{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:V6VBNJHL4UCNDADCPUGPTVODLC","short_pith_number":"pith:V6VBNJHL","schema_version":"1.0","canonical_sha256":"afaa16a4ebe504d180627d0cf9d5c358a579a0e1b1948a5c46ef448c40ef1994","source":{"kind":"arxiv","id":"1312.1755","version":1},"attestation_state":"computed","paper":{"title":"Beating the Generator-Enumeration Bound for $p$-Group Isomorphism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.DS","authors_text":"David J. Rosenbaum, Fabian Wagner","submitted_at":"2013-12-06T02:36:07Z","abstract_excerpt":"We consider the group isomorphism problem: given two finite groups G and H specified by their multiplication tables, decide if G cong H. For several decades, the n^(log_p n + O(1)) generator-enumeration bound (where p is the smallest prime dividing the order of the group) has been the best worst-case result for general groups. In this work, we show the first improvement over the generator-enumeration bound for p-groups, which are believed to be the hard case of the group isomorphism problem. We start by giving a Turing reduction from group isomorphism to n^((1 / 2) log_p n + O(1)) instances of"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1312.1755","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-12-06T02:36:07Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"b73fde3bd814cb9a5f23669d75d9dd3331c35f79d62eccd18ad74148cf3c8089","abstract_canon_sha256":"381d99a1f8821d61cbb8eaa70549231183a709f1f168661245d84652c0406d5b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:19.829158Z","signature_b64":"uG3wE1R+QyY8LJrrlAD4iBgVqu5CbJyu4n6HNjNSHodhClV+TmiCPxgtzNdlsHrBp9PlII5oRLyvT6/C5djjAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"afaa16a4ebe504d180627d0cf9d5c358a579a0e1b1948a5c46ef448c40ef1994","last_reissued_at":"2026-05-18T03:05:19.828728Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:19.828728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Beating the Generator-Enumeration Bound for $p$-Group Isomorphism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.DS","authors_text":"David J. Rosenbaum, Fabian Wagner","submitted_at":"2013-12-06T02:36:07Z","abstract_excerpt":"We consider the group isomorphism problem: given two finite groups G and H specified by their multiplication tables, decide if G cong H. For several decades, the n^(log_p n + O(1)) generator-enumeration bound (where p is the smallest prime dividing the order of the group) has been the best worst-case result for general groups. In this work, we show the first improvement over the generator-enumeration bound for p-groups, which are believed to be the hard case of the group isomorphism problem. We start by giving a Turing reduction from group isomorphism to n^((1 / 2) log_p n + O(1)) instances of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1755","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1312.1755","created_at":"2026-05-18T03:05:19.828793+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.1755v1","created_at":"2026-05-18T03:05:19.828793+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1755","created_at":"2026-05-18T03:05:19.828793+00:00"},{"alias_kind":"pith_short_12","alias_value":"V6VBNJHL4UCN","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_16","alias_value":"V6VBNJHL4UCNDADC","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_8","alias_value":"V6VBNJHL","created_at":"2026-05-18T12:28:04.890932+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/V6VBNJHL4UCNDADCPUGPTVODLC","json":"https://pith.science/pith/V6VBNJHL4UCNDADCPUGPTVODLC.json","graph_json":"https://pith.science/api/pith-number/V6VBNJHL4UCNDADCPUGPTVODLC/graph.json","events_json":"https://pith.science/api/pith-number/V6VBNJHL4UCNDADCPUGPTVODLC/events.json","paper":"https://pith.science/paper/V6VBNJHL"},"agent_actions":{"view_html":"https://pith.science/pith/V6VBNJHL4UCNDADCPUGPTVODLC","download_json":"https://pith.science/pith/V6VBNJHL4UCNDADCPUGPTVODLC.json","view_paper":"https://pith.science/paper/V6VBNJHL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.1755&json=true","fetch_graph":"https://pith.science/api/pith-number/V6VBNJHL4UCNDADCPUGPTVODLC/graph.json","fetch_events":"https://pith.science/api/pith-number/V6VBNJHL4UCNDADCPUGPTVODLC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V6VBNJHL4UCNDADCPUGPTVODLC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V6VBNJHL4UCNDADCPUGPTVODLC/action/storage_attestation","attest_author":"https://pith.science/pith/V6VBNJHL4UCNDADCPUGPTVODLC/action/author_attestation","sign_citation":"https://pith.science/pith/V6VBNJHL4UCNDADCPUGPTVODLC/action/citation_signature","submit_replication":"https://pith.science/pith/V6VBNJHL4UCNDADCPUGPTVODLC/action/replication_record"}},"created_at":"2026-05-18T03:05:19.828793+00:00","updated_at":"2026-05-18T03:05:19.828793+00:00"}