{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:34OKMLS7L5N7XB2L3O3EYVJ2NE","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":"a8fc076bd5e2dfba7b11aa3bc60fa66387baf83ff50303d1fadc6978a3a9b18c","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-11-20T13:21:31Z","title_canon_sha256":"fae8ab627185c8aa021a578139cc90b8a6b0e0958e30c29d0100b287cf4707ab"},"schema_version":"1.0","source":{"id":"0911.3923","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.3923","created_at":"2026-05-18T03:12:35Z"},{"alias_kind":"arxiv_version","alias_value":"0911.3923v6","created_at":"2026-05-18T03:12:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.3923","created_at":"2026-05-18T03:12:35Z"},{"alias_kind":"pith_short_12","alias_value":"34OKMLS7L5N7","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"34OKMLS7L5N7XB2L","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"34OKMLS7","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:bd8a62706fbec40a0545a2b05d9d295c76928d7dbc2ce49b12a50f6a23711825","target":"graph","created_at":"2026-05-18T03:12:35Z","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":"For all but finitely many compact orientable surfaces, we show that any superinjective map from the complex of separating curves into itself is induced by an element of the extended mapping class group. We apply this result to proving that any finite index subgroup of the Johnson kernel is co-Hopfian. Analogous properties are shown for the Torelli complex and the Torelli group.","authors_text":"Yoshikata Kida","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-11-20T13:21:31Z","title":"The co-Hopfian property of the Johnson kernel and the Torelli group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.3923","kind":"arxiv","version":6},"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:ee3c0f15c8930c13ef1274df38d5628574b199b9d8193e0b774928e6cb9393aa","target":"record","created_at":"2026-05-18T03:12:35Z","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":"a8fc076bd5e2dfba7b11aa3bc60fa66387baf83ff50303d1fadc6978a3a9b18c","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-11-20T13:21:31Z","title_canon_sha256":"fae8ab627185c8aa021a578139cc90b8a6b0e0958e30c29d0100b287cf4707ab"},"schema_version":"1.0","source":{"id":"0911.3923","kind":"arxiv","version":6}},"canonical_sha256":"df1ca62e5f5f5bfb874bdbb64c553a6927f83c3c240263543c93382bb38e1e99","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df1ca62e5f5f5bfb874bdbb64c553a6927f83c3c240263543c93382bb38e1e99","first_computed_at":"2026-05-18T03:12:35.480632Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:35.480632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AB4VUbMEUe7vkZUmkmJoV5BivgQxNTprb4TloCsg7E8tNT7QTfWIsVFV0bnKZoGQr7jHrnd3fZCedFZ+fPIcDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:35.481462Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.3923","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee3c0f15c8930c13ef1274df38d5628574b199b9d8193e0b774928e6cb9393aa","sha256:bd8a62706fbec40a0545a2b05d9d295c76928d7dbc2ce49b12a50f6a23711825"],"state_sha256":"c21e5594a4126f06e4e94a30480514bd18859d24d8e3be369130bcb860a7a76c"}