{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:C5QDZPTCMRW2N7Y6ZV26JDN6YR","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":"0bf1840e7d6556b1adc90911b1dc8eaa1fc5016dc2d1b630be7240324d3de156","cross_cats_sorted":["math.DS","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-09-21T12:49:03Z","title_canon_sha256":"53f2500825edbbce9f2d22a8fc9064bda047ca250402eabefad2fde0d429dee9"},"schema_version":"1.0","source":{"id":"1709.07287","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.07287","created_at":"2026-05-18T00:07:23Z"},{"alias_kind":"arxiv_version","alias_value":"1709.07287v2","created_at":"2026-05-18T00:07:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.07287","created_at":"2026-05-18T00:07:23Z"},{"alias_kind":"pith_short_12","alias_value":"C5QDZPTCMRW2","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"C5QDZPTCMRW2N7Y6","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"C5QDZPTC","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:41355d1e010cfec1d42623bd70328cd4cff389475985c3f562dbcad0b27d9f35","target":"graph","created_at":"2026-05-18T00:07:23Z","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 prove a general version of the amenability conjecture in the unified setting of a Gromov hyperbolic group G acting properly cocompactly either on its Cayley graph, or on a CAT(-1)-space. Namely, for any subgroup H of G, we show that H is co-amenable in G if and only if their exponential growth rates (with respect to the prescribed action) coincide. For this, we prove a quantified, representation-theoretical version of Stadlbauer's amenability criterion for group extensions of a topologically transitive subshift of finite type, in terms of the spectral radii of the classical Ruelle transfer ","authors_text":"Andrea Sambusetti, Fran\\c{c}oise Dal'Bo (IRMAR), R\\'emi Coulon (IRMAR)","cross_cats":["math.DS","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-09-21T12:49:03Z","title":"Growth gap in hyperbolic groups and amenability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.07287","kind":"arxiv","version":2},"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":"sha256:4317c2ddad9c50c84696e4c051b0b1e859dd7d992f7e1a9a56c40559f5f0e141","target":"record","created_at":"2026-05-18T00:07:23Z","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":"0bf1840e7d6556b1adc90911b1dc8eaa1fc5016dc2d1b630be7240324d3de156","cross_cats_sorted":["math.DS","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-09-21T12:49:03Z","title_canon_sha256":"53f2500825edbbce9f2d22a8fc9064bda047ca250402eabefad2fde0d429dee9"},"schema_version":"1.0","source":{"id":"1709.07287","kind":"arxiv","version":2}},"canonical_sha256":"17603cbe62646da6ff1ecd75e48dbec47a44ae4660e74cca2c0a68cf93f278cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"17603cbe62646da6ff1ecd75e48dbec47a44ae4660e74cca2c0a68cf93f278cb","first_computed_at":"2026-05-18T00:07:23.776463Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:23.776463Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"00c6d080Xhie+SCGxE2oNXKBREs+wrG35G+STineCKnvuFvybXJeEYCYK856y71QDEcgevwS335mQix7arD6Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:23.776921Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.07287","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4317c2ddad9c50c84696e4c051b0b1e859dd7d992f7e1a9a56c40559f5f0e141","sha256:41355d1e010cfec1d42623bd70328cd4cff389475985c3f562dbcad0b27d9f35"],"state_sha256":"d32282157dc90d8a361266605ff8f16978ace982f02a1292466e2a6b20a56dd0"}