{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:DKTXH526WTGFERJMQCMRRKFMAD","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":"85cb482304cb0c9e5bf868b5ea006e71674b7c52048c4cd25fe119fef1805d5e","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-12-20T21:19:30Z","title_canon_sha256":"5edf485c0daed3904c0c063f97e409fcb82625111ef1ae25fc080f9981899415"},"schema_version":"1.0","source":{"id":"1312.6141","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.6141","created_at":"2026-05-18T02:47:40Z"},{"alias_kind":"arxiv_version","alias_value":"1312.6141v2","created_at":"2026-05-18T02:47:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.6141","created_at":"2026-05-18T02:47:40Z"},{"alias_kind":"pith_short_12","alias_value":"DKTXH526WTGF","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DKTXH526WTGFERJM","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DKTXH526","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:b48c3837f8f70498e4e2a154a336222ba49536faa0baba70c73ad96dff38dbc7","target":"graph","created_at":"2026-05-18T02:47:40Z","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":"In this article, we propose two algorithms for determining the Nielsen-Thurston classification of a mapping class $\\psi$ on a surface $S$. We start with a finite generating set $X$ for the mapping class group and a word $\\psi$ in $\\langle X \\rangle$. We show that if $\\psi$ represents a reducible mapping class in $\\Mod(S)$ then $\\psi$ admits a canonical reduction system whose total length is exponential in the word length of $\\psi$. We use this fact to find the canonical reduction system of $\\psi$. We also prove an effective conjugacy separability result for $\\pi_1(S)$ which allows us to lift t","authors_text":"Johanna Mangahas, Thomas Koberda","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-12-20T21:19:30Z","title":"An effective algebraic detection of the Nielsen--Thurston classification of mapping classes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6141","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":"sha256:5c9f9a0039ccc074b123713ee44c5144d8ed7efa44914e5fac28d8569b4925de","target":"record","created_at":"2026-05-18T02:47:40Z","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":"85cb482304cb0c9e5bf868b5ea006e71674b7c52048c4cd25fe119fef1805d5e","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-12-20T21:19:30Z","title_canon_sha256":"5edf485c0daed3904c0c063f97e409fcb82625111ef1ae25fc080f9981899415"},"schema_version":"1.0","source":{"id":"1312.6141","kind":"arxiv","version":2}},"canonical_sha256":"1aa773f75eb4cc52452c809918a8ac00d70ae9e8e22851c48b6fe9f4bf8c03f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1aa773f75eb4cc52452c809918a8ac00d70ae9e8e22851c48b6fe9f4bf8c03f4","first_computed_at":"2026-05-18T02:47:40.732233Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:40.732233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GvqFnoQ9/sBFaLRQ3qEUp0IRKg7mu0G6CmzTqkEfOrxZHRs25VCEREUekL0lc3VUfx9r0LxUori0Dg8ZDNDsAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:40.732985Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.6141","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c9f9a0039ccc074b123713ee44c5144d8ed7efa44914e5fac28d8569b4925de","sha256:b48c3837f8f70498e4e2a154a336222ba49536faa0baba70c73ad96dff38dbc7"],"state_sha256":"d7b4ae65a734fbec988ae96bc2e28aff657d8515f8adad9f4fa1e9474a3bfa4a"}