{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:FQUU3HN6Z7GOQNGR3SH6OU3ZO2","short_pith_number":"pith:FQUU3HN6","canonical_record":{"source":{"id":"1704.03491","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-04-11T18:44:46Z","cross_cats_sorted":[],"title_canon_sha256":"a8942b1477c3e60390178116c1e954fe378697d86f77386676ebc4c83c24c376","abstract_canon_sha256":"d60593649a051b310627ce9fd73d3fb2dd5d7facf0516f6680f1bd9bef5458e8"},"schema_version":"1.0"},"canonical_sha256":"2c294d9dbecfcce834d1dc8fe7537976a7537a140862842a94ed9920445d6cf4","source":{"kind":"arxiv","id":"1704.03491","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:FQUU3HN6Z7GOQNGR3SH6OU3ZO2","target":"record","payload":{"canonical_record":{"source":{"id":"1704.03491","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-04-11T18:44:46Z","cross_cats_sorted":[],"title_canon_sha256":"a8942b1477c3e60390178116c1e954fe378697d86f77386676ebc4c83c24c376","abstract_canon_sha256":"d60593649a051b310627ce9fd73d3fb2dd5d7facf0516f6680f1bd9bef5458e8"},"schema_version":"1.0"},"canonical_sha256":"2c294d9dbecfcce834d1dc8fe7537976a7537a140862842a94ed9920445d6cf4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:28.702683Z","signature_b64":"gg2+BqqIW+OLz7C00p+p63A/KGcH2BM2hs50YzHTiy4bdkQrnzZaMipGAUI9WLOHuhE7IM6n8ks4NIhTuFfZCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c294d9dbecfcce834d1dc8fe7537976a7537a140862842a94ed9920445d6cf4","last_reissued_at":"2026-05-18T00:46:28.701887Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:28.701887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.03491","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:46:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HdWj/MKZP/AqZjgxTT4b46sZBLALQ7R/ESXGnX7dPYSPMmHmXbtDTbJLs67wlp6jhP0SSuWfb4ubYb9WxyIRDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T12:14:31.354642Z"},"content_sha256":"e35d6136fea547b4a26d56fee835f3e23244eabbe3084ed29c7d51e9251059ff","schema_version":"1.0","event_id":"sha256:e35d6136fea547b4a26d56fee835f3e23244eabbe3084ed29c7d51e9251059ff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:FQUU3HN6Z7GOQNGR3SH6OU3ZO2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Homomorphisms to acylindrically hyperbolic groups I: Equationally noetherian groups and families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Daniel Groves, Michael Hull","submitted_at":"2017-04-11T18:44:46Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03491","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:46:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ND+4z3H/PEuT4gS8yBk9qroT8CA6x8W2uO0KShAg7xegCIokPHEUXwmSO7xOevt3x7nGB1XwB9ModFLIBn5CCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T12:14:31.355381Z"},"content_sha256":"7c56430968e1fe6ca19f071e8cf4b796c8c5cdea4bc2292d318bbd36b57ae8ff","schema_version":"1.0","event_id":"sha256:7c56430968e1fe6ca19f071e8cf4b796c8c5cdea4bc2292d318bbd36b57ae8ff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FQUU3HN6Z7GOQNGR3SH6OU3ZO2/bundle.json","state_url":"https://pith.science/pith/FQUU3HN6Z7GOQNGR3SH6OU3ZO2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FQUU3HN6Z7GOQNGR3SH6OU3ZO2/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-23T12:14:31Z","links":{"resolver":"https://pith.science/pith/FQUU3HN6Z7GOQNGR3SH6OU3ZO2","bundle":"https://pith.science/pith/FQUU3HN6Z7GOQNGR3SH6OU3ZO2/bundle.json","state":"https://pith.science/pith/FQUU3HN6Z7GOQNGR3SH6OU3ZO2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FQUU3HN6Z7GOQNGR3SH6OU3ZO2/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E3mwP4Amx7T3JrrR4CiR+mVB97hpJ17kdy3hTDldU6px7VVYYrH8B+28x+Tqa6f337VKhhIWe+2CjaEvMKsTCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T12:14:31.359177Z","bundle_sha256":"e0f06924258a32195af4b807c3fa94cc87499bfce6f947f56e06af9fe45f6126"}}