{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:K53FPTPWGVLGAIUBTQN2VBXEBA","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":"c4877c24e9d716f238ac9098a553f13e9067bc480e3531f1950a8665f25845d9","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-05-24T15:23:01Z","title_canon_sha256":"97cbf65ebdad44393082d639e38663cebcebbca1885357f7f50fc45d732f1ee7"},"schema_version":"1.0","source":{"id":"1405.6310","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.6310","created_at":"2026-05-18T00:29:06Z"},{"alias_kind":"arxiv_version","alias_value":"1405.6310v3","created_at":"2026-05-18T00:29:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6310","created_at":"2026-05-18T00:29:06Z"},{"alias_kind":"pith_short_12","alias_value":"K53FPTPWGVLG","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"K53FPTPWGVLGAIUB","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"K53FPTPW","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:f887bb308a4c25f9ffadde916d4525f941911389402bccf16d1131e73317ade9","target":"graph","created_at":"2026-05-18T00:29:06Z","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":"It is proved that an endomorphism $\\varphi$ of a hyperbolic group $G$ satisfies a H\\\"older condition with respect to a visual metric if and only if $\\varphi$ is virtually injective and $G\\varphi$ is a quasiconvex subgroup of $G$. If $G$ is virtually free or torsion-free co-hopfian, then $\\varphi$ is uniformly continuous if and only if it it satisfies a H\\\"older condition if and only if it is virtually injective. Lipschitz conditions are discussed for free group automorphisms.","authors_text":"Pedro V. Silva, V\\'itor Ara\\'ujo","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-05-24T15:23:01Z","title":"H\\\"older conditions for endomorphisms of hyperbolic groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6310","kind":"arxiv","version":3},"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":"sha256:4e5d9807049cbb2b4e083172cbb64553011c30aea83e3cccefa329bd16e412d7","target":"record","created_at":"2026-05-18T00:29:06Z","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":"c4877c24e9d716f238ac9098a553f13e9067bc480e3531f1950a8665f25845d9","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-05-24T15:23:01Z","title_canon_sha256":"97cbf65ebdad44393082d639e38663cebcebbca1885357f7f50fc45d732f1ee7"},"schema_version":"1.0","source":{"id":"1405.6310","kind":"arxiv","version":3}},"canonical_sha256":"577657cdf635566022819c1baa86e4082ea41aa6acad5ca023baf75e3a1b4823","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"577657cdf635566022819c1baa86e4082ea41aa6acad5ca023baf75e3a1b4823","first_computed_at":"2026-05-18T00:29:06.066347Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:06.066347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2WIshN/SEzDfH6jThYUFzFupo0MCEVNkJBEJfo1mKVpoU9+CTY6SHcxQL+VgVLBxDQPztcRAbn2blKBSuMCABA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:06.066779Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.6310","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e5d9807049cbb2b4e083172cbb64553011c30aea83e3cccefa329bd16e412d7","sha256:f887bb308a4c25f9ffadde916d4525f941911389402bccf16d1131e73317ade9"],"state_sha256":"6ba34f4239609219809d2988b093b57e7050097e1523a4121f8a418497511fad"}