{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:XOHLXLU5IOE3MTDZOF76QZ2ORA","short_pith_number":"pith:XOHLXLU5","schema_version":"1.0","canonical_sha256":"bb8ebbae9d4389b64c79717fe8674e882afbe6f3347c393cfd552914ad3d5ca8","source":{"kind":"arxiv","id":"1609.06811","version":2},"attestation_state":"computed","paper":{"title":"A lower bound of the distortion of the Torelli group in the mapping class group with boundary components","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Erika Kuno, Genki Omori","submitted_at":"2016-09-22T04:09:57Z","abstract_excerpt":"We prove that each Torelli group of an orientable surface with any number of boundary components is at least exponentially distorted in the mapping class group by using Broaddus-Farb-Putman's techniques. Further we show that the distortion of each Torelli group in the level $d$ mapping class group is the same as that of in the mapping class group."},"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":"1609.06811","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-09-22T04:09:57Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"91a5a338eee2420a72eed7c583a0719f369dc482f554169e0f51f340fe6cc03f","abstract_canon_sha256":"2d2740dc5a76b8755eb3c8949dedc76980a92db4b2ba82ae3823d425b08eb606"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:22.764361Z","signature_b64":"30vzI2utHT9vAkohkdBXDRNA085NIlUV7rau6FNq4nV4AqydxsFCTFprd1l5eAmQiW10DSbXv5NwBLufpdw7Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bb8ebbae9d4389b64c79717fe8674e882afbe6f3347c393cfd552914ad3d5ca8","last_reissued_at":"2026-05-18T00:52:22.763650Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:22.763650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A lower bound of the distortion of the Torelli group in the mapping class group with boundary components","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Erika Kuno, Genki Omori","submitted_at":"2016-09-22T04:09:57Z","abstract_excerpt":"We prove that each Torelli group of an orientable surface with any number of boundary components is at least exponentially distorted in the mapping class group by using Broaddus-Farb-Putman's techniques. Further we show that the distortion of each Torelli group in the level $d$ mapping class group is the same as that of in the mapping class group."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06811","kind":"arxiv","version":2},"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":"1609.06811","created_at":"2026-05-18T00:52:22.763763+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.06811v2","created_at":"2026-05-18T00:52:22.763763+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.06811","created_at":"2026-05-18T00:52:22.763763+00:00"},{"alias_kind":"pith_short_12","alias_value":"XOHLXLU5IOE3","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_16","alias_value":"XOHLXLU5IOE3MTDZ","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_8","alias_value":"XOHLXLU5","created_at":"2026-05-18T12:30:51.357362+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/XOHLXLU5IOE3MTDZOF76QZ2ORA","json":"https://pith.science/pith/XOHLXLU5IOE3MTDZOF76QZ2ORA.json","graph_json":"https://pith.science/api/pith-number/XOHLXLU5IOE3MTDZOF76QZ2ORA/graph.json","events_json":"https://pith.science/api/pith-number/XOHLXLU5IOE3MTDZOF76QZ2ORA/events.json","paper":"https://pith.science/paper/XOHLXLU5"},"agent_actions":{"view_html":"https://pith.science/pith/XOHLXLU5IOE3MTDZOF76QZ2ORA","download_json":"https://pith.science/pith/XOHLXLU5IOE3MTDZOF76QZ2ORA.json","view_paper":"https://pith.science/paper/XOHLXLU5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.06811&json=true","fetch_graph":"https://pith.science/api/pith-number/XOHLXLU5IOE3MTDZOF76QZ2ORA/graph.json","fetch_events":"https://pith.science/api/pith-number/XOHLXLU5IOE3MTDZOF76QZ2ORA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XOHLXLU5IOE3MTDZOF76QZ2ORA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XOHLXLU5IOE3MTDZOF76QZ2ORA/action/storage_attestation","attest_author":"https://pith.science/pith/XOHLXLU5IOE3MTDZOF76QZ2ORA/action/author_attestation","sign_citation":"https://pith.science/pith/XOHLXLU5IOE3MTDZOF76QZ2ORA/action/citation_signature","submit_replication":"https://pith.science/pith/XOHLXLU5IOE3MTDZOF76QZ2ORA/action/replication_record"}},"created_at":"2026-05-18T00:52:22.763763+00:00","updated_at":"2026-05-18T00:52:22.763763+00:00"}