{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:ARMUJOSTIB67L6ABYHREOQUK7N","short_pith_number":"pith:ARMUJOST","schema_version":"1.0","canonical_sha256":"045944ba53407df5f801c1e247428afb53076d8eab84bd5cd941cec17d557c53","source":{"kind":"arxiv","id":"2608.10114","version":1},"attestation_state":"computed","paper":{"title":"A simple acylindrical recipe for non-split characteristic $2$ sharply $k$-transitive actions and their generalizations","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"J de la Nuez Gonzalez","submitted_at":"2026-08-10T18:32:19Z","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."},"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":"2608.10114","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.GR","submitted_at":"2026-08-10T18:32:19Z","cross_cats_sorted":[],"title_canon_sha256":"158aaca6dfaba89f941f7af2b18fee9b8c8873af16cd9d18f3726cc933dbffa1","abstract_canon_sha256":"daf498d3bf6f00504a202d71482d7bea60a932f8dcd95698cdfcf6cb8253bb8f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-12T00:22:50.778165Z","signature_b64":"OCOKVW00I42RAbTQL41LlD6RkjCQspHoY370VeJ4YwZzEpPtxfo53M7/pJYUXz3AW0T2kJbwq2aRg4I3KNkXDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"045944ba53407df5f801c1e247428afb53076d8eab84bd5cd941cec17d557c53","last_reissued_at":"2026-08-12T00:22:50.776359Z","signature_status":"signed_v1","first_computed_at":"2026-08-12T00:22:50.776359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A simple acylindrical recipe for non-split characteristic $2$ sharply $k$-transitive actions and their generalizations","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"J de la Nuez Gonzalez","submitted_at":"2026-08-10T18:32:19Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.10114","kind":"arxiv","version":1},"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/2608.10114/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":"2608.10114","created_at":"2026-08-12T00:22:50.779026+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.10114v1","created_at":"2026-08-12T00:22:50.779026+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.10114","created_at":"2026-08-12T00:22:50.779026+00:00"},{"alias_kind":"pith_short_12","alias_value":"ARMUJOSTIB67","created_at":"2026-08-12T00:22:50.779026+00:00"},{"alias_kind":"pith_short_16","alias_value":"ARMUJOSTIB67L6AB","created_at":"2026-08-12T00:22:50.779026+00:00"},{"alias_kind":"pith_short_8","alias_value":"ARMUJOST","created_at":"2026-08-12T00:22:50.779026+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/ARMUJOSTIB67L6ABYHREOQUK7N","json":"https://pith.science/pith/ARMUJOSTIB67L6ABYHREOQUK7N.json","graph_json":"https://pith.science/api/pith-number/ARMUJOSTIB67L6ABYHREOQUK7N/graph.json","events_json":"https://pith.science/api/pith-number/ARMUJOSTIB67L6ABYHREOQUK7N/events.json","paper":"https://pith.science/paper/ARMUJOST"},"agent_actions":{"view_html":"https://pith.science/pith/ARMUJOSTIB67L6ABYHREOQUK7N","download_json":"https://pith.science/pith/ARMUJOSTIB67L6ABYHREOQUK7N.json","view_paper":"https://pith.science/paper/ARMUJOST","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.10114&json=true","fetch_graph":"https://pith.science/api/pith-number/ARMUJOSTIB67L6ABYHREOQUK7N/graph.json","fetch_events":"https://pith.science/api/pith-number/ARMUJOSTIB67L6ABYHREOQUK7N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ARMUJOSTIB67L6ABYHREOQUK7N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ARMUJOSTIB67L6ABYHREOQUK7N/action/storage_attestation","attest_author":"https://pith.science/pith/ARMUJOSTIB67L6ABYHREOQUK7N/action/author_attestation","sign_citation":"https://pith.science/pith/ARMUJOSTIB67L6ABYHREOQUK7N/action/citation_signature","submit_replication":"https://pith.science/pith/ARMUJOSTIB67L6ABYHREOQUK7N/action/replication_record"}},"created_at":"2026-08-12T00:22:50.779026+00:00","updated_at":"2026-08-12T00:22:50.779026+00:00"}