{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2001:CO7VKGIDDVOYONFPUAOZXFIW5M","short_pith_number":"pith:CO7VKGID","canonical_record":{"source":{"id":"math/0110284","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GR","submitted_at":"2001-10-25T22:16:42Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"b361e0016a2b082c0b32c76cb48303e26638f3c9de6b4d33418847d35c0de92c","abstract_canon_sha256":"f88e3c7f9f0caca13c70ca99cc747b58d38ed7b219d9e3289d709efc740118cb"},"schema_version":"1.0"},"canonical_sha256":"13bf5519031d5d8734afa01d9b9516eb21f97092c0923a6efdf71e7720d451d4","source":{"kind":"arxiv","id":"math/0110284","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0110284","created_at":"2026-05-18T01:05:37Z"},{"alias_kind":"arxiv_version","alias_value":"math/0110284v1","created_at":"2026-05-18T01:05:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0110284","created_at":"2026-05-18T01:05:37Z"},{"alias_kind":"pith_short_12","alias_value":"CO7VKGIDDVOY","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"CO7VKGIDDVOYONFP","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"CO7VKGID","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2001:CO7VKGIDDVOYONFPUAOZXFIW5M","target":"record","payload":{"canonical_record":{"source":{"id":"math/0110284","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GR","submitted_at":"2001-10-25T22:16:42Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"b361e0016a2b082c0b32c76cb48303e26638f3c9de6b4d33418847d35c0de92c","abstract_canon_sha256":"f88e3c7f9f0caca13c70ca99cc747b58d38ed7b219d9e3289d709efc740118cb"},"schema_version":"1.0"},"canonical_sha256":"13bf5519031d5d8734afa01d9b9516eb21f97092c0923a6efdf71e7720d451d4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:37.516934Z","signature_b64":"/9dZL8+F0mTs6Zgbja7Zwfwi4UQTXU9hk8zEOzR2q1sKsPXGrX8WouougaB5tNWFMN8HJqZyaa8FlnAMP4FYAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13bf5519031d5d8734afa01d9b9516eb21f97092c0923a6efdf71e7720d451d4","last_reissued_at":"2026-05-18T01:05:37.516503Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:37.516503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0110284","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":"2026-05-18T01:05:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GfaObeZeLDYzb9HhJu402lPa3qI6k5qlpnn0EfSJKHuK7/AC6Sweo8G3c2umOppEWT4f58JJqbISa38k9wMKCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T05:30:07.655889Z"},"content_sha256":"537aa08e69aa64446c7ca4c1dc011a25937ea1669f7454dbce6ed9f44e76c098","schema_version":"1.0","event_id":"sha256:537aa08e69aa64446c7ca4c1dc011a25937ea1669f7454dbce6ed9f44e76c098"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2001:CO7VKGIDDVOYONFPUAOZXFIW5M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some Galois extensions of quadratic extensions associated with Witt rings","license":"","headline":"","cross_cats":["math.RA"],"primary_cat":"math.GR","authors_text":"J\\'an Min\\'a\\v{c}, Wenfeng Gao","submitted_at":"2001-10-25T22:16:42Z","abstract_excerpt":"A Galois field extension $E/F$ whose Galois group is a pro-2-group of an exponent of at most 8, with a nilpotency class of at most 4, is determined, such that it contains essential information about the Witt rings of all quadratic extensions of $F$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0110284","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":"2026-05-18T01:05:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"565idsb+zSUIp5H8Qf1Qg0vVoFvOI247iRiehJI2P/CmNVA+mZ/ZJmvlbELLvv5Oq8TGIhg+vRANuktUrPhSDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T05:30:07.656590Z"},"content_sha256":"44c089b070c7c1f1073dc0346d7180d6a87207f0c2d9b62e8015b2aa66415944","schema_version":"1.0","event_id":"sha256:44c089b070c7c1f1073dc0346d7180d6a87207f0c2d9b62e8015b2aa66415944"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CO7VKGIDDVOYONFPUAOZXFIW5M/bundle.json","state_url":"https://pith.science