{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:AWJV6DHRVQNL4WE5PF323I4KRQ","short_pith_number":"pith:AWJV6DHR","canonical_record":{"source":{"id":"1406.7365","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-06-28T07:19:09Z","cross_cats_sorted":[],"title_canon_sha256":"85e65b9875fd2c64f4d6bf629e8ad877e40df871aa63dbb4660e379bc48f66fe","abstract_canon_sha256":"527d6f8ce6df4525022dfdf5a57f48047c1cae12f6d97c80602b4a7b325be76a"},"schema_version":"1.0"},"canonical_sha256":"05935f0cf1ac1abe589d7977ada38a8c34b65af4509d81f01b749f9802b88e5b","source":{"kind":"arxiv","id":"1406.7365","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.7365","created_at":"2026-05-18T00:11:19Z"},{"alias_kind":"arxiv_version","alias_value":"1406.7365v1","created_at":"2026-05-18T00:11:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.7365","created_at":"2026-05-18T00:11:19Z"},{"alias_kind":"pith_short_12","alias_value":"AWJV6DHRVQNL","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AWJV6DHRVQNL4WE5","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AWJV6DHR","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:AWJV6DHRVQNL4WE5PF323I4KRQ","target":"record","payload":{"canonical_record":{"source":{"id":"1406.7365","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-06-28T07:19:09Z","cross_cats_sorted":[],"title_canon_sha256":"85e65b9875fd2c64f4d6bf629e8ad877e40df871aa63dbb4660e379bc48f66fe","abstract_canon_sha256":"527d6f8ce6df4525022dfdf5a57f48047c1cae12f6d97c80602b4a7b325be76a"},"schema_version":"1.0"},"canonical_sha256":"05935f0cf1ac1abe589d7977ada38a8c34b65af4509d81f01b749f9802b88e5b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:19.595132Z","signature_b64":"zB0xh3N/M3VcHYFIXiew0TmytoPFA9HcDETU+sck+d1sPUCeITQi3kDW/mRF7XOoQtN2JEvcG+g/Gqi4D2nKDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05935f0cf1ac1abe589d7977ada38a8c34b65af4509d81f01b749f9802b88e5b","last_reissued_at":"2026-05-18T00:11:19.594611Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:19.594611Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.7365","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":"2026-05-18T00:11:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CHxtfKtZGT5G42PoUZ80qgWXzXyMfnZ0i6vMSTqOipQZRDfq4ywz1kU82iqfu941xLk1RTg64BHVx+wibVzvBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T00:47:00.624966Z"},"content_sha256":"cd34f6ea123e9215f612c2678e824801c3ff16706a12bc7a822f898deaa87eaf","schema_version":"1.0","event_id":"sha256:cd34f6ea123e9215f612c2678e824801c3ff16706a12bc7a822f898deaa87eaf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:AWJV6DHRVQNL4WE5PF323I4KRQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Class-preserving automorphisms of finite $p$-groups II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Manoj K. Yadav","submitted_at":"2014-06-28T07:19:09Z","abstract_excerpt":"Let $G$ be a finite group minimally generated by $d(G)$ elements and $\\Aut_c(G)$ denote the group of all (conjugacy) class-preserving automorphisms of $G$. Continuing our work [Class preserving automorphisms of finite $p$-groups, J. London Math. Soc. \\textbf{75(3)} (2007), 755-772], we study finite $p$-groups $G$ such that $|\\Aut_c(G)| = |\\gamma_2(G)|^{d(G)}$, where $\\gamma_2(G)$ denotes the commutator subgroup of $G$. If $G$ is such a $p$-group of class $2$, then we show that $d(G)$ is even, $2d(\\gamma_2(G)) \\le d(G)$ and $G/\\Z(G)$ is homocyclic. When the nilpotency class of $G$ is larger tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7365","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":"2026-05-18T00:11:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ySSMjLM1VZWoAeJ2s0yLgXDEc0aCDLv9QvNNq8HRBQyt/+GsXQV/wTTD8QTu2DfVlHRsq/7AO29K7ZtTk4GwCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T00:47:00.625366Z"},"content_sha256":"f6ee1124a2be650571f54b038612fedc9f3de8324befff0a894dcec21b4119e9","schema_version":"1.0","event_id":"sha256:f6ee1124a2be650571f54b038612fedc9f3de8324befff0a894dcec21b4119e9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AWJV6DHRVQNL4WE5PF323I4KRQ/bundle.json","state_url":"https://pith.science