{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:4SSOSVZZQ3G7FJ7WJFZMTV6IPB","short_pith_number":"pith:4SSOSVZZ","schema_version":"1.0","canonical_sha256":"e4a4e9573986cdf2a7f64972c9d7c878744a4e2c646de73d342ad5278ad7d8d8","source":{"kind":"arxiv","id":"1409.6983","version":3},"attestation_state":"computed","paper":{"title":"Pseudo-Anosov stretch factors and homology of mapping tori","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Christopher J. Leininger, Dan Margalit, Ian Agol","submitted_at":"2014-09-24T14:58:45Z","abstract_excerpt":"We consider the pseudo-Anosov elements of the mapping class group of a surface of genus g that fix a rank k subgroup of the first homology of the surface. We show that the smallest entropy among these is comparable to (k+1)/g. This interpolates between results of Penner and of Farb and the second and third authors, who treated the cases of k=0 and k=2g, respectively, and answers a question of Ellenberg. We also show that the number of conjugacy classes of pseudo-Anosov mapping classes as above grows (as a function of g) like a polynomial of degree k."},"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":"1409.6983","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-09-24T14:58:45Z","cross_cats_sorted":[],"title_canon_sha256":"111cd8ff1fbebb568985ecbc9659ba1ecacdc9775b4a2daff9f1fb08952df81b","abstract_canon_sha256":"06e42f69dffa0d2982b20f1f987803e72ef9b509cb4270346f96a953472fadec"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:28.768578Z","signature_b64":"NX/+BZ3UfV6+eg2tiDYnuAucXKzxaBhzNnYLMepU0a3Jzm8tcR66NsujIOesRnrO+GdNh0eJzfRGM9DP+hj3Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4a4e9573986cdf2a7f64972c9d7c878744a4e2c646de73d342ad5278ad7d8d8","last_reissued_at":"2026-05-18T00:44:28.767954Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:28.767954Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pseudo-Anosov stretch factors and homology of mapping tori","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Christopher J. Leininger, Dan Margalit, Ian Agol","submitted_at":"2014-09-24T14:58:45Z","abstract_excerpt":"We consider the pseudo-Anosov elements of the mapping class group of a surface of genus g that fix a rank k subgroup of the first homology of the surface. We show that the smallest entropy among these is comparable to (k+1)/g. This interpolates between results of Penner and of Farb and the second and third authors, who treated the cases of k=0 and k=2g, respectively, and answers a question of Ellenberg. We also show that the number of conjugacy classes of pseudo-Anosov mapping classes as above grows (as a function of g) like a polynomial of degree k."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.6983","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":"1409.6983","created_at":"2026-05-18T00:44:28.768046+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.6983v3","created_at":"2026-05-18T00:44:28.768046+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.6983","created_at":"2026-05-18T00:44:28.768046+00:00"},{"alias_kind":"pith_short_12","alias_value":"4SSOSVZZQ3G7","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_16","alias_value":"4SSOSVZZQ3G7FJ7W","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_8","alias_value":"4SSOSVZZ","created_at":"2026-05-18T12:28:14.216126+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/4SSOSVZZQ3G7FJ7WJFZMTV6IPB","json":"https://pith.science/pith/4SSOSVZZQ3G7FJ7WJFZMTV6IPB.json","graph_json":"https://pith.science/api/pith-number/4SSOSVZZQ3G7FJ7WJFZMTV6IPB/graph.json","events_json":"https://pith.science/api/pith-number/4SSOSVZZQ3G7FJ7WJFZMTV6IPB/events.json","paper":"https://pith.science/paper/4SSOSVZZ"},"agent_actions":{"view_html":"https://pith.science/pith/4SSOSVZZQ3G7FJ7WJFZMTV6IPB","download_json":"https://pith.science/pith/4SSOSVZZQ3G7FJ7WJFZMTV6IPB.json","view_paper":"https://pith.science/paper/4SSOSVZZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.6983&json=true","fetch_graph":"https://pith.science/api/pith-number/4SSOSVZZQ3G7FJ7WJFZMTV6IPB/graph.json","fetch_events":"https://pith.science/api/pith-number/4SSOSVZZQ3G7FJ7WJFZMTV6IPB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4SSOSVZZQ3G7FJ7WJFZMTV6IPB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4SSOSVZZQ3G7FJ7WJFZMTV6IPB/action/storage_attestation","attest_author":"https://pith.science/pith/4SSOSVZZQ3G7FJ7WJFZMTV6IPB/action/author_attestation","sign_citation":"https://pith.science/pith/4SSOSVZZQ3G7FJ7WJFZMTV6IPB/action/citation_signature","submit_replication":"https://pith.science/pith/4SSOSVZZQ3G7FJ7WJFZMTV6IPB/action/replication_record"}},"created_at":"2026-05-18T00:44:28.768046+00:00","updated_at":"2026-05-18T00:44:28.768046+00:00"}