{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:62TENIHJKJBEDOSBVGGSEQT53T","short_pith_number":"pith:62TENIHJ","schema_version":"1.0","canonical_sha256":"f6a646a0e9524241ba41a98d22427ddcce8977122fd2f53bbce929d73c83bc82","source":{"kind":"arxiv","id":"1504.07506","version":3},"attestation_state":"computed","paper":{"title":"Minimal generation of transitive permutation groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Gareth M. Tracey","submitted_at":"2015-04-28T14:43:51Z","abstract_excerpt":"It is proved in [21] that there is a constant $c$ such that each transitive permutation group of degree $d\\ge 2$ can be generated by $\\lfloor cd/\\sqrt{\\log{d}}\\rfloor$ elements. In this paper, we explicitly estimate $c$."},"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":"1504.07506","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-04-28T14:43:51Z","cross_cats_sorted":[],"title_canon_sha256":"25152080cd086b773ab5a7b054f223aaff2cbedabeec273f49882fa5a1acdd21","abstract_canon_sha256":"6ac6102d2f58ad094803108d16478411784386e3c8564c350add72b867f60778"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:53.544743Z","signature_b64":"CJHD/qzgahFTLn98qZger9EeQdxrO6bu5L6ud4F07icl/9hSwCq7JiWkP7wX6m7M0ixEKb5YpJ7Ns/iKHlPjCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6a646a0e9524241ba41a98d22427ddcce8977122fd2f53bbce929d73c83bc82","last_reissued_at":"2026-05-18T00:24:53.543962Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:53.543962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimal generation of transitive permutation groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Gareth M. Tracey","submitted_at":"2015-04-28T14:43:51Z","abstract_excerpt":"It is proved in [21] that there is a constant $c$ such that each transitive permutation group of degree $d\\ge 2$ can be generated by $\\lfloor cd/\\sqrt{\\log{d}}\\rfloor$ elements. In this paper, we explicitly estimate $c$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.07506","kind":"arxiv","version":3},"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":"1504.07506","created_at":"2026-05-18T00:24:53.544097+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.07506v3","created_at":"2026-05-18T00:24:53.544097+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.07506","created_at":"2026-05-18T00:24:53.544097+00:00"},{"alias_kind":"pith_short_12","alias_value":"62TENIHJKJBE","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_16","alias_value":"62TENIHJKJBEDOSB","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_8","alias_value":"62TENIHJ","created_at":"2026-05-18T12:29:07.941421+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/62TENIHJKJBEDOSBVGGSEQT53T","json":"https://pith.science/pith/62TENIHJKJBEDOSBVGGSEQT53T.json","graph_json":"https://pith.science/api/pith-number/62TENIHJKJBEDOSBVGGSEQT53T/graph.json","events_json":"https://pith.science/api/pith-number/62TENIHJKJBEDOSBVGGSEQT53T/events.json","paper":"https://pith.science/paper/62TENIHJ"},"agent_actions":{"view_html":"https://pith.science/pith/62TENIHJKJBEDOSBVGGSEQT53T","download_json":"https://pith.science/pith/62TENIHJKJBEDOSBVGGSEQT53T.json","view_paper":"https://pith.science/paper/62TENIHJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.07506&json=true","fetch_graph":"https://pith.science/api/pith-number/62TENIHJKJBEDOSBVGGSEQT53T/graph.json","fetch_events":"https://pith.science/api/pith-number/62TENIHJKJBEDOSBVGGSEQT53T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/62TENIHJKJBEDOSBVGGSEQT53T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/62TENIHJKJBEDOSBVGGSEQT53T/action/storage_attestation","attest_author":"https://pith.science/pith/62TENIHJKJBEDOSBVGGSEQT53T/action/author_attestation","sign_citation":"https://pith.science/pith/62TENIHJKJBEDOSBVGGSEQT53T/action/citation_signature","submit_replication":"https://pith.science/pith/62TENIHJKJBEDOSBVGGSEQT53T/action/replication_record"}},"created_at":"2026-05-18T00:24:53.544097+00:00","updated_at":"2026-05-18T00:24:53.544097+00:00"}