{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:LTRSKQH4W3CVB4J7UTZHTHOWUT","short_pith_number":"pith:LTRSKQH4","canonical_record":{"source":{"id":"1710.04832","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-10-13T08:22:26Z","cross_cats_sorted":[],"title_canon_sha256":"2d673baf026c442b58483447197df566fe7ca406f7efcb24d1630cff69939dfd","abstract_canon_sha256":"755b66b2c074bbcfa6358069873b9a4ead2760cc586a4fc0063087a667bb8f42"},"schema_version":"1.0"},"canonical_sha256":"5ce32540fcb6c550f13fa4f2799dd6a4e992cac6f5d636865e3e97a91a2ddf04","source":{"kind":"arxiv","id":"1710.04832","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.04832","created_at":"2026-05-18T00:16:08Z"},{"alias_kind":"arxiv_version","alias_value":"1710.04832v1","created_at":"2026-05-18T00:16:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.04832","created_at":"2026-05-18T00:16:08Z"},{"alias_kind":"pith_short_12","alias_value":"LTRSKQH4W3CV","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LTRSKQH4W3CVB4J7","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LTRSKQH4","created_at":"2026-05-18T12:31:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:LTRSKQH4W3CVB4J7UTZHTHOWUT","target":"record","payload":{"canonical_record":{"source":{"id":"1710.04832","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-10-13T08:22:26Z","cross_cats_sorted":[],"title_canon_sha256":"2d673baf026c442b58483447197df566fe7ca406f7efcb24d1630cff69939dfd","abstract_canon_sha256":"755b66b2c074bbcfa6358069873b9a4ead2760cc586a4fc0063087a667bb8f42"},"schema_version":"1.0"},"canonical_sha256":"5ce32540fcb6c550f13fa4f2799dd6a4e992cac6f5d636865e3e97a91a2ddf04","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:08.570021Z","signature_b64":"AyKYzHQT6DUEn6TavTAAn05whjOyLlBnuXijpcBQ7gNfFdqOBM8rv4j6iiPN94ZJCa9afX4CCxsl7AD0HVOPCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ce32540fcb6c550f13fa4f2799dd6a4e992cac6f5d636865e3e97a91a2ddf04","last_reissued_at":"2026-05-18T00:16:08.569417Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:08.569417Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.04832","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":"2026-05-18T00:16:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qMEKy5tMmIYmcoy8+FSLUMHq9fZ9T8WFwCrngCYrO4RkvIpWLfWU5g4UdkJkmrl7A48MAUHZOkZuMtsUdTVBBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T04:10:37.686833Z"},"content_sha256":"c511c92c7eb0d2eadada3572bf64f0416a80f67d4465fec80ddf53d9ecaade3c","schema_version":"1.0","event_id":"sha256:c511c92c7eb0d2eadada3572bf64f0416a80f67d4465fec80ddf53d9ecaade3c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:LTRSKQH4W3CVB4J7UTZHTHOWUT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Subextensions for co-induced modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Andrei V. Zavarnitsine","submitted_at":"2017-10-13T08:22:26Z","abstract_excerpt":"Using cohomological methods, we prove a criterion for the embedding of a group extension with abelian kernel into the split extension of a co-induced module. This generalises some earlier similar results. We also prove an assertion about the conjugacy of complements in split extensions of co-induced modules. Both results follow from a relation between homomorphisms of certain cohomology groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.04832","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":"2026-05-18T00:16:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U2E2lG4wPVQ5hMixe4SGpu+RDFTWCfUmXkK1EwIp4zhxEm97lEUX7UahNhmvP8y4yz+bxGZXQm/sD5XmitE2BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T04:10:37.687167Z"},"content_sha256":"c53f6b717ccf5bef739297410865584d148f9969a2437369bd879b922bfe7caa","schema_version":"1.0","event_id":"sha256:c53f6b717ccf5bef739297410865584d148f9969a2437369bd879b922bfe7caa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LTRSKQH4W3CVB4J7UTZHTHOWUT/bundle.json","state_url":"https