{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:L7NHOR2L4FFJFYHNU6XRPDSQIK","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":"25e1d5eafb0d5cca9926fddb120013fc3e20c485ca4cafad3aca358168abf774","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-02-28T12:44:24Z","title_canon_sha256":"e733f95989bd370fdd170fe9ea3d9337df53183b80f24a6498353b942a35a35f"},"schema_version":"1.0","source":{"id":"1202.6200","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.6200","created_at":"2026-05-18T03:19:46Z"},{"alias_kind":"arxiv_version","alias_value":"1202.6200v2","created_at":"2026-05-18T03:19:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.6200","created_at":"2026-05-18T03:19:46Z"},{"alias_kind":"pith_short_12","alias_value":"L7NHOR2L4FFJ","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"L7NHOR2L4FFJFYHN","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"L7NHOR2L","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:97c64b09221ebe873309ea3328b31e1e895dbed46b1a4ec93a8fa912b479e737","target":"graph","created_at":"2026-05-18T03:19:46Z","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":"Given a finite set $S$ of places of a number field, we prove that the field of totally $S$-adic algebraic numbers is not Hilbertian.","authors_text":"Arno Fehm, Lior Bary-Soroker, with appendix by Florian Pop","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-02-28T12:44:24Z","title":"On fields of totally $S$-adic numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.6200","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":"sha256:79b374a0f14cb7b99b1642223795f805d814e0900d865cf7bb320941a1d13d3b","target":"record","created_at":"2026-05-18T03:19:46Z","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":"25e1d5eafb0d5cca9926fddb120013fc3e20c485ca4cafad3aca358168abf774","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-02-28T12:44:24Z","title_canon_sha256":"e733f95989bd370fdd170fe9ea3d9337df53183b80f24a6498353b942a35a35f"},"schema_version":"1.0","source":{"id":"1202.6200","kind":"arxiv","version":2}},"canonical_sha256":"5fda77474be14a92e0eda7af178e5042b6d4b6543094247fb50ada28f5d63be1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5fda77474be14a92e0eda7af178e5042b6d4b6543094247fb50ada28f5d63be1","first_computed_at":"2026-05-18T03:19:46.177157Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:46.177157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WQiE6yqx9eGiG8xjz3gXKYctnbetuAsFSLrb4AuBa+x0ys0+HCXE5ve9uVlcGNMEoMDP8EnO8Eq63eX21JdbAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:46.177784Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.6200","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:79b374a0f14cb7b99b1642223795f805d814e0900d865cf7bb320941a1d13d3b","sha256:97c64b09221ebe873309ea3328b31e1e895dbed46b1a4ec93a8fa912b479e737"],"state_sha256":"7291065cfff2e150aa813f634807d8a683220a351b7876849d05bb9acf5036b0"}