{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:IS3VE3UGZ7M6RSWCGIGRPLHF2D","short_pith_number":"pith:IS3VE3UG","canonical_record":{"source":{"id":"2303.17796","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-03-31T04:12:16Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"84591508732334c0084711a0dab00e3ae2323582acbad349af4afc3d151027bd","abstract_canon_sha256":"a6eabd0060cc86d6d95191d52233241e85bb2995c7ea51a829405a4916b5fba3"},"schema_version":"1.0"},"canonical_sha256":"44b7526e86cfd9e8cac2320d17ace5d0c3f4deb7a2d73894a3e4f28128e7dae4","source":{"kind":"arxiv","id":"2303.17796","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.17796","created_at":"2026-07-05T05:56:45Z"},{"alias_kind":"arxiv_version","alias_value":"2303.17796v1","created_at":"2026-07-05T05:56:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.17796","created_at":"2026-07-05T05:56:45Z"},{"alias_kind":"pith_short_12","alias_value":"IS3VE3UGZ7M6","created_at":"2026-07-05T05:56:45Z"},{"alias_kind":"pith_short_16","alias_value":"IS3VE3UGZ7M6RSWC","created_at":"2026-07-05T05:56:45Z"},{"alias_kind":"pith_short_8","alias_value":"IS3VE3UG","created_at":"2026-07-05T05:56:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:IS3VE3UGZ7M6RSWCGIGRPLHF2D","target":"record","payload":{"canonical_record":{"source":{"id":"2303.17796","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-03-31T04:12:16Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"84591508732334c0084711a0dab00e3ae2323582acbad349af4afc3d151027bd","abstract_canon_sha256":"a6eabd0060cc86d6d95191d52233241e85bb2995c7ea51a829405a4916b5fba3"},"schema_version":"1.0"},"canonical_sha256":"44b7526e86cfd9e8cac2320d17ace5d0c3f4deb7a2d73894a3e4f28128e7dae4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:56:45.897092Z","signature_b64":"SIBZR8/M4yOY2kCFgB9xNWOdYqII9mqI16sYWnM4JC6ukg6hj9vqIEsBAZj9Sho7U/a9R4bdXYEb34mXaxYBDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"44b7526e86cfd9e8cac2320d17ace5d0c3f4deb7a2d73894a3e4f28128e7dae4","last_reissued_at":"2026-07-05T05:56:45.896624Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:56:45.896624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2303.17796","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:56:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y9Fq/eeIhDjNK0UIaogmNsyXhxxNULJ+Ti5tlLQJcQPcEY97q7coUWytoFaUIhuP3u8s9BcBU29AjnoqO3T1DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-24T03:07:19.129548Z"},"content_sha256":"6171901cfd97aa53ce77f4af492394e434a3394dc54aecd99f347d88d92151e0","schema_version":"1.0","event_id":"sha256:6171901cfd97aa53ce77f4af492394e434a3394dc54aecd99f347d88d92151e0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:IS3VE3UGZ7M6RSWCGIGRPLHF2D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rational points on varieties and the Brauer-Manin obstruction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Bianca Viray","submitted_at":"2023-03-31T04:12:16Z","abstract_excerpt":"These lecture notes give an introduction to the Brauer-Manin obstruction to the existence of rational points, focusing on the interplay between theory and computation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.17796","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/2303.17796/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:56:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gqpIxzsPkIuYjWT9toF1FfiE1hLq+rsYlPQXnJggyYqWGcSVX57Q2NYJR1tL6s3GAyrIi6gQPD1qLAujPZE3CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-24T03:07:19.130111Z"},"content_sha256":"e9a43bb04f3a01311acfe3cec9eb0e7329bb416166183621dceae1a9252a2ca7","schema_version":"1.0","event_id":"sha256:e9a43bb04f3a01311acfe3cec9eb0e7329bb416166183621dceae1a9252a2ca7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IS3VE3UGZ7M6RSWCGIGRPLHF2D/bundle.json","state_url":"https://pith.science/pith/IS