{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:UF4W7TKF7MNIK4VHDKLZYFETDC","short_pith_number":"pith:UF4W7TKF","schema_version":"1.0","canonical_sha256":"a1796fcd45fb1a8572a71a979c149318bfa640f641787d23dd4c6b55f854982c","source":{"kind":"arxiv","id":"2606.18238","version":1},"attestation_state":"computed","paper":{"title":"Exceptional collections for canonical stacks of log del Pezzo surfaces with $\\frac13(1,1)$ singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alex Junior Gomez Saltachin","submitted_at":"2026-06-16T17:58:07Z","abstract_excerpt":"We study derived categories associated with log del Pezzo surfaces whose singularities are of type $\\frac{1}{3}(1,1)$. For such a surface $X$, we consider the canonical smooth Deligne--Mumford stack $\\pi:\\mathcal X\\to X$ and compare it with the singular coarse surface $X$. Our main result proves that, if $X$ is a complex log del Pezzo surface whose singularities are all of type $\\frac{1}{3}(1,1)$, then $D^b(\\operatorname{coh}\\mathcal X)$ admits a full exceptional collection. The proof combines rationality of log del Pezzo surfaces, Orlov's blow-up formula, and the special McKay correspondence "},"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":"2606.18238","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-06-16T17:58:07Z","cross_cats_sorted":[],"title_canon_sha256":"43e4d5e193386cd5a8070265b71be120f5869fa51dd8234664c5b3cc6cf2c180","abstract_canon_sha256":"e63162720a4504d8ec9d86be64b7e4e7aee882aa93f33e5788331e4b8249816c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:10:52.003323Z","signature_b64":"VZZnU+XX3zdlh91TYG3kJKXmLOo1do6N0mcHNaejhakpQMWIHVLmA/OTEqD23CUmHK54ujw3BhLOUbJDLg7oDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a1796fcd45fb1a8572a71a979c149318bfa640f641787d23dd4c6b55f854982c","last_reissued_at":"2026-06-19T16:10:52.002952Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:10:52.002952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exceptional collections for canonical stacks of log del Pezzo surfaces with $\\frac13(1,1)$ singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alex Junior Gomez Saltachin","submitted_at":"2026-06-16T17:58:07Z","abstract_excerpt":"We study derived categories associated with log del Pezzo surfaces whose singularities are of type $\\frac{1}{3}(1,1)$. For such a surface $X$, we consider the canonical smooth Deligne--Mumford stack $\\pi:\\mathcal X\\to X$ and compare it with the singular coarse surface $X$. Our main result proves that, if $X$ is a complex log del Pezzo surface whose singularities are all of type $\\frac{1}{3}(1,1)$, then $D^b(\\operatorname{coh}\\mathcal X)$ admits a full exceptional collection. The proof combines rationality of log del Pezzo surfaces, Orlov's blow-up formula, and the special McKay correspondence "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.18238","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.18238/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2606.18238","created_at":"2026-06-19T16:10:52.003013+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.18238v1","created_at":"2026-06-19T16:10:52.003013+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.18238","created_at":"2026-06-19T16:10:52.003013+00:00"},{"alias_kind":"pith_short_12","alias_value":"UF4W7TKF7MNI","created_at":"2026-06-19T16:10:52.003013+00:00"},{"alias_kind":"pith_short_16","alias_value":"UF4W7TKF7MNIK4VH","created_at":"2026-06-19T16:10:52.003013+00:00"},{"alias_kind":"pith_short_8","alias_value":"UF4W7TKF","created_at":"2026-06-19T16:10:52.003013+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/UF4W7TKF7MNIK4VHDKLZYFETDC","json":"https://pith.science/pith/UF4W7TKF7MNIK4VHDKLZYFETDC.json","graph_json":"https://pith.science/api/pith-number/UF4W7TKF7MNIK4VHDKLZYFETDC/graph.json","events_json":"https://pith.science/api/pith-number/UF4W7TKF7MNIK4VHDKLZYFETDC/events.json","paper":"https://pith.science/paper/UF4W7TKF"},"agent_actions":{"view_html":"https://pith.science/pith/UF4W7TKF7MNIK4VHDKLZYFETDC","download_json":"https://pith.science/pith/UF4W7TKF7MNIK4VHDKLZYFETDC.json","view_paper":"https://pith.science/paper/UF4W7TKF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.18238&json=true","fetch_graph":"https://pith.science/api/pith-number/UF4W7TKF7MNIK4VHDKLZYFETDC/graph.json","fetch_events":"https://pith.science/api/pith-number/UF4W7TKF7MNIK4VHDKLZYFETDC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UF4W7TKF7MNIK4VHDKLZYFETDC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UF4W7TKF7MNIK4VHDKLZYFETDC/action/storage_attestation","attest_author":"https://pith.science/pith/UF4W7TKF7MNIK4VHDKLZYFETDC/action/author_attestation","sign_citation":"https://pith.science/pith/UF4W7TKF7MNIK4VHDKLZYFETDC/action/citation_signature","submit_replication":"https://pith.science/pith/UF4W7TKF7MNIK4VHDKLZYFETDC/action/replication_record"}},"created_at":"2026-06-19T16:10:52.003013+00:00","updated_at":"2026-06-19T16:10:52.003013+00:00"}