{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CAFUW7PECJ5SMCCAFO7G2H5HJI","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":"1d84ea4dbd6c38f05dcc045d89c43a33adc677b55dc5bb52d859fa3e827aa596","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-03-02T03:24:11Z","title_canon_sha256":"7a5c054acd350f87c36def45e7b36de1181cabee70a27d8cbfceb4b3894d16c0"},"schema_version":"1.0","source":{"id":"1203.0359","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.0359","created_at":"2026-05-18T04:01:01Z"},{"alias_kind":"arxiv_version","alias_value":"1203.0359v1","created_at":"2026-05-18T04:01:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.0359","created_at":"2026-05-18T04:01:01Z"},{"alias_kind":"pith_short_12","alias_value":"CAFUW7PECJ5S","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CAFUW7PECJ5SMCCA","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CAFUW7PE","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:ca8a2f3ea8cce6c542661d30fb28cb22039a3eae1e67965c43c86af2ebc224de","target":"graph","created_at":"2026-05-18T04:01:01Z","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":"Let L_1 and L_2 be finite separable extensions of a global field K, and let E_i be the Galois closure of L_i over K for i=1,2. We establish a local-global principle for the product of norms from L_1 and L_2 (so-called multinorm principle) provided that the extensions E_1 and E_2 are linearly disjoint over K.","authors_text":"Andrei S. Rapinchuk, Timothy P. Pollio","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-03-02T03:24:11Z","title":"The Multinorm Principle For Linearly Disjoint Galois Extensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.0359","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:b434ba49623d40ac7fbf961bc80686c723f7284cdd00d8f9609609239e2473ad","target":"record","created_at":"2026-05-18T04:01:01Z","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":"1d84ea4dbd6c38f05dcc045d89c43a33adc677b55dc5bb52d859fa3e827aa596","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-03-02T03:24:11Z","title_canon_sha256":"7a5c054acd350f87c36def45e7b36de1181cabee70a27d8cbfceb4b3894d16c0"},"schema_version":"1.0","source":{"id":"1203.0359","kind":"arxiv","version":1}},"canonical_sha256":"100b4b7de4127b2608402bbe6d1fa74a2dbec60ce17868d6ef69d8ec681ded81","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"100b4b7de4127b2608402bbe6d1fa74a2dbec60ce17868d6ef69d8ec681ded81","first_computed_at":"2026-05-18T04:01:01.080088Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:01:01.080088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eCYa59spM4HOiztCR4RkZAFH0AmBw1fO9gIrY//OghKJeYbBXUvzljHhmw0N/ZCsZy1fR0To169a/5HID+OWBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:01:01.080901Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.0359","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b434ba49623d40ac7fbf961bc80686c723f7284cdd00d8f9609609239e2473ad","sha256:ca8a2f3ea8cce6c542661d30fb28cb22039a3eae1e67965c43c86af2ebc224de"],"state_sha256":"32c7e3a65fabd3febe7dd3c55fd469edd083af025e3802a55d0ecec70775bb1f"}