/pith/AWJV6DHRVQNL4WE5PF323I4KRQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AWJV6DHRVQNL4WE5PF323I4KRQ/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":"2026-06-06T00:47:00Z","links":{"resolver":"https://pith.science/pith/AWJV6DHRVQNL4WE5PF323I4KRQ","bundle":"https://pith.science/pith/AWJV6DHRVQNL4WE5PF323I4KRQ/bundle.json","state":"https://pith.science/pith/AWJV6DHRVQNL4WE5PF323I4KRQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AWJV6DHRVQNL4WE5PF323I4KRQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:AWJV6DHRVQNL4WE5PF323I4KRQ","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":"527d6f8ce6df4525022dfdf5a57f48047c1cae12f6d97c80602b4a7b325be76a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-06-28T07:19:09Z","title_canon_sha256":"85e65b9875fd2c64f4d6bf629e8ad877e40df871aa63dbb4660e379bc48f66fe"},"schema_version":"1.0","source":{"id":"1406.7365","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.7365","created_at":"2026-05-18T00:11:19Z"},{"alias_kind":"arxiv_version","alias_value":"1406.7365v1","created_at":"2026-05-18T00:11:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.7365","created_at":"2026-05-18T00:11:19Z"},{"alias_kind":"pith_short_12","alias_value":"AWJV6DHRVQNL","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AWJV6DHRVQNL4WE5","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AWJV6DHR","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:f6ee1124a2be650571f54b038612fedc9f3de8324befff0a894dcec21b4119e9","target":"graph","created_at":"2026-05-18T00:11:19Z","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":"Let $G$ be a finite group minimally generated by $d(G)$ elements and $\\Aut_c(G)$ denote the group of all (conjugacy) class-preserving automorphisms of $G$. Continuing our work [Class preserving automorphisms of finite $p$-groups, J. London Math. Soc. \\textbf{75(3)} (2007), 755-772], we study finite $p$-groups $G$ such that $|\\Aut_c(G)| = |\\gamma_2(G)|^{d(G)}$, where $\\gamma_2(G)$ denotes the commutator subgroup of $G$. If $G$ is such a $p$-group of class $2$, then we show that $d(G)$ is even, $2d(\\gamma_2(G)) \\le d(G)$ and $G/\\Z(G)$ is homocyclic. When the nilpotency class of $G$ is larger tha","authors_text":"Manoj K. Yadav","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-06-28T07:19:09Z","title":"Class-preserving automorphisms of finite $p$-groups II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7365","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:cd34f6ea123e9215f612c2678e824801c3ff16706a12bc7a822f898deaa87eaf","target":"record","created_at":"2026-05-18T00:11:19Z","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":"527d6f8ce6df4525022dfdf5a57f48047c1cae12f6d97c80602b4a7b325be76a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-06-28T07:19:09Z","title_canon_sha256":"85e65b9875fd2c64f4d6bf629e8ad877e40df871aa63dbb4660e379bc48f66fe"},"schema_version":"1.0","source":{"id":"1406.7365","kind":"arxiv","version":1}},"canonical_sha256":"05935f0cf1ac1abe589d7977ada38a8c34b65af4509d81f01b749f9802b88e5b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05935f0cf1ac1abe589d7977ada38a8c34b65af4509d81f01b749f9802b88e5b","first_computed_at":"2026-05-18T00:11:19.594611Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:19.594611Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zB0xh3N/M3VcHYFIXiew0TmytoPFA9HcDETU+sck+d1sPUCeITQi3kDW/mRF7XOoQtN2JEvcG+g/Gqi4D2nKDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:19.595132Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.7365","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd34f6ea123e9215f612c2678e824801c3ff16706a12bc7a822f898deaa87eaf","sha256:f6ee1124a2be650571f54b038612fedc9f3de8324befff0a894dcec21b4119e9"],"state_sha256":"8f3ca1ef894b97bec2713b46ea1145a4cbaf625208238302ccb437ee15e54978"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3kttkof2AlX8NZ2pmB5wnYGtxkWnMeNJ37R/21da9Oae0ISRjc5nOYwVIh53zN2BaHe9dBrNay9OXLW+ojvpBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T00:47:00.628766Z","bundle_sha256":"ab9e011517656e32d27d5542d933c0f1a06c1dcf9ff942438e83ad356b6ae1fd"}}