{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:O45MPKLK2WNUJF2Z5AJ5VR35AW","short_pith_number":"pith:O45MPKLK","schema_version":"1.0","canonical_sha256":"773ac7a96ad59b449759e813dac77d05b0f4441e989660eaebd130f358f695da","source":{"kind":"arxiv","id":"1401.0499","version":4},"attestation_state":"computed","paper":{"title":"Growth Tight Actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Christopher H. Cashen, Goulnara N. Arzhantseva, Jing Tao","submitted_at":"2014-01-02T18:29:45Z","abstract_excerpt":"We introduce and systematically study the concept of a growth tight action. This generalizes growth tightness for word metrics as initiated by Grigorchuk and de la Harpe. Given a finitely generated, non-elementary group $G$ acting on a $G$--space $\\mathcal{X}$, we prove that if $G$ contains a strongly contracting element and if $G$ is not too badly distorted in $\\mathcal{X}$, then the action of $G$ on $\\mathcal{X}$ is a growth tight action. It follows that if $\\mathcal{X}$ is a cocompact, relatively hyperbolic $G$--space, then the action of $G$ on $\\mathcal{X}$ is a growth tight action. This g"},"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":"1401.0499","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-01-02T18:29:45Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"8e28f90159fb563a4e8b662d8132d1940d2cd819ddb4d4e5eccd7d49c6f82993","abstract_canon_sha256":"c2d36d4078392762dae8f4ac533044fd7509bfabebc184261d28b1073d9bd6f9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:24.538904Z","signature_b64":"/AelFs/zMNfPTMKJjN6n3Oeu48xzzMta+qR1X3R0UQDMBVo0DYpvQIqCrzkictvOavuk+SPtB69xpSACz1+HAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"773ac7a96ad59b449759e813dac77d05b0f4441e989660eaebd130f358f695da","last_reissued_at":"2026-05-18T01:22:24.538311Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:24.538311Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Growth Tight Actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Christopher H. Cashen, Goulnara N. Arzhantseva, Jing Tao","submitted_at":"2014-01-02T18:29:45Z","abstract_excerpt":"We introduce and systematically study the concept of a growth tight action. This generalizes growth tightness for word metrics as initiated by Grigorchuk and de la Harpe. Given a finitely generated, non-elementary group $G$ acting on a $G$--space $\\mathcal{X}$, we prove that if $G$ contains a strongly contracting element and if $G$ is not too badly distorted in $\\mathcal{X}$, then the action of $G$ on $\\mathcal{X}$ is a growth tight action. It follows that if $\\mathcal{X}$ is a cocompact, relatively hyperbolic $G$--space, then the action of $G$ on $\\mathcal{X}$ is a growth tight action. This g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0499","kind":"arxiv","version":4},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1401.0499","created_at":"2026-05-18T01:22:24.538406+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.0499v4","created_at":"2026-05-18T01:22:24.538406+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0499","created_at":"2026-05-18T01:22:24.538406+00:00"},{"alias_kind":"pith_short_12","alias_value":"O45MPKLK2WNU","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_16","alias_value":"O45MPKLK2WNUJF2Z","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_8","alias_value":"O45MPKLK","created_at":"2026-05-18T12:28:41.024544+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/O45MPKLK2WNUJF2Z5AJ5VR35AW","json":"https://pith.science/pith/O45MPKLK2WNUJF2Z5AJ5VR35AW.json","graph_json":"https://pith.science/api/pith-number/O45MPKLK2WNUJF2Z5AJ5VR35AW/graph.json","events_json":"https://pith.science/api/pith-number/O45MPKLK2WNUJF2Z5AJ5VR35AW/events.json","paper":"https://pith.science/paper/O45MPKLK"},"agent_actions":{"view_html":"https://pith.science/pith/O45MPKLK2WNUJF2Z5AJ5VR35AW","download_json":"https://pith.science/pith/O45MPKLK2WNUJF2Z5AJ5VR35AW.json","view_paper":"https://pith.science/paper/O45MPKLK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.0499&json=true","fetch_graph":"https://pith.science/api/pith-number/O45MPKLK2WNUJF2Z5AJ5VR35AW/graph.json","fetch_events":"https://pith.science/api/pith-number/O45MPKLK2WNUJF2Z5AJ5VR35AW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O45MPKLK2WNUJF2Z5AJ5VR35AW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O45MPKLK2WNUJF2Z5AJ5VR35AW/action/storage_attestation","attest_author":"https://pith.science/pith/O45MPKLK2WNUJF2Z5AJ5VR35AW/action/author_attestation","sign_citation":"https://pith.science/pith/O45MPKLK2WNUJF2Z5AJ5VR35AW/action/citation_signature","submit_replication":"https://pith.science/pith/O45MPKLK2WNUJF2Z5AJ5VR35AW/action/replication_record"}},"created_at":"2026-05-18T01:22:24.538406+00:00","updated_at":"2026-05-18T01:22:24.538406+00:00"}