{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:Y74YA3SF4VGIS6LFUVE4F4E6FL","short_pith_number":"pith:Y74YA3SF","canonical_record":{"source":{"id":"1005.2066","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-05-12T12:18:12Z","cross_cats_sorted":[],"title_canon_sha256":"91b0a202ea444c6288059c80daf432767fed67e5d4d2c696d9856af0b8060567","abstract_canon_sha256":"1393eefc4782506b9d1d2778dd6d40bfaaaf0971218cfb4d24d613e97c913e9a"},"schema_version":"1.0"},"canonical_sha256":"c7f9806e45e54c897965a549c2f09e2af9fe4474b06b1e4b165eedabe4bdabd1","source":{"kind":"arxiv","id":"1005.2066","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.2066","created_at":"2026-05-18T03:48:46Z"},{"alias_kind":"arxiv_version","alias_value":"1005.2066v2","created_at":"2026-05-18T03:48:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.2066","created_at":"2026-05-18T03:48:46Z"},{"alias_kind":"pith_short_12","alias_value":"Y74YA3SF4VGI","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"Y74YA3SF4VGIS6LF","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"Y74YA3SF","created_at":"2026-05-18T12:26:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:Y74YA3SF4VGIS6LFUVE4F4E6FL","target":"record","payload":{"canonical_record":{"source":{"id":"1005.2066","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-05-12T12:18:12Z","cross_cats_sorted":[],"title_canon_sha256":"91b0a202ea444c6288059c80daf432767fed67e5d4d2c696d9856af0b8060567","abstract_canon_sha256":"1393eefc4782506b9d1d2778dd6d40bfaaaf0971218cfb4d24d613e97c913e9a"},"schema_version":"1.0"},"canonical_sha256":"c7f9806e45e54c897965a549c2f09e2af9fe4474b06b1e4b165eedabe4bdabd1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:46.732238Z","signature_b64":"aMJbGhIATWPc0eIF2HjHYfIqJxwc3Pml5rjVS/2n6HYumjSmWgW+z5u2vna0JyB0RzAv7z+R6aGjtD1+2oYpCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c7f9806e45e54c897965a549c2f09e2af9fe4474b06b1e4b165eedabe4bdabd1","last_reissued_at":"2026-05-18T03:48:46.731503Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:46.731503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1005.2066","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:48:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MaIAMTl2SPctZfcGkWg7kpDvdC4D3hgzFRKw11oK1dRD1SwMtn5p6urdTVDg4iC2vKwv0Agvrs/Xtur6PTQzCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T05:27:43.168673Z"},"content_sha256":"ffd378fe8d17542d3e043f09be48ed50c843a42b5d1da4fe7e51bb5780752e63","schema_version":"1.0","event_id":"sha256:ffd378fe8d17542d3e043f09be48ed50c843a42b5d1da4fe7e51bb5780752e63"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:Y74YA3SF4VGIS6LFUVE4F4E6FL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On finite $p$-groups whose automorphisms are all central","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Manoj K. Yadav, Vivek K. Jain","submitted_at":"2010-05-12T12:18:12Z","abstract_excerpt":"An automorphism $\\alpha$ of a group $G$ is said to be central if $\\alpha$ commutes with every inner automorphism of $G$. We construct a family of non-special finite $p$-groups having abelian automorphism groups. These groups provide counter examples to a conjecture of A. Mahalanobis [Israel J. Math., {\\bf 165} (2008), 161 - 187]. We also construct a family of finite $p$-groups having non-abelian automorphism groups and all automorphisms central. This solves a problem of I. Malinowska [Advances in group theory, Aracne Editrice, Rome 2002, 111-127]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.2066","kind":"arxiv","version":2},"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":"2026-05-18T03:48:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4oDeUAIWiiKogUDt0Ss56pra+RNOWxn691jBmcJRQXnyF7XXRHV5JbyxTHjsTxthWAB7l1criBG4sqUAV5UGCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T05:27:43.169266Z"},"content_sha256":"0c51c02568df30add3641315334500c72a06d531dbc05dadb6d373c0c2b2582f","schema_version":"1.0","event_id":"sha256:0c51c02568df30add3641315334500c72a06d531dbc05dadb6d373c0c2b2582f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y74YA3SF4VGIS6LFUVE4F4E6FL/bundle.json","state_url":"https://