{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:R2KHKXQK5LOOQIYSV4KRSJVGZK","short_pith_number":"pith:R2KHKXQK","canonical_record":{"source":{"id":"1405.0881","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-05-05T12:57:56Z","cross_cats_sorted":[],"title_canon_sha256":"be4e18019cd409b849d65b247cf98825dce71db7bc36cd538740353e05774149","abstract_canon_sha256":"6e40f48764ddcb9c9e625e54cb456ffd39c32c7b68f9335865819d189de8269c"},"schema_version":"1.0"},"canonical_sha256":"8e94755e0aeadce82312af151926a6caa352fe418479e1599e994530d9f07f7b","source":{"kind":"arxiv","id":"1405.0881","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.0881","created_at":"2026-05-18T00:46:21Z"},{"alias_kind":"arxiv_version","alias_value":"1405.0881v1","created_at":"2026-05-18T00:46:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.0881","created_at":"2026-05-18T00:46:21Z"},{"alias_kind":"pith_short_12","alias_value":"R2KHKXQK5LOO","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"R2KHKXQK5LOOQIYS","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"R2KHKXQK","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:R2KHKXQK5LOOQIYSV4KRSJVGZK","target":"record","payload":{"canonical_record":{"source":{"id":"1405.0881","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-05-05T12:57:56Z","cross_cats_sorted":[],"title_canon_sha256":"be4e18019cd409b849d65b247cf98825dce71db7bc36cd538740353e05774149","abstract_canon_sha256":"6e40f48764ddcb9c9e625e54cb456ffd39c32c7b68f9335865819d189de8269c"},"schema_version":"1.0"},"canonical_sha256":"8e94755e0aeadce82312af151926a6caa352fe418479e1599e994530d9f07f7b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:21.386364Z","signature_b64":"+lFl+ns3sEv7wV5AfQn6kssIaz82RJ1SVu8KiFlUssP55RAd7KdraZAQnMQaslWZlfJooLStujPWg7+rYQttDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e94755e0aeadce82312af151926a6caa352fe418479e1599e994530d9f07f7b","last_reissued_at":"2026-05-18T00:46:21.385957Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:21.385957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.0881","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":"2026-05-18T00:46:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AGXesbpO5SKTuP3N3pHY8IDQbBM2macLH5aFV3sNX4Xbdk6BbIcfLnpDzBVUEyuouIa5kQBB58QmeiUUA0ziAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T14:18:04.735287Z"},"content_sha256":"b0b5fad12296f94389d3eaf237bc4b2bfdfc6f1cf634cd345e2747ef7eefbc48","schema_version":"1.0","event_id":"sha256:b0b5fad12296f94389d3eaf237bc4b2bfdfc6f1cf634cd345e2747ef7eefbc48"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:R2KHKXQK5LOOQIYSV4KRSJVGZK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Galois correspondence theorem in separable Hopf Galois theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Anna Rio, Montserrat Vela, Teresa Crespo","submitted_at":"2014-05-05T12:57:56Z","abstract_excerpt":"In this paper we present a reformulation of the Galois correspondence theorem of Hopf Galois theory in terms of groups carrying farther the description of Greither and Pareigis. We prove that the class of Hopf Galois extensions for which the Galois correspondence is bijective is larger than the class of almost classically Galois extensions but not equal to the whole class. We show as well that the image of the Galois correspondence does not determine the Hopf Galois structure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0881","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":"2026-05-18T00:46:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZbU0ko9KzAAU/uECKSD6hw7Aiy5AUWFIdV61Y6RleXumWgowlOl3I8UvommI2jb9IWwZU1WEiQHDindB4q1XDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T14:18:04.735633Z"},"content_sha256":"98b24673b787b5919a05763387ecfbe056dcb45cbbadc2a006547a52c61e8ff8","schema_version":"1.0","event_id":"sha256:98b24673b787b5919a05763387ecfbe056dcb45cbbadc2a006547a52c61e8ff8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R2KHKXQK5LOOQIYSV4KRSJVGZK/bundle.json","state_url":"https://pith.science