{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:G2V5PARS2XFVFSLRKKA2J3RODF","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":"2c47137db2c248d08f901d0f0ffeab3f13c02980723edeed9bd928aadcc6c891","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-06-30T15:54:23Z","title_canon_sha256":"2a62f3acf1af4b3c196e53683365e207d58ae406d43f6ab8f795ef04559ec1f9"},"schema_version":"1.0","source":{"id":"1106.6279","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.6279","created_at":"2026-05-18T04:19:03Z"},{"alias_kind":"arxiv_version","alias_value":"1106.6279v1","created_at":"2026-05-18T04:19:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.6279","created_at":"2026-05-18T04:19:03Z"},{"alias_kind":"pith_short_12","alias_value":"G2V5PARS2XFV","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"G2V5PARS2XFVFSLR","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"G2V5PARS","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:98175b54c57ad453bb78e241d1581195f463223468fdba56b0d450a3154b56a1","target":"graph","created_at":"2026-05-18T04:19:03Z","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 implement a noncommutative analogue of the well-known commutative cyclic covering trick and implement it to explicitly construct a vast collection of numerically Calabi-Yau orders, noncommutative analogues of surfaces of Kodaira dimension 0. We construct maximal orders, noncommutative analogues of normal schemes, on rational surfaces and ruled surfaces. We also use Ogg-Shafarevich theory to construct Azumaya algebras and, more generally, maximal orders on elliptically fibred surfaces.","authors_text":"Hugo Bowne-Anderson","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-06-30T15:54:23Z","title":"The Explicit Construction of Orders on Surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.6279","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":"sha256:9c78c79809a5e67899b250b02f8c0cd7594382bd758453f01db2013e86838122","target":"record","created_at":"2026-05-18T04:19:03Z","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":"2c47137db2c248d08f901d0f0ffeab3f13c02980723edeed9bd928aadcc6c891","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-06-30T15:54:23Z","title_canon_sha256":"2a62f3acf1af4b3c196e53683365e207d58ae406d43f6ab8f795ef04559ec1f9"},"schema_version":"1.0","source":{"id":"1106.6279","kind":"arxiv","version":1}},"canonical_sha256":"36abd78232d5cb52c9715281a4ee2e197dafb2f9acb641fcab9c1c6eecf11f43","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36abd78232d5cb52c9715281a4ee2e197dafb2f9acb641fcab9c1c6eecf11f43","first_computed_at":"2026-05-18T04:19:03.611871Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:19:03.611871Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Dy203jBel+zPaxfDJ9Fj8NQu8GBcHbEexTlMHHobnmXkJGUdvJ8iBtCUKh82WUPwlZXAYup9JiS7rQLCwT0IAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:19:03.612532Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.6279","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c78c79809a5e67899b250b02f8c0cd7594382bd758453f01db2013e86838122","sha256:98175b54c57ad453bb78e241d1581195f463223468fdba56b0d450a3154b56a1"],"state_sha256":"d40eceff34a9e2eb273bf240bf587b6207f471bebeb35b5ef8d9df5fed6d5a27"}