2307","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6cdb220dc35041a91e77d48941c3b56984d6e661423999a2fb9d0e1f86d2307","first_computed_at":"2026-05-18T02:42:27.040027Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:27.040027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"57vp6/8uRXVCR9Z/T4iPIvEMKM1+/q6ACjpfAgvV9ENMfftUF5MwW0C1KB0T9TBvgzj737a7kCK0Lqj5hjlpCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:27.040889Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.5568","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd8f1488b88620e99724741a8ef54e58531f8deb1a2e2655635d8c20da7e5fef","sha256:e2fc35c3e465c36a29946d446e684725b47190405e058da80674ea5e780f9e26"],"state_sha256":"8e62ed270a89f1ceec24f3929399afcc6c12bdca98aa136bd612252d4f01dd3b"}