pith.science/pith/Y74YA3SF4VGIS6LFUVE4F4E6FL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y74YA3SF4VGIS6LFUVE4F4E6FL/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":"2026-06-02T05:27:43Z","links":{"resolver":"https://pith.science/pith/Y74YA3SF4VGIS6LFUVE4F4E6FL","bundle":"https://pith.science/pith/Y74YA3SF4VGIS6LFUVE4F4E6FL/bundle.json","state":"https://pith.science/pith/Y74YA3SF4VGIS6LFUVE4F4E6FL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y74YA3SF4VGIS6LFUVE4F4E6FL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:Y74YA3SF4VGIS6LFUVE4F4E6FL","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":"1393eefc4782506b9d1d2778dd6d40bfaaaf0971218cfb4d24d613e97c913e9a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-05-12T12:18:12Z","title_canon_sha256":"91b0a202ea444c6288059c80daf432767fed67e5d4d2c696d9856af0b8060567"},"schema_version":"1.0","source":{"id":"1005.2066","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.2066","created_at":"2026-05-18T03:48:46Z"},{"alias_kind":"arxiv_version","alias_value":"1005.2066v2","created_at":"2026-05-18T03:48:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.2066","created_at":"2026-05-18T03:48:46Z"},{"alias_kind":"pith_short_12","alias_value":"Y74YA3SF4VGI","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"Y74YA3SF4VGIS6LF","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"Y74YA3SF","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:0c51c02568df30add3641315334500c72a06d531dbc05dadb6d373c0c2b2582f","target":"graph","created_at":"2026-05-18T03:48:46Z","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":"An automorphism $\\alpha$ of a group $G$ is said to be central if $\\alpha$ commutes with every inner automorphism of $G$. We construct a family of non-special finite $p$-groups having abelian automorphism groups. These groups provide counter examples to a conjecture of A. Mahalanobis [Israel J. Math., {\\bf 165} (2008), 161 - 187]. We also construct a family of finite $p$-groups having non-abelian automorphism groups and all automorphisms central. This solves a problem of I. Malinowska [Advances in group theory, Aracne Editrice, Rome 2002, 111-127].","authors_text":"Manoj K. Yadav, Vivek K. Jain","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-05-12T12:18:12Z","title":"On finite $p$-groups whose automorphisms are all central"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.2066","kind":"arxiv","version":2},"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:ffd378fe8d17542d3e043f09be48ed50c843a42b5d1da4fe7e51bb5780752e63","target":"record","created_at":"2026-05-18T03:48:46Z","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":"1393eefc4782506b9d1d2778dd6d40bfaaaf0971218cfb4d24d613e97c913e9a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-05-12T12:18:12Z","title_canon_sha256":"91b0a202ea444c6288059c80daf432767fed67e5d4d2c696d9856af0b8060567"},"schema_version":"1.0","source":{"id":"1005.2066","kind":"arxiv","version":2}},"canonical_sha256":"c7f9806e45e54c897965a549c2f09e2af9fe4474b06b1e4b165eedabe4bdabd1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c7f9806e45e54c897965a549c2f09e2af9fe4474b06b1e4b165eedabe4bdabd1","first_computed_at":"2026-05-18T03:48:46.731503Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:48:46.731503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aMJbGhIATWPc0eIF2HjHYfIqJxwc3Pml5rjVS/2n6HYumjSmWgW+z5u2vna0JyB0RzAv7z+R6aGjtD1+2oYpCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:48:46.732238Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.2066","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ffd378fe8d17542d3e043f09be48ed50c843a42b5d1da4fe7e51bb5780752e63","sha256:0c51c02568df30add3641315334500c72a06d531dbc05dadb6d373c0c2b2582f"],"state_sha256":"87c5ab839c7b0de9093053df7eef762172b66eb9bb4cb7303f780bd8d61c4530"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6uAyGPLo3g6dcLh5CpvsFdepSXNd6xyqZui/Uent9cf6samIVD49jP94bc0W8cbf/hKOfqy6T9vpwJE07/W/Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T05:27:43.172448Z","bundle_sha256":"69a57b0f52c6cd46ed89363aa20b2949d56ccff1015215a77b502e4c684bb44f"}}