{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:B4WNEQSQRYL32PJTCDNITSL5W7","short_pith_number":"pith:B4WNEQSQ","schema_version":"1.0","canonical_sha256":"0f2cd242508e17bd3d3310da89c97db7c69a24371d9e8d2fd75814166dbd6fcd","source":{"kind":"arxiv","id":"1707.07095","version":1},"attestation_state":"computed","paper":{"title":"Counting Conjugacy Classes in $Out(F_N)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GT"],"primary_cat":"math.GR","authors_text":"Ilya Kapovich, Michael Hull","submitted_at":"2017-07-22T03:10:34Z","abstract_excerpt":"We show that if a f.g. group $G$ has a non-elementary WPD action on a hyperbolic metric space $X$, then the number of $G$-conjugacy classes of $X$-loxodromic elements of $G$ coming from a ball of radius $R$ in the Cayley graph of $G$ grows exponentially in $R$. As an application we prove that for $N\\ge 3$ the number of distinct $Out(F_N)$-conjugacy classes of fully irreducibles $\\phi$ from an $R$-ball in the Cayley graph of $Out(F_N)$ with $\\log\\lambda(\\phi)$ on the order of $R$ grows exponentially in $R$."},"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":"1707.07095","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-07-22T03:10:34Z","cross_cats_sorted":["math.DS","math.GT"],"title_canon_sha256":"0b06a9d6fb7ffc2ae519f0e8dd2124f555cb94898e9cc00a026ba7b4d1717eb1","abstract_canon_sha256":"8e65569e6e04e24bbe3989f6d91fde0408467b642cf30084c9c5c9ac86d0ac1e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:45.377682Z","signature_b64":"rmXUuWM4zAxpdOwCiQLOjCqNqrgkitEECFCP2UXm29QSQQjsrfEzlr5Y9uTNHbi1AxPB29MYOOSABqiPUX3tAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f2cd242508e17bd3d3310da89c97db7c69a24371d9e8d2fd75814166dbd6fcd","last_reissued_at":"2026-05-18T00:39:45.377007Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:45.377007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Counting Conjugacy Classes in $Out(F_N)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GT"],"primary_cat":"math.GR","authors_text":"Ilya Kapovich, Michael Hull","submitted_at":"2017-07-22T03:10:34Z","abstract_excerpt":"We show that if a f.g. group $G$ has a non-elementary WPD action on a hyperbolic metric space $X$, then the number of $G$-conjugacy classes of $X$-loxodromic elements of $G$ coming from a ball of radius $R$ in the Cayley graph of $G$ grows exponentially in $R$. As an application we prove that for $N\\ge 3$ the number of distinct $Out(F_N)$-conjugacy classes of fully irreducibles $\\phi$ from an $R$-ball in the Cayley graph of $Out(F_N)$ with $\\log\\lambda(\\phi)$ on the order of $R$ grows exponentially in $R$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07095","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":"1707.07095","created_at":"2026-05-18T00:39:45.377105+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.07095v1","created_at":"2026-05-18T00:39:45.377105+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.07095","created_at":"2026-05-18T00:39:45.377105+00:00"},{"alias_kind":"pith_short_12","alias_value":"B4WNEQSQRYL3","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_16","alias_value":"B4WNEQSQRYL32PJT","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_8","alias_value":"B4WNEQSQ","created_at":"2026-05-18T12:31:08.081275+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/B4WNEQSQRYL32PJTCDNITSL5W7","json":"https://pith.science/pith/B4WNEQSQRYL32PJTCDNITSL5W7.json","graph_json":"https://pith.science/api/pith-number/B4WNEQSQRYL32PJTCDNITSL5W7/graph.json","events_json":"https://pith.science/api/pith-number/B4WNEQSQRYL32PJTCDNITSL5W7/events.json","paper":"https://pith.science/paper/B4WNEQSQ"},"agent_actions":{"view_html":"https://pith.science/pith/B4WNEQSQRYL32PJTCDNITSL5W7","download_json":"https://pith.science/pith/B4WNEQSQRYL32PJTCDNITSL5W7.json","view_paper":"https://pith.science/paper/B4WNEQSQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.07095&json=true","fetch_graph":"https://pith.science/api/pith-number/B4WNEQSQRYL32PJTCDNITSL5W7/graph.json","fetch_events":"https://pith.science/api/pith-number/B4WNEQSQRYL32PJTCDNITSL5W7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B4WNEQSQRYL32PJTCDNITSL5W7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B4WNEQSQRYL32PJTCDNITSL5W7/action/storage_attestation","attest_author":"https://pith.science/pith/B4WNEQSQRYL32PJTCDNITSL5W7/action/author_attestation","sign_citation":"https://pith.science/pith/B4WNEQSQRYL32PJTCDNITSL5W7/action/citation_signature","submit_replication":"https://pith.science/pith/B4WNEQSQRYL32PJTCDNITSL5W7/action/replication_record"}},"created_at":"2026-05-18T00:39:45.377105+00:00","updated_at":"2026-05-18T00:39:45.377105+00:00"}