/pith/R2KHKXQK5LOOQIYSV4KRSJVGZK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R2KHKXQK5LOOQIYSV4KRSJVGZK/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":"2026-06-26T14:18:04Z","links":{"resolver":"https://pith.science/pith/R2KHKXQK5LOOQIYSV4KRSJVGZK","bundle":"https://pith.science/pith/R2KHKXQK5LOOQIYSV4KRSJVGZK/bundle.json","state":"https://pith.science/pith/R2KHKXQK5LOOQIYSV4KRSJVGZK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R2KHKXQK5LOOQIYSV4KRSJVGZK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:R2KHKXQK5LOOQIYSV4KRSJVGZK","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":"6e40f48764ddcb9c9e625e54cb456ffd39c32c7b68f9335865819d189de8269c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-05-05T12:57:56Z","title_canon_sha256":"be4e18019cd409b849d65b247cf98825dce71db7bc36cd538740353e05774149"},"schema_version":"1.0","source":{"id":"1405.0881","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.0881","created_at":"2026-05-18T00:46:21Z"},{"alias_kind":"arxiv_version","alias_value":"1405.0881v1","created_at":"2026-05-18T00:46:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.0881","created_at":"2026-05-18T00:46:21Z"},{"alias_kind":"pith_short_12","alias_value":"R2KHKXQK5LOO","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"R2KHKXQK5LOOQIYS","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"R2KHKXQK","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:98b24673b787b5919a05763387ecfbe056dcb45cbbadc2a006547a52c61e8ff8","target":"graph","created_at":"2026-05-18T00:46:21Z","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 this paper we present a reformulation of the Galois correspondence theorem of Hopf Galois theory in terms of groups carrying farther the description of Greither and Pareigis. We prove that the class of Hopf Galois extensions for which the Galois correspondence is bijective is larger than the class of almost classically Galois extensions but not equal to the whole class. We show as well that the image of the Galois correspondence does not determine the Hopf Galois structure.","authors_text":"Anna Rio, Montserrat Vela, Teresa Crespo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-05-05T12:57:56Z","title":"On the Galois correspondence theorem in separable Hopf Galois theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0881","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:b0b5fad12296f94389d3eaf237bc4b2bfdfc6f1cf634cd345e2747ef7eefbc48","target":"record","created_at":"2026-05-18T00:46:21Z","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":"6e40f48764ddcb9c9e625e54cb456ffd39c32c7b68f9335865819d189de8269c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-05-05T12:57:56Z","title_canon_sha256":"be4e18019cd409b849d65b247cf98825dce71db7bc36cd538740353e05774149"},"schema_version":"1.0","source":{"id":"1405.0881","kind":"arxiv","version":1}},"canonical_sha256":"8e94755e0aeadce82312af151926a6caa352fe418479e1599e994530d9f07f7b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8e94755e0aeadce82312af151926a6caa352fe418479e1599e994530d9f07f7b","first_computed_at":"2026-05-18T00:46:21.385957Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:21.385957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+lFl+ns3sEv7wV5AfQn6kssIaz82RJ1SVu8KiFlUssP55RAd7KdraZAQnMQaslWZlfJooLStujPWg7+rYQttDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:21.386364Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.0881","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0b5fad12296f94389d3eaf237bc4b2bfdfc6f1cf634cd345e2747ef7eefbc48","sha256:98b24673b787b5919a05763387ecfbe056dcb45cbbadc2a006547a52c61e8ff8"],"state_sha256":"613ca89f70dfb08f02fb9d2b8c664bcbb85633c31f77506ee029367a91a08cae"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b7I6H90kXaf+rrSMSIwcw5aGen6emM8nt/P/8/X05btejgepfaIDN6zwaW+w+Vu5KQVtM7h+gTOsMWF/E9hqAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T14:18:04.737462Z","bundle_sha256":"69d004961266e97a3ee9b35cd60b62175e5f550af099de2b48e227cc45a2407e"}}