{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XOHLXLU5IOE3MTDZOF76QZ2ORA","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"2d2740dc5a76b8755eb3c8949dedc76980a92db4b2ba82ae3823d425b08eb606","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-09-22T04:09:57Z","title_canon_sha256":"91a5a338eee2420a72eed7c583a0719f369dc482f554169e0f51f340fe6cc03f"},"schema_version":"1.0","source":{"id":"1609.06811","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.06811","created_at":"2026-05-18T00:52:22Z"},{"alias_kind":"arxiv_version","alias_value":"1609.06811v2","created_at":"2026-05-18T00:52:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.06811","created_at":"2026-05-18T00:52:22Z"},{"alias_kind":"pith_short_12","alias_value":"XOHLXLU5IOE3","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XOHLXLU5IOE3MTDZ","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XOHLXLU5","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:29f076cf722d31685c8180e439db318f426cf88462695c13268787659ecb573c","target":"graph","created_at":"2026-05-18T00:52:22Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"Erika Kuno, Genki Omori","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-09-22T04:09:57Z","title":"A lower bound of the distortion of the Torelli group in the mapping class group with boundary components"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06811","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:0452447f7d9510788c3c46b1489d6e5c7f2b1e58ba3be90e007f45eb6091221e","target":"record","created_at":"2026-05-18T00:52:22Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"2d2740dc5a76b8755eb3c8949dedc76980a92db4b2ba82ae3823d425b08eb606","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-09-22T04:09:57Z","title_canon_sha256":"91a5a338eee2420a72eed7c583a0719f369dc482f554169e0f51f340fe6cc03f"},"schema_version":"1.0","source":{"id":"1609.06811","kind":"arxiv","version":2}},"canonical_sha256":"bb8ebbae9d4389b64c79717fe8674e882afbe6f3347c393cfd552914ad3d5ca8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bb8ebbae9d4389b64c79717fe8674e882afbe6f3347c393cfd552914ad3d5ca8","first_computed_at":"2026-05-18T00:52:22.763650Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:22.763650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"30vzI2utHT9vAkohkdBXDRNA085NIlUV7rau6FNq4nV4AqydxsFCTFprd1l5eAmQiW10DSbXv5NwBLufpdw7Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:22.764361Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.06811","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0452447f7d9510788c3c46b1489d6e5c7f2b1e58ba3be90e007f45eb6091221e","sha256:29f076cf722d31685c8180e439db318f426cf88462695c13268787659ecb573c"],"state_sha256":"2923fa2534618e65dd6eac4d7e738ae1d30da318ebcc666a4e81bee985bb6969"}