{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:EFON44WF6FTKSXVCTSAXJKRBAH","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":"9d7ff38957163ad075c22c228e2549826e4d848a1853acdf4ec3b3a239ae0354","cross_cats_sorted":["math.NT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-05-15T15:07:37Z","title_canon_sha256":"ca9389a6009e805147cea96571d6c7925e6e5567d8bddd0a488d3959bed88e8a"},"schema_version":"1.0","source":{"id":"2505.10386","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.10386","created_at":"2026-07-05T12:09:17Z"},{"alias_kind":"arxiv_version","alias_value":"2505.10386v2","created_at":"2026-07-05T12:09:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.10386","created_at":"2026-07-05T12:09:17Z"},{"alias_kind":"pith_short_12","alias_value":"EFON44WF6FTK","created_at":"2026-07-05T12:09:17Z"},{"alias_kind":"pith_short_16","alias_value":"EFON44WF6FTKSXVC","created_at":"2026-07-05T12:09:17Z"},{"alias_kind":"pith_short_8","alias_value":"EFON44WF","created_at":"2026-07-05T12:09:17Z"}],"graph_snapshots":[{"event_id":"sha256:e11c0475a563a7ebf38c16936cf2b0515aba041b05b18d9e35cc97b5ca933a34","target":"graph","created_at":"2026-07-05T12:09:17Z","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/2505.10386/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Using Mackey functors, we provide a general framework for classifying torsors of algebraic tori in terms of Brauer groups of finite field extensions of the base field. This generalizes Blunk's description of the tori associated to del Pezzo surfaces of degree 6 to all retract rational tori, essentially the largest class for which this is possible.","authors_text":"Alexander Duncan, Pankaj Singh","cross_cats":["math.NT","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-05-15T15:07:37Z","title":"Classifying torsors of tori with Brauer groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.10386","kind":"arxiv","version":2},"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":"sha256:2f07e200afabf564aacb3f67b29c3609cdc75da606e4f7e4c242b27aeb77efaf","target":"record","created_at":"2026-07-05T12:09:17Z","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":"9d7ff38957163ad075c22c228e2549826e4d848a1853acdf4ec3b3a239ae0354","cross_cats_sorted":["math.NT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-05-15T15:07:37Z","title_canon_sha256":"ca9389a6009e805147cea96571d6c7925e6e5567d8bddd0a488d3959bed88e8a"},"schema_version":"1.0","source":{"id":"2505.10386","kind":"arxiv","version":2}},"canonical_sha256":"215cde72c5f166a95ea29c8174aa2101e3d6a86174ef9491e3cc58539a8c1554","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"215cde72c5f166a95ea29c8174aa2101e3d6a86174ef9491e3cc58539a8c1554","first_computed_at":"2026-07-05T12:09:17.721437Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:09:17.721437Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ivEPqi/i7NYa2H4YnN+gNyrizM9/W5t6Ecwix72pYE3NXEurZGB/5Dyx5Dn+ospF/Hb6w9Op7mxpWmukA2lRAA==","signature_status":"signed_v1","signed_at":"2026-07-05T12:09:17.721962Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.10386","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f07e200afabf564aacb3f67b29c3609cdc75da606e4f7e4c242b27aeb77efaf","sha256:e11c0475a563a7ebf38c16936cf2b0515aba041b05b18d9e35cc97b5ca933a34"],"state_sha256":"937e80797a1f35172c3207bee55cc3460abdb6635e7bfaf48db886de186a3efb"}