{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:HYSVQCS64BZZIS4EG26U5ISXDR","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":"3ec6a8d9c39e65ad388f17d126a57ad28cd314dd4ab1ea946dbc0e92d34bb895","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-12-31T18:55:02Z","title_canon_sha256":"895b3c9ef280eb722ae9441eb08db5c41536df68e119867e7dd0859372c31697"},"schema_version":"1.0","source":{"id":"2601.00052","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.00052","created_at":"2026-06-23T03:14:27Z"},{"alias_kind":"arxiv_version","alias_value":"2601.00052v2","created_at":"2026-06-23T03:14:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.00052","created_at":"2026-06-23T03:14:27Z"},{"alias_kind":"pith_short_12","alias_value":"HYSVQCS64BZZ","created_at":"2026-06-23T03:14:27Z"},{"alias_kind":"pith_short_16","alias_value":"HYSVQCS64BZZIS4E","created_at":"2026-06-23T03:14:27Z"},{"alias_kind":"pith_short_8","alias_value":"HYSVQCS6","created_at":"2026-06-23T03:14:27Z"}],"graph_snapshots":[{"event_id":"sha256:de8d43c9359b7bbda08be7a607fe60657c2c80b4ded6a2eecac96fcbff8ad90d","target":"graph","created_at":"2026-06-23T03:14:27Z","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/2601.00052/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We compute the vertical unramified Brauer group of the Galois normic bundles, which are given by $\\mathrm{N}_{K/k}(\\mathbf{z})=P(x)$. Our main result gives combinatorial formulas for the vertical unramified Brauer groups in terms of the Galois group structure of $K/k$ and the irreducible factors of $P(x)$.","authors_text":"Yufan Liu","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-12-31T18:55:02Z","title":"Vertical unramified Brauer groups of Galois normic bundles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.00052","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":"sha256:5297304d7cbf1e1fc3a63f63acb4812f737fc0cbd57a6e190445e03618183e2e","target":"record","created_at":"2026-06-23T03:14:27Z","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":"3ec6a8d9c39e65ad388f17d126a57ad28cd314dd4ab1ea946dbc0e92d34bb895","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-12-31T18:55:02Z","title_canon_sha256":"895b3c9ef280eb722ae9441eb08db5c41536df68e119867e7dd0859372c31697"},"schema_version":"1.0","source":{"id":"2601.00052","kind":"arxiv","version":2}},"canonical_sha256":"3e25580a5ee073944b8436bd4ea2571c75c9f1fb9ae68d3d0d28eb392c9c7c47","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e25580a5ee073944b8436bd4ea2571c75c9f1fb9ae68d3d0d28eb392c9c7c47","first_computed_at":"2026-06-23T03:14:27.890755Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T03:14:27.890755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fljoRnWdUXKNNm8TWt5qX+kr8kqhgBrFqdL8CPod/Jlrjirhp/U+vRCyhZ9jCGFO1SqQge6301+1wk24wsdBDw==","signature_status":"signed_v1","signed_at":"2026-06-23T03:14:27.891242Z","signed_message":"canonical_sha256_bytes"},"source_id":"2601.00052","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5297304d7cbf1e1fc3a63f63acb4812f737fc0cbd57a6e190445e03618183e2e","sha256:de8d43c9359b7bbda08be7a607fe60657c2c80b4ded6a2eecac96fcbff8ad90d"],"state_sha256":"671adc127eb7c8893074fa01853cae933226ae2ab2047e41b4b547fd2f8a3284"}