{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ARMUJOSTIB67L6ABYHREOQUK7N","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":"daf498d3bf6f00504a202d71482d7bea60a932f8dcd95698cdfcf6cb8253bb8f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.GR","submitted_at":"2026-08-10T18:32:19Z","title_canon_sha256":"158aaca6dfaba89f941f7af2b18fee9b8c8873af16cd9d18f3726cc933dbffa1"},"schema_version":"1.0","source":{"id":"2608.10114","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.10114","created_at":"2026-08-12T00:22:50Z"},{"alias_kind":"arxiv_version","alias_value":"2608.10114v1","created_at":"2026-08-12T00:22:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.10114","created_at":"2026-08-12T00:22:50Z"},{"alias_kind":"pith_short_12","alias_value":"ARMUJOSTIB67","created_at":"2026-08-12T00:22:50Z"},{"alias_kind":"pith_short_16","alias_value":"ARMUJOSTIB67L6AB","created_at":"2026-08-12T00:22:50Z"},{"alias_kind":"pith_short_8","alias_value":"ARMUJOST","created_at":"2026-08-12T00:22:50Z"}],"graph_snapshots":[{"event_id":"sha256:cd5360c8df3791410b6593cee8cf86c859bbde5eec8fdb303bdd6d59b2f5c3e4","target":"graph","created_at":"2026-08-12T00:22:50Z","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/2608.10114/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We provide a fairly simple list of conditions on a group $G$ acting acylindrically on a $\\delta$-hyperbolic metric space implying that the group admits an action on a set that is $k$-sharp, transitive on $k$-sets and has the property that for any $k$-set $A$ the setwise stabilizer of $A$ acts on $A$ as prescribed by some fixed subgroup $\\Theta\\leq\\sym_{k}$. In particular, this yields many easy examples of finitely generated and even presented split sharply $2$ and $3$-transitive actions.","authors_text":"J de la Nuez Gonzalez","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.GR","submitted_at":"2026-08-10T18:32:19Z","title":"A simple acylindrical recipe for non-split characteristic $2$ sharply $k$-transitive actions and their generalizations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.10114","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":"sha256:407b6f96735a23c2dce4785796e40e78c7a826588b99c65e7268465601517827","target":"record","created_at":"2026-08-12T00:22:50Z","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":"daf498d3bf6f00504a202d71482d7bea60a932f8dcd95698cdfcf6cb8253bb8f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.GR","submitted_at":"2026-08-10T18:32:19Z","title_canon_sha256":"158aaca6dfaba89f941f7af2b18fee9b8c8873af16cd9d18f3726cc933dbffa1"},"schema_version":"1.0","source":{"id":"2608.10114","kind":"arxiv","version":1}},"canonical_sha256":"045944ba53407df5f801c1e247428afb53076d8eab84bd5cd941cec17d557c53","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"045944ba53407df5f801c1e247428afb53076d8eab84bd5cd941cec17d557c53","first_computed_at":"2026-08-12T00:22:50.776359Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-12T00:22:50.776359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OCOKVW00I42RAbTQL41LlD6RkjCQspHoY370VeJ4YwZzEpPtxfo53M7/pJYUXz3AW0T2kJbwq2aRg4I3KNkXDA==","signature_status":"signed_v1","signed_at":"2026-08-12T00:22:50.778165Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.10114","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:407b6f96735a23c2dce4785796e40e78c7a826588b99c65e7268465601517827","sha256:cd5360c8df3791410b6593cee8cf86c859bbde5eec8fdb303bdd6d59b2f5c3e4"],"state_sha256":"c7836a2f696445ce955d80fb4ded45491760727d0e2cf242340c0f79e6b2ec15"}