{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:OIY5GXZ7N6U772ZLNNZ53G4QB7","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":"4612b30477e5d0b402f564ab963809bb186ba272f6cb025551952a9a40120ca7","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-06-02T13:04:53Z","title_canon_sha256":"4cf4123f1d6cc1b69eecf1660768049407a9879316cc37b704dc2aa1d65ea742"},"schema_version":"1.0","source":{"id":"1106.0422","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.0422","created_at":"2026-05-18T04:20:49Z"},{"alias_kind":"arxiv_version","alias_value":"1106.0422v2","created_at":"2026-05-18T04:20:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.0422","created_at":"2026-05-18T04:20:49Z"},{"alias_kind":"pith_short_12","alias_value":"OIY5GXZ7N6U7","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"OIY5GXZ7N6U772ZL","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"OIY5GXZ7","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:f759d29f3f85bcc8bf890cd35ac90c81150882ab32b01a908373f72884d29182","target":"graph","created_at":"2026-05-18T04:20:49Z","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 give new upper bounds on the stable commutator lengths of Dehn twists in mapping class groups and new lower bounds on the stable commutator lengths of Dehn twists in hyperelliptic mapping class groups. In particular, we show that the stable commutator lengths of Dehn twists about a nonseparating and a separating curve on an oriented closed surface of genus 2 are not equal to each other.","authors_text":"Naoyuki Monden","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-06-02T13:04:53Z","title":"On upper bounds on stable commutator lengths in mapping class groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0422","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:dc10d873539bef58cb3ca670d9230001421e92a57b3a2ed0b581eab11cc6d438","target":"record","created_at":"2026-05-18T04:20:49Z","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":"4612b30477e5d0b402f564ab963809bb186ba272f6cb025551952a9a40120ca7","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-06-02T13:04:53Z","title_canon_sha256":"4cf4123f1d6cc1b69eecf1660768049407a9879316cc37b704dc2aa1d65ea742"},"schema_version":"1.0","source":{"id":"1106.0422","kind":"arxiv","version":2}},"canonical_sha256":"7231d35f3f6fa9ffeb2b6b73dd9b900ffe932c69bf12855b92c92ed58a104012","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7231d35f3f6fa9ffeb2b6b73dd9b900ffe932c69bf12855b92c92ed58a104012","first_computed_at":"2026-05-18T04:20:49.336434Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:49.336434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DGQ1WG7+DJ1V0RYTgpPI6ZTE6VQR3oo+4knFSYtuzvRtDTDB1JYzKBt1vpbU67oVBQ5BnvAZsg9uNHkWqYIGDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:49.337719Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.0422","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dc10d873539bef58cb3ca670d9230001421e92a57b3a2ed0b581eab11cc6d438","sha256:f759d29f3f85bcc8bf890cd35ac90c81150882ab32b01a908373f72884d29182"],"state_sha256":"3a4d7b8dd98c9743130225935fdf5abd45412e3f0b622697f08386cf474bc688"}