{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IKHTLRA74FDYHXSFWIIL5CO22V","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":"e9e03d2b79a964e7c370993df4f5842433cc7417b4ef75d1a3b02a4e276c248c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-12-29T14:03:16Z","title_canon_sha256":"678a7b531ef8cab7cb1dd75bfea38eaee7ccfc072c5904e11b340c62b1fe1c6a"},"schema_version":"1.0","source":{"id":"1312.7539","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.7539","created_at":"2026-05-18T03:03:43Z"},{"alias_kind":"arxiv_version","alias_value":"1312.7539v1","created_at":"2026-05-18T03:03:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.7539","created_at":"2026-05-18T03:03:43Z"},{"alias_kind":"pith_short_12","alias_value":"IKHTLRA74FDY","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"IKHTLRA74FDYHXSF","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"IKHTLRA7","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:5cdf5ae6ab1f20e98f41489ac3da48c7836430d55c473558cbc25a8c4bd5bc01","target":"graph","created_at":"2026-05-18T03:03:43Z","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 describe descent on families of torsors of a constant torus. A recent result of Browning and Matthiesen then implies that the Brauer--Manin obstruction controls the Hasse principle and weak approximation when the ground field is the field of rational numbers and the singular fibres are all defined over this field.","authors_text":"Alexei N. Skorobogatov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-12-29T14:03:16Z","title":"Descent on toric fibrations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7539","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:d6d86a6cea2d2903f0ede7a524149980780f7b9ae138b3f46eea818efb8ecf30","target":"record","created_at":"2026-05-18T03:03:43Z","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":"e9e03d2b79a964e7c370993df4f5842433cc7417b4ef75d1a3b02a4e276c248c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-12-29T14:03:16Z","title_canon_sha256":"678a7b531ef8cab7cb1dd75bfea38eaee7ccfc072c5904e11b340c62b1fe1c6a"},"schema_version":"1.0","source":{"id":"1312.7539","kind":"arxiv","version":1}},"canonical_sha256":"428f35c41fe14783de45b210be89dad55873323d8db4570db50a05b96cac3c88","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"428f35c41fe14783de45b210be89dad55873323d8db4570db50a05b96cac3c88","first_computed_at":"2026-05-18T03:03:43.101516Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:43.101516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w0fqy/sDWFfkRp/H/O++cg2AmYZTr5qSzM1z92Eyh7pZlifxCsV8NVNFTV3TG/Z6caGJfPhmKheK+D6SWjTaAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:43.102333Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.7539","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d6d86a6cea2d2903f0ede7a524149980780f7b9ae138b3f46eea818efb8ecf30","sha256:5cdf5ae6ab1f20e98f41489ac3da48c7836430d55c473558cbc25a8c4bd5bc01"],"state_sha256":"d248f01309aaf5f3c9e92b64fcd7b991f4ae3328ef79e2c5378f98c60a0a4073"}