{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:MEB5OHW3LBJ5WWC7P4MSX4U456","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":"2ade3658964285cd9c0a54458fd0583359485023d3e616085a50ac159fd374b9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-09-14T14:23:10Z","title_canon_sha256":"b65780dcdf658681e679698a83e36b353cfa77d914ea748f36a046872f4a7b43"},"schema_version":"1.0","source":{"id":"1609.04288","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.04288","created_at":"2026-05-18T01:04:38Z"},{"alias_kind":"arxiv_version","alias_value":"1609.04288v1","created_at":"2026-05-18T01:04:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.04288","created_at":"2026-05-18T01:04:38Z"},{"alias_kind":"pith_short_12","alias_value":"MEB5OHW3LBJ5","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MEB5OHW3LBJ5WWC7","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MEB5OHW3","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:75d307d95f148aa0359f5628b8539b22e2dcd0fc78bb4212b72849578ee4841a","target":"graph","created_at":"2026-05-18T01:04:38Z","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 construct $2$-generator non-Hopfian groups $G_m, m=3, 4, 5, \\dots$, where each $G_m$ has a specific presentation $G_m=\\langle a, b \\, | \\, u_{r_{m,0}}=u_{r_{m,1}}=u_{r_{m,2}}= \\cdots =1 \\rangle$ which satisfies small cancellation conditions $C(4)$ and $T(4)$. Here, $u_{r_{m,i}}$ is the single relator of the upper presentation of the $2$-bridge link group of slope $r_{m,i}$, where $r_{m,0}=[m+1,m,m]$ and $r_{m,i}=[m+1,m-1,(i-1)\\langle m \\rangle,m+1,m]$ in continued fraction expansion for every integer $i \\ge 1$.","authors_text":"Donghi Lee, Makoto Sakuma","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-09-14T14:23:10Z","title":"A family of two generator non-Hopfian groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04288","kind":"arxiv","version":1},"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":"sha256:187dd94d87264a706f2b1d8ae530a2de692f4858eeb0f4211ef9a435450e7bff","target":"record","created_at":"2026-05-18T01:04:38Z","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":"2ade3658964285cd9c0a54458fd0583359485023d3e616085a50ac159fd374b9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-09-14T14:23:10Z","title_canon_sha256":"b65780dcdf658681e679698a83e36b353cfa77d914ea748f36a046872f4a7b43"},"schema_version":"1.0","source":{"id":"1609.04288","kind":"arxiv","version":1}},"canonical_sha256":"6103d71edb5853db585f7f192bf29cefae86dfe6737a266422ae39fdf024e006","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6103d71edb5853db585f7f192bf29cefae86dfe6737a266422ae39fdf024e006","first_computed_at":"2026-05-18T01:04:38.374149Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:38.374149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3ZXv9N3e7AW8UFxxb5kXU1BN80bKCsagRJREvDP7d07Qm2LftGRPudmj6mcdS7fkkE6D2Ul/4MDeaDdm35xvCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:38.374865Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.04288","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:187dd94d87264a706f2b1d8ae530a2de692f4858eeb0f4211ef9a435450e7bff","sha256:75d307d95f148aa0359f5628b8539b22e2dcd0fc78bb4212b72849578ee4841a"],"state_sha256":"c0e8cb71c8d7d50f56cd270688e09b0af6ec29230c8d65248bb141e36e462ff6"}