://pith.science/pith/LTRSKQH4W3CVB4J7UTZHTHOWUT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LTRSKQH4W3CVB4J7UTZHTHOWUT/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":"2026-05-28T04:10:37Z","links":{"resolver":"https://pith.science/pith/LTRSKQH4W3CVB4J7UTZHTHOWUT","bundle":"https://pith.science/pith/LTRSKQH4W3CVB4J7UTZHTHOWUT/bundle.json","state":"https://pith.science/pith/LTRSKQH4W3CVB4J7UTZHTHOWUT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LTRSKQH4W3CVB4J7UTZHTHOWUT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LTRSKQH4W3CVB4J7UTZHTHOWUT","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":"755b66b2c074bbcfa6358069873b9a4ead2760cc586a4fc0063087a667bb8f42","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-10-13T08:22:26Z","title_canon_sha256":"2d673baf026c442b58483447197df566fe7ca406f7efcb24d1630cff69939dfd"},"schema_version":"1.0","source":{"id":"1710.04832","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.04832","created_at":"2026-05-18T00:16:08Z"},{"alias_kind":"arxiv_version","alias_value":"1710.04832v1","created_at":"2026-05-18T00:16:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.04832","created_at":"2026-05-18T00:16:08Z"},{"alias_kind":"pith_short_12","alias_value":"LTRSKQH4W3CV","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LTRSKQH4W3CVB4J7","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LTRSKQH4","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:c53f6b717ccf5bef739297410865584d148f9969a2437369bd879b922bfe7caa","target":"graph","created_at":"2026-05-18T00:16:08Z","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":"Using cohomological methods, we prove a criterion for the embedding of a group extension with abelian kernel into the split extension of a co-induced module. This generalises some earlier similar results. We also prove an assertion about the conjugacy of complements in split extensions of co-induced modules. Both results follow from a relation between homomorphisms of certain cohomology groups.","authors_text":"Andrei V. Zavarnitsine","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-10-13T08:22:26Z","title":"Subextensions for co-induced modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.04832","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:c511c92c7eb0d2eadada3572bf64f0416a80f67d4465fec80ddf53d9ecaade3c","target":"record","created_at":"2026-05-18T00:16:08Z","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":"755b66b2c074bbcfa6358069873b9a4ead2760cc586a4fc0063087a667bb8f42","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-10-13T08:22:26Z","title_canon_sha256":"2d673baf026c442b58483447197df566fe7ca406f7efcb24d1630cff69939dfd"},"schema_version":"1.0","source":{"id":"1710.04832","kind":"arxiv","version":1}},"canonical_sha256":"5ce32540fcb6c550f13fa4f2799dd6a4e992cac6f5d636865e3e97a91a2ddf04","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ce32540fcb6c550f13fa4f2799dd6a4e992cac6f5d636865e3e97a91a2ddf04","first_computed_at":"2026-05-18T00:16:08.569417Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:08.569417Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AyKYzHQT6DUEn6TavTAAn05whjOyLlBnuXijpcBQ7gNfFdqOBM8rv4j6iiPN94ZJCa9afX4CCxsl7AD0HVOPCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:08.570021Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.04832","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c511c92c7eb0d2eadada3572bf64f0416a80f67d4465fec80ddf53d9ecaade3c","sha256:c53f6b717ccf5bef739297410865584d148f9969a2437369bd879b922bfe7caa"],"state_sha256":"9b26b6e4c1d44a6a34e0cc2f0b21e09ad99ab81036fb65a3bbda0e2bee310e9c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iquRRlwzDZiJAWSuj2d6Y24Jj2gkCkNF6K/fRLWuJD1mp7K+9RnOJef/IZFtSL+bazUFe5kVk6axkMPrZAMiCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T04:10:37.689194Z","bundle_sha256":"79443ae4a17fb53efaf8eb0529d125ade7049fb7bb3fb4f3f10dfec3b0456907"}}