/pith/CO7VKGIDDVOYONFPUAOZXFIW5M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CO7VKGIDDVOYONFPUAOZXFIW5M/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":"2026-06-06T05:30:07Z","links":{"resolver":"https://pith.science/pith/CO7VKGIDDVOYONFPUAOZXFIW5M","bundle":"https://pith.science/pith/CO7VKGIDDVOYONFPUAOZXFIW5M/bundle.json","state":"https://pith.science/pith/CO7VKGIDDVOYONFPUAOZXFIW5M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CO7VKGIDDVOYONFPUAOZXFIW5M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:CO7VKGIDDVOYONFPUAOZXFIW5M","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":"f88e3c7f9f0caca13c70ca99cc747b58d38ed7b219d9e3289d709efc740118cb","cross_cats_sorted":["math.RA"],"license":"","primary_cat":"math.GR","submitted_at":"2001-10-25T22:16:42Z","title_canon_sha256":"b361e0016a2b082c0b32c76cb48303e26638f3c9de6b4d33418847d35c0de92c"},"schema_version":"1.0","source":{"id":"math/0110284","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0110284","created_at":"2026-05-18T01:05:37Z"},{"alias_kind":"arxiv_version","alias_value":"math/0110284v1","created_at":"2026-05-18T01:05:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0110284","created_at":"2026-05-18T01:05:37Z"},{"alias_kind":"pith_short_12","alias_value":"CO7VKGIDDVOY","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"CO7VKGIDDVOYONFP","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"CO7VKGID","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:44c089b070c7c1f1073dc0346d7180d6a87207f0c2d9b62e8015b2aa66415944","target":"graph","created_at":"2026-05-18T01:05:37Z","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":"A Galois field extension $E/F$ whose Galois group is a pro-2-group of an exponent of at most 8, with a nilpotency class of at most 4, is determined, such that it contains essential information about the Witt rings of all quadratic extensions of $F$.","authors_text":"J\\'an Min\\'a\\v{c}, Wenfeng Gao","cross_cats":["math.RA"],"headline":"","license":"","primary_cat":"math.GR","submitted_at":"2001-10-25T22:16:42Z","title":"Some Galois extensions of quadratic extensions associated with Witt rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0110284","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":"sha256:537aa08e69aa64446c7ca4c1dc011a25937ea1669f7454dbce6ed9f44e76c098","target":"record","created_at":"2026-05-18T01:05:37Z","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":"f88e3c7f9f0caca13c70ca99cc747b58d38ed7b219d9e3289d709efc740118cb","cross_cats_sorted":["math.RA"],"license":"","primary_cat":"math.GR","submitted_at":"2001-10-25T22:16:42Z","title_canon_sha256":"b361e0016a2b082c0b32c76cb48303e26638f3c9de6b4d33418847d35c0de92c"},"schema_version":"1.0","source":{"id":"math/0110284","kind":"arxiv","version":1}},"canonical_sha256":"13bf5519031d5d8734afa01d9b9516eb21f97092c0923a6efdf71e7720d451d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13bf5519031d5d8734afa01d9b9516eb21f97092c0923a6efdf71e7720d451d4","first_computed_at":"2026-05-18T01:05:37.516503Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:37.516503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/9dZL8+F0mTs6Zgbja7Zwfwi4UQTXU9hk8zEOzR2q1sKsPXGrX8WouougaB5tNWFMN8HJqZyaa8FlnAMP4FYAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:37.516934Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0110284","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:537aa08e69aa64446c7ca4c1dc011a25937ea1669f7454dbce6ed9f44e76c098","sha256:44c089b070c7c1f1073dc0346d7180d6a87207f0c2d9b62e8015b2aa66415944"],"state_sha256":"07134933165add2c4ef1c62595157ae870c76ed55285cad2c3dee8d0765a29ff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8nO6hNDTokvGUfjOac9PbuyKMbj1N3Ti5TuNkWjQWje0cWkz393a0bp/qR9cagr1s98R1NztEkfK65ESZa/8CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T05:30:07.659818Z","bundle_sha256":"88c3b60c68d9650a878a4ac8cde924bbf2fb22fcb880fb9983180a1f6243a46d"}}