{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:6FXP27BWUTW5UKUZU52VXVXIOD","short_pith_number":"pith:6FXP27BW","canonical_record":{"source":{"id":"1202.5774","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-02-26T16:31:43Z","cross_cats_sorted":["math.HO"],"title_canon_sha256":"093ba0452a9cf00bad1af13138a27b913d0801da7405f94202988eadc44dd3b7","abstract_canon_sha256":"b809f2e993ffd5efa53719fbccf5b32aa4dcfcfe1abf3e96252083a69c044b5c"},"schema_version":"1.0"},"canonical_sha256":"f16efd7c36a4edda2a99a7755bd6e870f17068f4de11cfd9226151e71a72343d","source":{"kind":"arxiv","id":"1202.5774","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.5774","created_at":"2026-05-18T04:01:24Z"},{"alias_kind":"arxiv_version","alias_value":"1202.5774v1","created_at":"2026-05-18T04:01:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.5774","created_at":"2026-05-18T04:01:24Z"},{"alias_kind":"pith_short_12","alias_value":"6FXP27BWUTW5","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6FXP27BWUTW5UKUZ","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6FXP27BW","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:6FXP27BWUTW5UKUZU52VXVXIOD","target":"record","payload":{"canonical_record":{"source":{"id":"1202.5774","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-02-26T16:31:43Z","cross_cats_sorted":["math.HO"],"title_canon_sha256":"093ba0452a9cf00bad1af13138a27b913d0801da7405f94202988eadc44dd3b7","abstract_canon_sha256":"b809f2e993ffd5efa53719fbccf5b32aa4dcfcfe1abf3e96252083a69c044b5c"},"schema_version":"1.0"},"canonical_sha256":"f16efd7c36a4edda2a99a7755bd6e870f17068f4de11cfd9226151e71a72343d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:01:24.713126Z","signature_b64":"ryNAXNui5zUVXYCBZSgHO5unvITFou87HsQB4gBeagB7/MwlOVa7SvUwJV/RuZksrz2V+w54u+4Er/vwGQPuCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f16efd7c36a4edda2a99a7755bd6e870f17068f4de11cfd9226151e71a72343d","last_reissued_at":"2026-05-18T04:01:24.712505Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:01:24.712505Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.5774","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:01:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D0MB8bZM2lADSFv0i0JzjNjIluvnEZoaXruQPj+/L3SXbyf9MIV3aFwWZK0YvuRrls0WTYn96sdoyGD1laA0Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T21:29:02.361910Z"},"content_sha256":"5bef3a5eb55f01f39218e07f69bbc8ced29918dc275d23fcfef50b79bfa35884","schema_version":"1.0","event_id":"sha256:5bef3a5eb55f01f39218e07f69bbc8ced29918dc275d23fcfef50b79bfa35884"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:6FXP27BWUTW5UKUZU52VXVXIOD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Harbingers of Artin's Reciprocity Law. IV. Bernstein's Reciprocity Law","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.HO"],"primary_cat":"math.NT","authors_text":"Franz Lemmermeyer","submitted_at":"2012-02-26T16:31:43Z","abstract_excerpt":"In the last article of this series we will first explain how Artin's reciprocity law for unramified abelian extensions can be formulated with the help of power residue symbols, and then show that, in this case, Artin's reciprocity law was already stated by Bernstein in the case where the base field contains the roots of unity necessary for realizing the Hilbert class field as a Kummer extension. Bernstein's article appeared in 1904, almost 20 years before Artin conjectured his version of the reciprocity law, and seems to have been overlooked completely."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.5774","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:01:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8k58ERt/3+4K6501yVbDiRcCn146f+DhJVGrkuXb0ghIrDmWhP3rSaRD/mDJ26jp0qhSmEYEVZhqQfJhtG7OAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T21:29:02.362650Z"},"content_sha256":"ccebcb3c931f53ec45bc2646a4bffd6cb185fafabbb7cea2ca5f10dff4677444","schema_version":"1.0","event_id":"sha256:ccebcb3c931f53ec45bc2646a4bffd6cb185fafabbb7cea2ca5f10dff4677444"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6FXP27BWUTW5UKUZU52VXVXIOD/bundle.json","state_url":"https://pith.science/pith/6FXP27BWUTW5UKUZU52VXVXIOD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6FXP27BWUTW5UKUZU52VXVXIOD/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-11T21:29:02Z","links":{"resolver":"https://pith.science/pith/6FXP27BWUTW5UKUZU52VXVXIOD","bundle":"https://pith.science/pith/6FXP27BWUTW5UKUZU52VXVXIOD/bundle.json","state":"https://pith.science/pith/6FXP27BWUTW5UKUZU52VXVXIOD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6FXP27BWUTW5UKUZU52VXVXIOD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6FXP27BWUTW5UKUZU52VXVXIOD","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":"b809f2e993ffd5efa53719fbccf5b32aa4dcfcfe1abf3e96252083a69c044b5c","cross_cats_sorted":["math.HO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-02-26T16:31:43Z","title_canon_sha256":"093ba0452a9cf00bad1af13138a27b913d0801da7405f94202988eadc44dd3b7"},"schema_version":"1.0","source":{"id":"1202.5774","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.5774","created_at":"2026-05-18T04:01:24Z"},{"alias_kind":"arxiv_version","alias_value":"1202.5774v1","created_at":"2026-05-18T04:01:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.5774","created_at":"2026-05-18T04:01:24Z"},{"alias_kind":"pith_short_12","alias_value":"6FXP27BWUTW5","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6FXP27BWUTW5UKUZ","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6FXP27BW","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:ccebcb3c931f53ec45bc2646a4bffd6cb185fafabbb7cea2ca5f10dff4677444","target":"graph","created_at":"2026-05-18T04:01:24Z","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":"In the last article of this series we will first explain how Artin's reciprocity law for unramified abelian extensions can be formulated with the help of power residue symbols, and then show that, in this case, Artin's reciprocity law was already stated by Bernstein in the case where the base field contains the roots of unity necessary for realizing the Hilbert class field as a Kummer extension. Bernstein's article appeared in 1904, almost 20 years before Artin conjectured his version of the reciprocity law, and seems to have been overlooked completely.","authors_text":"Franz Lemmermeyer","cross_cats":["math.HO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-02-26T16:31:43Z","title":"Harbingers of Artin's Reciprocity Law. IV. Bernstein's Reciprocity Law"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.5774","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":"sha256:5bef3a5eb55f01f39218e07f69bbc8ced29918dc275d23fcfef50b79bfa35884","target":"record","created_at":"2026-05-18T04:01:24Z","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":"b809f2e993ffd5efa53719fbccf5b32aa4dcfcfe1abf3e96252083a69c044b5c","cross_cats_sorted":["math.HO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-02-26T16:31:43Z","title_canon_sha256":"093ba0452a9cf00bad1af13138a27b913d0801da7405f94202988eadc44dd3b7"},"schema_version":"1.0","source":{"id":"1202.5774","kind":"arxiv","version":1}},"canonical_sha256":"f16efd7c36a4edda2a99a7755bd6e870f17068f4de11cfd9226151e71a72343d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f16efd7c36a4edda2a99a7755bd6e870f17068f4de11cfd9226151e71a72343d","first_computed_at":"2026-05-18T04:01:24.712505Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:01:24.712505Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ryNAXNui5zUVXYCBZSgHO5unvITFou87HsQB4gBeagB7/MwlOVa7SvUwJV/RuZksrz2V+w54u+4Er/vwGQPuCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:01:24.713126Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.5774","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5bef3a5eb55f01f39218e07f69bbc8ced29918dc275d23fcfef50b79bfa35884","sha256:ccebcb3c931f53ec45bc2646a4bffd6cb185fafabbb7cea2ca5f10dff4677444"],"state_sha256":"2d58dc9d67b4b1c86e2e371ef7abe1a1c90b39d18fde347afc7046a7001523b3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"99xjX/B38oIV2Ciz9GyPMIacqsui1Tl7q4kyz2ig1qeAJoUKMv1GEzlR6CUMHdEitOtMetc7Ts1+f1AoDJgTBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T21:29:02.366539Z","bundle_sha256":"69239a658c7751058a274e28c65e25d1cdfc2a9b9630f846dfd55fb98698aedd"}}