3VE3UGZ7M6RSWCGIGRPLHF2D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IS3VE3UGZ7M6RSWCGIGRPLHF2D/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":"2026-08-24T03:07:19Z","links":{"resolver":"https://pith.science/pith/IS3VE3UGZ7M6RSWCGIGRPLHF2D","bundle":"https://pith.science/pith/IS3VE3UGZ7M6RSWCGIGRPLHF2D/bundle.json","state":"https://pith.science/pith/IS3VE3UGZ7M6RSWCGIGRPLHF2D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IS3VE3UGZ7M6RSWCGIGRPLHF2D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:IS3VE3UGZ7M6RSWCGIGRPLHF2D","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":"a6eabd0060cc86d6d95191d52233241e85bb2995c7ea51a829405a4916b5fba3","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-03-31T04:12:16Z","title_canon_sha256":"84591508732334c0084711a0dab00e3ae2323582acbad349af4afc3d151027bd"},"schema_version":"1.0","source":{"id":"2303.17796","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.17796","created_at":"2026-07-05T05:56:45Z"},{"alias_kind":"arxiv_version","alias_value":"2303.17796v1","created_at":"2026-07-05T05:56:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.17796","created_at":"2026-07-05T05:56:45Z"},{"alias_kind":"pith_short_12","alias_value":"IS3VE3UGZ7M6","created_at":"2026-07-05T05:56:45Z"},{"alias_kind":"pith_short_16","alias_value":"IS3VE3UGZ7M6RSWC","created_at":"2026-07-05T05:56:45Z"},{"alias_kind":"pith_short_8","alias_value":"IS3VE3UG","created_at":"2026-07-05T05:56:45Z"}],"graph_snapshots":[{"event_id":"sha256:e9a43bb04f3a01311acfe3cec9eb0e7329bb416166183621dceae1a9252a2ca7","target":"graph","created_at":"2026-07-05T05:56:45Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2303.17796/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"These lecture notes give an introduction to the Brauer-Manin obstruction to the existence of rational points, focusing on the interplay between theory and computation.","authors_text":"Bianca Viray","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-03-31T04:12:16Z","title":"Rational points on varieties and the Brauer-Manin obstruction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.17796","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":"sha256:6171901cfd97aa53ce77f4af492394e434a3394dc54aecd99f347d88d92151e0","target":"record","created_at":"2026-07-05T05:56:45Z","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":"a6eabd0060cc86d6d95191d52233241e85bb2995c7ea51a829405a4916b5fba3","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-03-31T04:12:16Z","title_canon_sha256":"84591508732334c0084711a0dab00e3ae2323582acbad349af4afc3d151027bd"},"schema_version":"1.0","source":{"id":"2303.17796","kind":"arxiv","version":1}},"canonical_sha256":"44b7526e86cfd9e8cac2320d17ace5d0c3f4deb7a2d73894a3e4f28128e7dae4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"44b7526e86cfd9e8cac2320d17ace5d0c3f4deb7a2d73894a3e4f28128e7dae4","first_computed_at":"2026-07-05T05:56:45.896624Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:56:45.896624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SIBZR8/M4yOY2kCFgB9xNWOdYqII9mqI16sYWnM4JC6ukg6hj9vqIEsBAZj9Sho7U/a9R4bdXYEb34mXaxYBDw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:56:45.897092Z","signed_message":"canonical_sha256_bytes"},"source_id":"2303.17796","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6171901cfd97aa53ce77f4af492394e434a3394dc54aecd99f347d88d92151e0","sha256:e9a43bb04f3a01311acfe3cec9eb0e7329bb416166183621dceae1a9252a2ca7"],"state_sha256":"7ec17410653dd434aaea4e27a200ab28dde0ae0f927c30b6eeb8f5ca0ca7c2be"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SUU0mK5qoJNIXAoKDviU/SMfN1tFwYBQLKK/t4TefKHNotS6MMgAubAextWHZikRz0SLNOePh9wj8N1PRYyfCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-24T03:07:19.134960Z","bundle_sha256":"cc6e261897498dac4280342b6d58b445a62b0ac08d22ef63d27fbc747958c802"}}