{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:NUYDR6NPL2QCF2YVOS66U2EJ65","short_pith_number":"pith:NUYDR6NP","schema_version":"1.0","canonical_sha256":"6d3038f9af5ea022eb1574bdea6889f75f7be8f73ed7499ad48e5227ed4c7a2b","source":{"kind":"arxiv","id":"2307.08400","version":3},"attestation_state":"computed","paper":{"title":"Uniform exponential growth for groups with proper product actions on hyperbolic spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Renxing Wan, Wenyuan Yang","submitted_at":"2023-07-17T11:33:52Z","abstract_excerpt":"This paper studies the locally uniform exponential growth and product set growth for a finitely generated group $G$ acting properly on a finite product of hyperbolic spaces. Under the assumption of coarsely dense orbits or shadowing property on factors, we prove that any finitely generated non-virtually abelian subgroup has uniform exponential growth. These assumptions are fulfilled in many hierarchically hyperbolic groups, including mapping class groups, specially cubulated groups and BMW groups.\n  Moreover, if $G$ acts weakly acylindrically on each factor, we show that, with two exceptional "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2307.08400","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2023-07-17T11:33:52Z","cross_cats_sorted":[],"title_canon_sha256":"931eff5feac84f015ce628a1103be93317d01c9659e7b36a5539d0ddfb17d42f","abstract_canon_sha256":"a65b421dea81cb2034d005905cf1e1a4a734b78d4c40966dda03cfde7b46a422"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:46:51.137792Z","signature_b64":"yDK6iRtnTFIRXE5sw96UhQ6L3ACQhMnI+NNrhlAR8yU0BfkycHAi2qT82tUcKgekl23qt9XUlwXtssWlhABMDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d3038f9af5ea022eb1574bdea6889f75f7be8f73ed7499ad48e5227ed4c7a2b","last_reissued_at":"2026-07-05T08:46:51.137373Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:46:51.137373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uniform exponential growth for groups with proper product actions on hyperbolic spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Renxing Wan, Wenyuan Yang","submitted_at":"2023-07-17T11:33:52Z","abstract_excerpt":"This paper studies the locally uniform exponential growth and product set growth for a finitely generated group $G$ acting properly on a finite product of hyperbolic spaces. Under the assumption of coarsely dense orbits or shadowing property on factors, we prove that any finitely generated non-virtually abelian subgroup has uniform exponential growth. These assumptions are fulfilled in many hierarchically hyperbolic groups, including mapping class groups, specially cubulated groups and BMW groups.\n  Moreover, if $G$ acts weakly acylindrically on each factor, we show that, with two exceptional "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.08400","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2307.08400/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2307.08400","created_at":"2026-07-05T08:46:51.137427+00:00"},{"alias_kind":"arxiv_version","alias_value":"2307.08400v3","created_at":"2026-07-05T08:46:51.137427+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.08400","created_at":"2026-07-05T08:46:51.137427+00:00"},{"alias_kind":"pith_short_12","alias_value":"NUYDR6NPL2QC","created_at":"2026-07-05T08:46:51.137427+00:00"},{"alias_kind":"pith_short_16","alias_value":"NUYDR6NPL2QCF2YV","created_at":"2026-07-05T08:46:51.137427+00:00"},{"alias_kind":"pith_short_8","alias_value":"NUYDR6NP","created_at":"2026-07-05T08:46:51.137427+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2410.06751","citing_title":"Short positive loxodromics in graph products","ref_index":49,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NUYDR6NPL2QCF2YVOS66U2EJ65","json":"https://pith.science/pith/NUYDR6NPL2QCF2YVOS66U2EJ65.json","graph_json":"https://pith.science/api/pith-number/NUYDR6NPL2QCF2YVOS66U2EJ65/graph.json","events_json":"https://pith.science/api/pith-number/NUYDR6NPL2QCF2YVOS66U2EJ65/events.json","paper":"https://pith.science/paper/NUYDR6NP"},"agent_actions":{"view_html":"https://pith.science/pith/NUYDR6NPL2QCF2YVOS66U2EJ65","download_json":"https://pith.science/pith/NUYDR6NPL2QCF2YVOS66U2EJ65.json","view_paper":"https://pith.science/paper/NUYDR6NP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2307.08400&json=true","fetch_graph":"https://pith.science/api/pith-number/NUYDR6NPL2QCF2YVOS66U2EJ65/graph.json","fetch_events":"https://pith.science/api/pith-number/NUYDR6NPL2QCF2YVOS66U2EJ65/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NUYDR6NPL2QCF2YVOS66U2EJ65/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NUYDR6NPL2QCF2YVOS66U2EJ65/action/storage_attestation","attest_author":"https://pith.science/pith/NUYDR6NPL2QCF2YVOS66U2EJ65/action/author_attestation","sign_citation":"https://pith.science/pith/NUYDR6NPL2QCF2YVOS66U2EJ65/action/citation_signature","submit_replication":"https://pith.science/pith/NUYDR6NPL2QCF2YVOS66U2EJ65/action/replication_record"}},"created_at":"2026-07-05T08:46:51.137427+00:00","updated_at":"2026-07-05T08:46:51.137427+00:00"}