{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:5E43TCDITU5H6KS3XUCYWSTFS3","short_pith_number":"pith:5E43TCDI","canonical_record":{"source":{"id":"1301.1404","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-01-08T03:28:01Z","cross_cats_sorted":[],"title_canon_sha256":"76db1eb81e1582505db42c5a36820037186254010acb2a1c24683b85d5a06aa7","abstract_canon_sha256":"36b5e72b2c0d0c35b7d27d2774a8b4d6e46b465180b7b9d732091a96ddd38741"},"schema_version":"1.0"},"canonical_sha256":"e939b988689d3a7f2a5bbd058b4a6596f116961dccb5644cb694c6bd7515494c","source":{"kind":"arxiv","id":"1301.1404","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1404","created_at":"2026-05-18T03:36:57Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1404v1","created_at":"2026-05-18T03:36:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1404","created_at":"2026-05-18T03:36:57Z"},{"alias_kind":"pith_short_12","alias_value":"5E43TCDITU5H","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5E43TCDITU5H6KS3","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5E43TCDI","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:5E43TCDITU5H6KS3XUCYWSTFS3","target":"record","payload":{"canonical_record":{"source":{"id":"1301.1404","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-01-08T03:28:01Z","cross_cats_sorted":[],"title_canon_sha256":"76db1eb81e1582505db42c5a36820037186254010acb2a1c24683b85d5a06aa7","abstract_canon_sha256":"36b5e72b2c0d0c35b7d27d2774a8b4d6e46b465180b7b9d732091a96ddd38741"},"schema_version":"1.0"},"canonical_sha256":"e939b988689d3a7f2a5bbd058b4a6596f116961dccb5644cb694c6bd7515494c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:57.597034Z","signature_b64":"w3Sxyx3o4ZQDAw2zyJ95NY4wenr1RkePJ+PkydykWS8u/YSwI+X6mBBvb6vg33clYcMYVLGQGczh6R1/Hn95BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e939b988689d3a7f2a5bbd058b4a6596f116961dccb5644cb694c6bd7515494c","last_reissued_at":"2026-05-18T03:36:57.596549Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:57.596549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.1404","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":"2026-05-18T03:36:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pqr08Tnx0n5M65e6en3GZN9GyjvzgglaVETWAtWevniZGTqiXB/iUCmHSCqLyCqIGu+Y/mAnF3LpQqU/xSBADw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:24:16.652457Z"},"content_sha256":"1aa3381909ab4031e514c4269e30d04fb95837991d34cce4380b24d545f01304","schema_version":"1.0","event_id":"sha256:1aa3381909ab4031e514c4269e30d04fb95837991d34cce4380b24d545f01304"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:5E43TCDITU5H6KS3XUCYWSTFS3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The prolongation of central extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Che T. Kim Phung, Nguyen Tien Quang, Pham Thi Cuc","submitted_at":"2013-01-08T03:28:01Z","abstract_excerpt":"The aim of this paper is to study the $(\\alpha, \\gamma)$-prolongation of central extensions. We obtain the obstruction theory for $(\\alpha, \\gamma)$-prolongations and classify $(\\alpha, \\gamma)$-prolongations thanks to low-dimensional cohomology groups of groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1404","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":"2026-05-18T03:36:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XOz/CQ7JCBaVH6ZWPgX1dXSbMXJgQvEQiS+xy6wquLXgumEsHQd6W26tdYFT6YOH+D+aNeNnBdkQ4MAA00fAAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:24:16.652795Z"},"content_sha256":"e809a9e2078ffc0266a33d2789c4039897264ee11b9f44c85ba3d38e687afd48","schema_version":"1.0","event_id":"sha256:e809a9e2078ffc0266a33d2789c4039897264ee11b9f44c85ba3d38e687afd48"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5E43TCDITU5H6KS3XUCYWSTFS3/bundle.json","state_url":"https://pith.science/pith/5E43TCDITU5H6KS3XUCYWSTFS3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5E43TCDITU5H6KS3XUCYWSTFS3/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":"2026-06-24T22:24:16Z","links":{"resolver":"https://pith.science/pith/5E43TCDITU5H6KS3XUCYWSTFS3","bundle":"https://pith.science/pith/5E43TCDITU5H6KS3XUCYWSTFS3/bundle.json","state":"https://pith.science/pith/5E43TCDITU5H6KS3XUCYWSTFS3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5E43TCDITU5H6KS3XUCYWSTFS3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:5E43TCDITU5H6KS3XUCYWSTFS3","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":"36b5e72b2c0d0c35b7d27d2774a8b4d6e46b465180b7b9d732091a96ddd38741","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-01-08T03:28:01Z","title_canon_sha256":"76db1eb81e1582505db42c5a36820037186254010acb2a1c24683b85d5a06aa7"},"schema_version":"1.0","source":{"id":"1301.1404","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1404","created_at":"2026-05-18T03:36:57Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1404v1","created_at":"2026-05-18T03:36:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1404","created_at":"2026-05-18T03:36:57Z"},{"alias_kind":"pith_short_12","alias_value":"5E43TCDITU5H","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5E43TCDITU5H6KS3","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5E43TCDI","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:e809a9e2078ffc0266a33d2789c4039897264ee11b9f44c85ba3d38e687afd48","target":"graph","created_at":"2026-05-18T03:36:57Z","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":"The aim of this paper is to study the $(\\alpha, \\gamma)$-prolongation of central extensions. We obtain the obstruction theory for $(\\alpha, \\gamma)$-prolongations and classify $(\\alpha, \\gamma)$-prolongations thanks to low-dimensional cohomology groups of groups.","authors_text":"Che T. Kim Phung, Nguyen Tien Quang, Pham Thi Cuc","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-01-08T03:28:01Z","title":"The prolongation of central extensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1404","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":"sha256:1aa3381909ab4031e514c4269e30d04fb95837991d34cce4380b24d545f01304","target":"record","created_at":"2026-05-18T03:36:57Z","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":"36b5e72b2c0d0c35b7d27d2774a8b4d6e46b465180b7b9d732091a96ddd38741","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-01-08T03:28:01Z","title_canon_sha256":"76db1eb81e1582505db42c5a36820037186254010acb2a1c24683b85d5a06aa7"},"schema_version":"1.0","source":{"id":"1301.1404","kind":"arxiv","version":1}},"canonical_sha256":"e939b988689d3a7f2a5bbd058b4a6596f116961dccb5644cb694c6bd7515494c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e939b988689d3a7f2a5bbd058b4a6596f116961dccb5644cb694c6bd7515494c","first_computed_at":"2026-05-18T03:36:57.596549Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:57.596549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w3Sxyx3o4ZQDAw2zyJ95NY4wenr1RkePJ+PkydykWS8u/YSwI+X6mBBvb6vg33clYcMYVLGQGczh6R1/Hn95BA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:57.597034Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.1404","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1aa3381909ab4031e514c4269e30d04fb95837991d34cce4380b24d545f01304","sha256:e809a9e2078ffc0266a33d2789c4039897264ee11b9f44c85ba3d38e687afd48"],"state_sha256":"b948fea5e99a23e60586ca2d385b54f5f160e195ffe4c5300e9e0dc2a8f3a264"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AMnQh48DstERq4SAJ9wPPSPlgI9eZmA9osCAN1t1B2L8OaXdRB5kXuskls1BZzD3T3ssXsxAAsXjfqlK1b6TBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T22:24:16.654959Z","bundle_sha256":"1aa933f5ccb54ebe9a77f63b5f2f52fe4b987e8bc91e91f3667a20d9c119df55"}}