{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:SAKKKVK3JGGH5UPOEYBGMVQUPW","short_pith_number":"pith:SAKKKVK3","schema_version":"1.0","canonical_sha256":"9014a5555b498c7ed1ee26026656147db46e3d78a8623624ee183e902c03a4e8","source":{"kind":"arxiv","id":"1907.01135","version":2},"attestation_state":"computed","paper":{"title":"On strong exceptional collections of line bundles of maximal length on Fano toric Deligne-Mumford stacks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Chengxi Wang, Lev Borisov","submitted_at":"2019-07-02T03:00:16Z","abstract_excerpt":"We study strong exceptional collections of line bundles on Fano toric Deligne-Mumford stacks $\\mathbb{P}_{\\mathbf{\\Sigma}}$ with rank of Picard group at most two. We prove that any strong exceptional collection of line bundles generates the derived category of $\\mathbb{P}_{\\mathbf{\\Sigma}}$, as long as the number of elements in the collection equals the rank of the (Grothendieck) $K$-theory group of $\\mathbb{P}_{\\mathbf{\\Sigma}}$."},"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":"1907.01135","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-07-02T03:00:16Z","cross_cats_sorted":[],"title_canon_sha256":"9c05e72d6e5e2cc43a9fe7dc4c67ada09cad311015d40646d39405eab2cd0792","abstract_canon_sha256":"63fee691d43cca115e802eda7cd41cb2f70728e452050a448e9b81381ff6afae"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:29.862896Z","signature_b64":"bQMb2tiYkdPhHoMa3QRISHST5h8Tk1qPhUNQ87gulqUJh7c0TmIG0JMN0szH1PnoA8PhyWT6abqlavqq5YDzBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9014a5555b498c7ed1ee26026656147db46e3d78a8623624ee183e902c03a4e8","last_reissued_at":"2026-05-17T23:40:29.862295Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:29.862295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On strong exceptional collections of line bundles of maximal length on Fano toric Deligne-Mumford stacks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Chengxi Wang, Lev Borisov","submitted_at":"2019-07-02T03:00:16Z","abstract_excerpt":"We study strong exceptional collections of line bundles on Fano toric Deligne-Mumford stacks $\\mathbb{P}_{\\mathbf{\\Sigma}}$ with rank of Picard group at most two. We prove that any strong exceptional collection of line bundles generates the derived category of $\\mathbb{P}_{\\mathbf{\\Sigma}}$, as long as the number of elements in the collection equals the rank of the (Grothendieck) $K$-theory group of $\\mathbb{P}_{\\mathbf{\\Sigma}}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.01135","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1907.01135","created_at":"2026-05-17T23:40:29.862416+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.01135v2","created_at":"2026-05-17T23:40:29.862416+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.01135","created_at":"2026-05-17T23:40:29.862416+00:00"},{"alias_kind":"pith_short_12","alias_value":"SAKKKVK3JGGH","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_16","alias_value":"SAKKKVK3JGGH5UPO","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_8","alias_value":"SAKKKVK3","created_at":"2026-05-18T12:33:27.125529+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/SAKKKVK3JGGH5UPOEYBGMVQUPW","json":"https://pith.science/pith/SAKKKVK3JGGH5UPOEYBGMVQUPW.json","graph_json":"https://pith.science/api/pith-number/SAKKKVK3JGGH5UPOEYBGMVQUPW/graph.json","events_json":"https://pith.science/api/pith-number/SAKKKVK3JGGH5UPOEYBGMVQUPW/events.json","paper":"https://pith.science/paper/SAKKKVK3"},"agent_actions":{"view_html":"https://pith.science/pith/SAKKKVK3JGGH5UPOEYBGMVQUPW","download_json":"https://pith.science/pith/SAKKKVK3JGGH5UPOEYBGMVQUPW.json","view_paper":"https://pith.science/paper/SAKKKVK3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.01135&json=true","fetch_graph":"https://pith.science/api/pith-number/SAKKKVK3JGGH5UPOEYBGMVQUPW/graph.json","fetch_events":"https://pith.science/api/pith-number/SAKKKVK3JGGH5UPOEYBGMVQUPW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SAKKKVK3JGGH5UPOEYBGMVQUPW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SAKKKVK3JGGH5UPOEYBGMVQUPW/action/storage_attestation","attest_author":"https://pith.science/pith/SAKKKVK3JGGH5UPOEYBGMVQUPW/action/author_attestation","sign_citation":"https://pith.science/pith/SAKKKVK3JGGH5UPOEYBGMVQUPW/action/citation_signature","submit_replication":"https://pith.science/pith/SAKKKVK3JGGH5UPOEYBGMVQUPW/action/replication_record"}},"created_at":"2026-05-17T23:40:29.862416+00:00","updated_at":"2026-05-17T23:40:29.862416+00:00"}