{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:K4F4VGGBBL3GPM5GKU2IP3I7XW","short_pith_number":"pith:K4F4VGGB","schema_version":"1.0","canonical_sha256":"570bca98c10af667b3a6553487ed1fbd804b244b524c55bf430762074ef485fa","source":{"kind":"arxiv","id":"1811.05135","version":1},"attestation_state":"computed","paper":{"title":"Categorical duality between joins and intersections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Naichung Conan Leung, Qingyuan Jiang","submitted_at":"2018-11-13T07:26:10Z","abstract_excerpt":"Classically, the projective duality between joins of varieties and the intersections of varieties only holds in good cases. In this paper, we show that categorically, the duality between joins and intersections holds in the framework of homological projective duality (HPD) [K07], as long as the intersections have expected dimensions. This result together with its various applications provide further evidences for the proposal of homological projective geometry of Kuznetsov and Perry [KP18]. When the varieties are inside disjoint linear subspaces, our approach also provides a new proof of the m"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1811.05135","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-11-13T07:26:10Z","cross_cats_sorted":[],"title_canon_sha256":"7f98966f943d9aff02be7ef6b67927dc0bc54664c8ac2084e391e88e6bef82a4","abstract_canon_sha256":"0e6262eb3c711a69b100fbe1eb469d7f16bad3e4e78b922a4720e8b8203689c7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:46.808953Z","signature_b64":"gJGssisWdRxlfX/CzCdNzQP0C+5tq2cMGmVHjoUwYfbcVRvb6togHagtCIAiqsX6X4LfL8bfb1vwmRsd4PXsCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"570bca98c10af667b3a6553487ed1fbd804b244b524c55bf430762074ef485fa","last_reissued_at":"2026-05-18T00:00:46.808548Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:46.808548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Categorical duality between joins and intersections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Naichung Conan Leung, Qingyuan Jiang","submitted_at":"2018-11-13T07:26:10Z","abstract_excerpt":"Classically, the projective duality between joins of varieties and the intersections of varieties only holds in good cases. In this paper, we show that categorically, the duality between joins and intersections holds in the framework of homological projective duality (HPD) [K07], as long as the intersections have expected dimensions. This result together with its various applications provide further evidences for the proposal of homological projective geometry of Kuznetsov and Perry [KP18]. When the varieties are inside disjoint linear subspaces, our approach also provides a new proof of the m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.05135","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1811.05135","created_at":"2026-05-18T00:00:46.808616+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.05135v1","created_at":"2026-05-18T00:00:46.808616+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.05135","created_at":"2026-05-18T00:00:46.808616+00:00"},{"alias_kind":"pith_short_12","alias_value":"K4F4VGGBBL3G","created_at":"2026-05-18T12:32:33.847187+00:00"},{"alias_kind":"pith_short_16","alias_value":"K4F4VGGBBL3GPM5G","created_at":"2026-05-18T12:32:33.847187+00:00"},{"alias_kind":"pith_short_8","alias_value":"K4F4VGGB","created_at":"2026-05-18T12:32:33.847187+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/K4F4VGGBBL3GPM5GKU2IP3I7XW","json":"https://pith.science/pith/K4F4VGGBBL3GPM5GKU2IP3I7XW.json","graph_json":"https://pith.science/api/pith-number/K4F4VGGBBL3GPM5GKU2IP3I7XW/graph.json","events_json":"https://pith.science/api/pith-number/K4F4VGGBBL3GPM5GKU2IP3I7XW/events.json","paper":"https://pith.science/paper/K4F4VGGB"},"agent_actions":{"view_html":"https://pith.science/pith/K4F4VGGBBL3GPM5GKU2IP3I7XW","download_json":"https://pith.science/pith/K4F4VGGBBL3GPM5GKU2IP3I7XW.json","view_paper":"https://pith.science/paper/K4F4VGGB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.05135&json=true","fetch_graph":"https://pith.science/api/pith-number/K4F4VGGBBL3GPM5GKU2IP3I7XW/graph.json","fetch_events":"https://pith.science/api/pith-number/K4F4VGGBBL3GPM5GKU2IP3I7XW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K4F4VGGBBL3GPM5GKU2IP3I7XW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K4F4VGGBBL3GPM5GKU2IP3I7XW/action/storage_attestation","attest_author":"https://pith.science/pith/K4F4VGGBBL3GPM5GKU2IP3I7XW/action/author_attestation","sign_citation":"https://pith.science/pith/K4F4VGGBBL3GPM5GKU2IP3I7XW/action/citation_signature","submit_replication":"https://pith.science/pith/K4F4VGGBBL3GPM5GKU2IP3I7XW/action/replication_record"}},"created_at":"2026-05-18T00:00:46.808616+00:00","updated_at":"2026-05-18T00:00:46.808616+00:00"}