{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:O5H7CS5XHQY575ZOSPZMSUHLZH","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":"765b2bc76da01b218d1ca5f610fc41dba9c79b7c4a33aecbad32fba5989e0d72","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-08-14T19:27:27Z","title_canon_sha256":"b3249dbab95e2302421ec585706697703cf42f6a2791090e108f249040ccec3c"},"schema_version":"1.0","source":{"id":"1908.05321","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.05321","created_at":"2026-07-04T23:56:50Z"},{"alias_kind":"arxiv_version","alias_value":"1908.05321v1","created_at":"2026-07-04T23:56:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.05321","created_at":"2026-07-04T23:56:50Z"},{"alias_kind":"pith_short_12","alias_value":"O5H7CS5XHQY5","created_at":"2026-07-04T23:56:50Z"},{"alias_kind":"pith_short_16","alias_value":"O5H7CS5XHQY575ZO","created_at":"2026-07-04T23:56:50Z"},{"alias_kind":"pith_short_8","alias_value":"O5H7CS5X","created_at":"2026-07-04T23:56:50Z"}],"graph_snapshots":[{"event_id":"sha256:495261b92cbe4a94a71c367026b571281892de48cbff86bb6613e9b484e7c36d","target":"graph","created_at":"2026-07-04T23:56:50Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.05321/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we give asymptotics for the conjugacy growth of the soluble Baumslag-Solitar groups $BS(1,k)$, $k\\geq 2$, with respect to the standard generating set, by providing a complete description of geodesic conjugacy representatives. We show that the conjugacy growth series for these groups are transcendental, and give formulas for the series. As a result of our computation we also establish that in each $BS(1,k)$ the conjugacy and standard growth rates are equal.","authors_text":"Alex Evetts, Laura Ciobanu, Meng-Che \"Turbo\" Ho","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-08-14T19:27:27Z","title":"The conjugacy growth of the soluble Baumslag-Solitar groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.05321","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:c7e823f73df3205d4fc5816a62c8d4bf6d6b7bb0cf3c09d7de5e22f14df0e043","target":"record","created_at":"2026-07-04T23:56:50Z","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":"765b2bc76da01b218d1ca5f610fc41dba9c79b7c4a33aecbad32fba5989e0d72","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-08-14T19:27:27Z","title_canon_sha256":"b3249dbab95e2302421ec585706697703cf42f6a2791090e108f249040ccec3c"},"schema_version":"1.0","source":{"id":"1908.05321","kind":"arxiv","version":1}},"canonical_sha256":"774ff14bb73c31dff72e93f2c950ebc9e87caac24bd909154eeaca51e299aa12","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"774ff14bb73c31dff72e93f2c950ebc9e87caac24bd909154eeaca51e299aa12","first_computed_at":"2026-07-04T23:56:50.103253Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:56:50.103253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QnRhpwdjgUBgw1eZsWnAzcpj0wFAEUJ5bXhA1kO29CK9tHCAojWDEIGGq4indsH0Lzz4jMn9tVFtdqBprIsICQ==","signature_status":"signed_v1","signed_at":"2026-07-04T23:56:50.103732Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.05321","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7e823f73df3205d4fc5816a62c8d4bf6d6b7bb0cf3c09d7de5e22f14df0e043","sha256:495261b92cbe4a94a71c367026b571281892de48cbff86bb6613e9b484e7c36d"],"state_sha256":"520a44b5ad2e98e21c64f4ba5aaf27ff8cc0d7cd07163161b51ece0ff9383f4c"}