{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FQUU3HN6Z7GOQNGR3SH6OU3ZO2","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":"d60593649a051b310627ce9fd73d3fb2dd5d7facf0516f6680f1bd9bef5458e8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-04-11T18:44:46Z","title_canon_sha256":"a8942b1477c3e60390178116c1e954fe378697d86f77386676ebc4c83c24c376"},"schema_version":"1.0","source":{"id":"1704.03491","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.03491","created_at":"2026-05-18T00:46:28Z"},{"alias_kind":"arxiv_version","alias_value":"1704.03491v1","created_at":"2026-05-18T00:46:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.03491","created_at":"2026-05-18T00:46:28Z"},{"alias_kind":"pith_short_12","alias_value":"FQUU3HN6Z7GO","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FQUU3HN6Z7GOQNGR","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FQUU3HN6","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:7c56430968e1fe6ca19f071e8cf4b796c8c5cdea4bc2292d318bbd36b57ae8ff","target":"graph","created_at":"2026-05-18T00:46:28Z","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 study the set of homomorphisms from a fixed finitely generated group into a family of groups which are `uniformly acylindrically hyperbolic'. Our main results reduce this study to sets of homomorphisms which do not diverge in an appropriate sense. As an application, we prove that any relatively hyperbolic group with equationally noetherian peripheral subgroups is itself equationally noetherian.","authors_text":"Daniel Groves, Michael Hull","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-04-11T18:44:46Z","title":"Homomorphisms to acylindrically hyperbolic groups I: Equationally noetherian groups and families"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03491","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:e35d6136fea547b4a26d56fee835f3e23244eabbe3084ed29c7d51e9251059ff","target":"record","created_at":"2026-05-18T00:46:28Z","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":"d60593649a051b310627ce9fd73d3fb2dd5d7facf0516f6680f1bd9bef5458e8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-04-11T18:44:46Z","title_canon_sha256":"a8942b1477c3e60390178116c1e954fe378697d86f77386676ebc4c83c24c376"},"schema_version":"1.0","source":{"id":"1704.03491","kind":"arxiv","version":1}},"canonical_sha256":"2c294d9dbecfcce834d1dc8fe7537976a7537a140862842a94ed9920445d6cf4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c294d9dbecfcce834d1dc8fe7537976a7537a140862842a94ed9920445d6cf4","first_computed_at":"2026-05-18T00:46:28.701887Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:28.701887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gg2+BqqIW+OLz7C00p+p63A/KGcH2BM2hs50YzHTiy4bdkQrnzZaMipGAUI9WLOHuhE7IM6n8ks4NIhTuFfZCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:28.702683Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.03491","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e35d6136fea547b4a26d56fee835f3e23244eabbe3084ed29c7d51e9251059ff","sha256:7c56430968e1fe6ca19f071e8cf4b796c8c5cdea4bc2292d318bbd36b57ae8ff"],"state_sha256":"88abf0c45fffb6d89a9d7c5c74a61b246afe935839b75b52d7868e8c6f738d61"}