{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:QKCIERJZX7ND5DXDPT5L6ZJ5VN","short_pith_number":"pith:QKCIERJZ","schema_version":"1.0","canonical_sha256":"8284824539bfda3e8ee37cfabf653dab475708402ab7888cb984efbe78fef527","source":{"kind":"arxiv","id":"0912.4291","version":4},"attestation_state":"computed","paper":{"title":"Algebraic Surfaces in Positive Characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Christian Liedtke","submitted_at":"2009-12-21T23:20:00Z","abstract_excerpt":"These notes are an introduction to and an overview of the theory of algebraic surfaces over algebraically closed fields of positive characteristic. After some background in characteristic-p-geometry, we sketch the Kodaira-Enriques classification. Next, we turn to more special characteristic-p topics, and end by lifting results and applications to characteristic zero. We assume that the reader has a background in complex geometry and has seen the Kodaira-Enriques classification of complex surfaces before."},"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":"0912.4291","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-12-21T23:20:00Z","cross_cats_sorted":[],"title_canon_sha256":"6257e5eac726956b5717f310649d743df13ccf5f66b04f36a7c538ae0ac64da7","abstract_canon_sha256":"31d002c0fa65078ae02b59cb3b40d88e85e9c59be9b1094ab6641cb8b2d1bdbc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:22.841868Z","signature_b64":"qWnl9BDg/TW7Nu2/wORrjNpkA4HGklNuUAIY8sTX8LgeDgRcPJ95schns2Epuk67vtrAW3rTltEa8XBI8AdcAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8284824539bfda3e8ee37cfabf653dab475708402ab7888cb984efbe78fef527","last_reissued_at":"2026-05-18T02:32:22.841470Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:22.841470Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Algebraic Surfaces in Positive Characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Christian Liedtke","submitted_at":"2009-12-21T23:20:00Z","abstract_excerpt":"These notes are an introduction to and an overview of the theory of algebraic surfaces over algebraically closed fields of positive characteristic. After some background in characteristic-p-geometry, we sketch the Kodaira-Enriques classification. Next, we turn to more special characteristic-p topics, and end by lifting results and applications to characteristic zero. We assume that the reader has a background in complex geometry and has seen the Kodaira-Enriques classification of complex surfaces before."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.4291","kind":"arxiv","version":4},"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":"0912.4291","created_at":"2026-05-18T02:32:22.841539+00:00"},{"alias_kind":"arxiv_version","alias_value":"0912.4291v4","created_at":"2026-05-18T02:32:22.841539+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.4291","created_at":"2026-05-18T02:32:22.841539+00:00"},{"alias_kind":"pith_short_12","alias_value":"QKCIERJZX7ND","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_16","alias_value":"QKCIERJZX7ND5DXD","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_8","alias_value":"QKCIERJZ","created_at":"2026-05-18T12:26:01.383474+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/QKCIERJZX7ND5DXDPT5L6ZJ5VN","json":"https://pith.science/pith/QKCIERJZX7ND5DXDPT5L6ZJ5VN.json","graph_json":"https://pith.science/api/pith-number/QKCIERJZX7ND5DXDPT5L6ZJ5VN/graph.json","events_json":"https://pith.science/api/pith-number/QKCIERJZX7ND5DXDPT5L6ZJ5VN/events.json","paper":"https://pith.science/paper/QKCIERJZ"},"agent_actions":{"view_html":"https://pith.science/pith/QKCIERJZX7ND5DXDPT5L6ZJ5VN","download_json":"https://pith.science/pith/QKCIERJZX7ND5DXDPT5L6ZJ5VN.json","view_paper":"https://pith.science/paper/QKCIERJZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0912.4291&json=true","fetch_graph":"https://pith.science/api/pith-number/QKCIERJZX7ND5DXDPT5L6ZJ5VN/graph.json","fetch_events":"https://pith.science/api/pith-number/QKCIERJZX7ND5DXDPT5L6ZJ5VN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QKCIERJZX7ND5DXDPT5L6ZJ5VN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QKCIERJZX7ND5DXDPT5L6ZJ5VN/action/storage_attestation","attest_author":"https://pith.science/pith/QKCIERJZX7ND5DXDPT5L6ZJ5VN/action/author_attestation","sign_citation":"https://pith.science/pith/QKCIERJZX7ND5DXDPT5L6ZJ5VN/action/citation_signature","submit_replication":"https://pith.science/pith/QKCIERJZX7ND5DXDPT5L6ZJ5VN/action/replication_record"}},"created_at":"2026-05-18T02:32:22.841539+00:00","updated_at":"2026-05-18T02:32:22.841539+00:00"}