{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:X4CR3M3K36I5S7AA7DTQNKEL2I","short_pith_number":"pith:X4CR3M3K","schema_version":"1.0","canonical_sha256":"bf051db36adf91d97c00f8e706a88bd21a37a6bcdb091dbf202f88288bce3f84","source":{"kind":"arxiv","id":"1404.4335","version":2},"attestation_state":"computed","paper":{"title":"Growth Tight Actions of Product Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Christopher H. Cashen, Jing Tao","submitted_at":"2014-04-16T18:18:40Z","abstract_excerpt":"A group action on a metric space is called growth tight if the exponential growth rate of the group with respect to the induced pseudo-metric is strictly greater than that of its quotients. A prototypical example is the action of a free group on its Cayley graph with respect to a free generating set. More generally, with Arzhantseva we have shown that group actions with strongly contracting elements are growth tight.\n  Examples of non-growth tight actions are product groups acting on the $L^1$ products of Cayley graphs of the factors.\n  In this paper we consider actions of product groups on pr"},"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":"1404.4335","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-04-16T18:18:40Z","cross_cats_sorted":[],"title_canon_sha256":"1ac11d9cdf2240c5fecf629e6add10748a25346e580d486edda72749f34fbba7","abstract_canon_sha256":"5408c2ae16858474bdd81bde8627b560d50f1985b7074c959253a5ce211319d0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:01.997484Z","signature_b64":"y1zwPM33k7+rEYahh1ozEhLXtpRjQGAB74FInaTsosqjhM+H9R5U/duv6SxsMWrw7XSAV6ZzDU0XSs5WZ++lCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf051db36adf91d97c00f8e706a88bd21a37a6bcdb091dbf202f88288bce3f84","last_reissued_at":"2026-05-18T01:12:01.997149Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:01.997149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Growth Tight Actions of Product Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Christopher H. Cashen, Jing Tao","submitted_at":"2014-04-16T18:18:40Z","abstract_excerpt":"A group action on a metric space is called growth tight if the exponential growth rate of the group with respect to the induced pseudo-metric is strictly greater than that of its quotients. A prototypical example is the action of a free group on its Cayley graph with respect to a free generating set. More generally, with Arzhantseva we have shown that group actions with strongly contracting elements are growth tight.\n  Examples of non-growth tight actions are product groups acting on the $L^1$ products of Cayley graphs of the factors.\n  In this paper we consider actions of product groups on pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4335","kind":"arxiv","version":2},"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":"1404.4335","created_at":"2026-05-18T01:12:01.997200+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.4335v2","created_at":"2026-05-18T01:12:01.997200+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.4335","created_at":"2026-05-18T01:12:01.997200+00:00"},{"alias_kind":"pith_short_12","alias_value":"X4CR3M3K36I5","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_16","alias_value":"X4CR3M3K36I5S7AA","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_8","alias_value":"X4CR3M3K","created_at":"2026-05-18T12:28:54.890064+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/X4CR3M3K36I5S7AA7DTQNKEL2I","json":"https://pith.science/pith/X4CR3M3K36I5S7AA7DTQNKEL2I.json","graph_json":"https://pith.science/api/pith-number/X4CR3M3K36I5S7AA7DTQNKEL2I/graph.json","events_json":"https://pith.science/api/pith-number/X4CR3M3K36I5S7AA7DTQNKEL2I/events.json","paper":"https://pith.science/paper/X4CR3M3K"},"agent_actions":{"view_html":"https://pith.science/pith/X4CR3M3K36I5S7AA7DTQNKEL2I","download_json":"https://pith.science/pith/X4CR3M3K36I5S7AA7DTQNKEL2I.json","view_paper":"https://pith.science/paper/X4CR3M3K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.4335&json=true","fetch_graph":"https://pith.science/api/pith-number/X4CR3M3K36I5S7AA7DTQNKEL2I/graph.json","fetch_events":"https://pith.science/api/pith-number/X4CR3M3K36I5S7AA7DTQNKEL2I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X4CR3M3K36I5S7AA7DTQNKEL2I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X4CR3M3K36I5S7AA7DTQNKEL2I/action/storage_attestation","attest_author":"https://pith.science/pith/X4CR3M3K36I5S7AA7DTQNKEL2I/action/author_attestation","sign_citation":"https://pith.science/pith/X4CR3M3K36I5S7AA7DTQNKEL2I/action/citation_signature","submit_replication":"https://pith.science/pith/X4CR3M3K36I5S7AA7DTQNKEL2I/action/replication_record"}},"created_at":"2026-05-18T01:12:01.997200+00:00","updated_at":"2026-05-18T01:12:01.997200+00:00"}