{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:Q2RICD3B5FZKLHQKAUHYU7DEJI","short_pith_number":"pith:Q2RICD3B","canonical_record":{"source":{"id":"1408.3748","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-08-16T17:01:51Z","cross_cats_sorted":[],"title_canon_sha256":"71bb0e45ea88e0518551ba81e20ae98df13e0724a1f8ea7ee64680902c16a7a2","abstract_canon_sha256":"ba39931d741f9bdfedda6486eca9a25c8c20137be103a7ad24704343c652aeb6"},"schema_version":"1.0"},"canonical_sha256":"86a2810f61e972a59e0a050f8a7c644a210703ca6cb6b433d37c17a3ca1d8d29","source":{"kind":"arxiv","id":"1408.3748","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.3748","created_at":"2026-05-18T02:29:10Z"},{"alias_kind":"arxiv_version","alias_value":"1408.3748v3","created_at":"2026-05-18T02:29:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.3748","created_at":"2026-05-18T02:29:10Z"},{"alias_kind":"pith_short_12","alias_value":"Q2RICD3B5FZK","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"Q2RICD3B5FZKLHQK","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"Q2RICD3B","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:Q2RICD3B5FZKLHQKAUHYU7DEJI","target":"record","payload":{"canonical_record":{"source":{"id":"1408.3748","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-08-16T17:01:51Z","cross_cats_sorted":[],"title_canon_sha256":"71bb0e45ea88e0518551ba81e20ae98df13e0724a1f8ea7ee64680902c16a7a2","abstract_canon_sha256":"ba39931d741f9bdfedda6486eca9a25c8c20137be103a7ad24704343c652aeb6"},"schema_version":"1.0"},"canonical_sha256":"86a2810f61e972a59e0a050f8a7c644a210703ca6cb6b433d37c17a3ca1d8d29","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:10.733753Z","signature_b64":"njaz63jR8DyX3yNaRCkVffwRL9+fFj/QIhZbAaT9Q1WnQhew4DP3lvCKITDCIzU89SVhRWVgc2TSIMHAT8XsBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86a2810f61e972a59e0a050f8a7c644a210703ca6cb6b433d37c17a3ca1d8d29","last_reissued_at":"2026-05-18T02:29:10.733095Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:10.733095Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.3748","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:29:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zkNiDgYIBGwaYWpt04EqleanYc1ZwWHWCMrrMRAwtCFbyRKJksQBQoPWRcR7RURcMb7k03pv9n3mrtEXk2HlDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:01:46.422628Z"},"content_sha256":"f79b7ff8f6f36ccf3be3a90b19ae50f7227e93b9d9329fc5ef4b1a7ec3c195ad","schema_version":"1.0","event_id":"sha256:f79b7ff8f6f36ccf3be3a90b19ae50f7227e93b9d9329fc5ef4b1a7ec3c195ad"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:Q2RICD3B5FZKLHQKAUHYU7DEJI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Noncommutative Tsen's theorem in dimension one","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"A. Nyman","submitted_at":"2014-08-16T17:01:51Z","abstract_excerpt":"Let k be a field. In this paper, we find necessary and sufficient conditions for a noncommutative curve of genus zero over k to be a noncommutative P^1-bundle. This result can be considered a noncommutative, one-dimensional version of Tsen's theorem. By specializing this theorem, we show that every arithmetic noncommutative projective line is a noncommutative curve, and conversely we characterize exactly those noncommutative curves of genus zero which are arithmetic. We then use this characterization, together with results regarding arithmetic noncommutative projective lines, to address some p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3748","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:29:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ruKxd1gH5cYsmJqKthtiytz9bzyQWnr6/HvVNHmgTkVXdXNMjybwMUGUp84A7jW6YV15JroqtNSIwnLD4VJPDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:01:46.422968Z"},"content_sha256":"8179e0044ee6c4dc60f178da486fef5e152564bf31d5661a67bd978246f1c25f","schema_version":"1.0","event_id":"sha256:8179e0044ee6c4dc60f178da486fef5e152564bf31d5661a67bd978246f1c25f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q2RICD3B5FZKLHQKAUHYU7DEJI/bundle.json","state_url":"https://pith.science/pith/Q2RICD3B5FZKLHQKAUHYU7DEJI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q2RICD3B5FZKLHQKAUHYU7DEJI/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-03T18:01:46Z","links":{"resolver":"https://pith.science/pith/Q2RICD3B5FZKLHQKAUHYU7DEJI","bundle":"https://pith.science/pith/Q2RICD3B5FZKLHQKAUHYU7DEJI/bundle.json","state":"https://pith.science/pith/Q2RICD3B5FZKLHQKAUHYU7DEJI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q2RICD3B5FZKLHQKAUHYU7DEJI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:Q2RICD3B5FZKLHQKAUHYU7DEJI","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":"ba39931d741f9bdfedda6486eca9a25c8c20137be103a7ad24704343c652aeb6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-08-16T17:01:51Z","title_canon_sha256":"71bb0e45ea88e0518551ba81e20ae98df13e0724a1f8ea7ee64680902c16a7a2"},"schema_version":"1.0","source":{"id":"1408.3748","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.3748","created_at":"2026-05-18T02:29:10Z"},{"alias_kind":"arxiv_version","alias_value":"1408.3748v3","created_at":"2026-05-18T02:29:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.3748","created_at":"2026-05-18T02:29:10Z"},{"alias_kind":"pith_short_12","alias_value":"Q2RICD3B5FZK","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"Q2RICD3B5FZKLHQK","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"Q2RICD3B","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:8179e0044ee6c4dc60f178da486fef5e152564bf31d5661a67bd978246f1c25f","target":"graph","created_at":"2026-05-18T02:29:10Z","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":"Let k be a field. In this paper, we find necessary and sufficient conditions for a noncommutative curve of genus zero over k to be a noncommutative P^1-bundle. This result can be considered a noncommutative, one-dimensional version of Tsen's theorem. By specializing this theorem, we show that every arithmetic noncommutative projective line is a noncommutative curve, and conversely we characterize exactly those noncommutative curves of genus zero which are arithmetic. We then use this characterization, together with results regarding arithmetic noncommutative projective lines, to address some p","authors_text":"A. Nyman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-08-16T17:01:51Z","title":"Noncommutative Tsen's theorem in dimension one"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3748","kind":"arxiv","version":3},"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:f79b7ff8f6f36ccf3be3a90b19ae50f7227e93b9d9329fc5ef4b1a7ec3c195ad","target":"record","created_at":"2026-05-18T02:29:10Z","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":"ba39931d741f9bdfedda6486eca9a25c8c20137be103a7ad24704343c652aeb6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-08-16T17:01:51Z","title_canon_sha256":"71bb0e45ea88e0518551ba81e20ae98df13e0724a1f8ea7ee64680902c16a7a2"},"schema_version":"1.0","source":{"id":"1408.3748","kind":"arxiv","version":3}},"canonical_sha256":"86a2810f61e972a59e0a050f8a7c644a210703ca6cb6b433d37c17a3ca1d8d29","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86a2810f61e972a59e0a050f8a7c644a210703ca6cb6b433d37c17a3ca1d8d29","first_computed_at":"2026-05-18T02:29:10.733095Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:10.733095Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"njaz63jR8DyX3yNaRCkVffwRL9+fFj/QIhZbAaT9Q1WnQhew4DP3lvCKITDCIzU89SVhRWVgc2TSIMHAT8XsBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:10.733753Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.3748","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f79b7ff8f6f36ccf3be3a90b19ae50f7227e93b9d9329fc5ef4b1a7ec3c195ad","sha256:8179e0044ee6c4dc60f178da486fef5e152564bf31d5661a67bd978246f1c25f"],"state_sha256":"d699f76dfd42a05869dc1dc1d23e37f8039223b2f4a88b4b20d333f0b243902c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MlCohSasopGJnVIv8dAlRJSDn4x88yLz4fAtHvQCgXrIhyH+tm7YqUKPZx/+W8K8ubC/C6Xli1IOFsyseIk5Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T18:01:46.424946Z","bundle_sha256":"a816f13ee6ec7f509e6086b33291760cc49a0c029c0df14769b82cf64e7ce959"}}