{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:GFRDQNEDK3PCZJB4XOC6SFXDAU","short_pith_number":"pith:GFRDQNED","canonical_record":{"source":{"id":"1610.06864","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-10-21T17:13:25Z","cross_cats_sorted":[],"title_canon_sha256":"eb8f2bf5433bdb3f82350feee281c6be3aa59d86e84d945886293c0458e37466","abstract_canon_sha256":"7aac4354480b94b9e000a6f3c3aa0f3488b6cb67959fdd06bc9e23d67925dee9"},"schema_version":"1.0"},"canonical_sha256":"316238348356de2ca43cbb85e916e305093bf44c17387b8bc96ae58ed39001f5","source":{"kind":"arxiv","id":"1610.06864","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.06864","created_at":"2026-05-18T00:24:53Z"},{"alias_kind":"arxiv_version","alias_value":"1610.06864v3","created_at":"2026-05-18T00:24:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06864","created_at":"2026-05-18T00:24:53Z"},{"alias_kind":"pith_short_12","alias_value":"GFRDQNEDK3PC","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GFRDQNEDK3PCZJB4","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GFRDQNED","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:GFRDQNEDK3PCZJB4XOC6SFXDAU","target":"record","payload":{"canonical_record":{"source":{"id":"1610.06864","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-10-21T17:13:25Z","cross_cats_sorted":[],"title_canon_sha256":"eb8f2bf5433bdb3f82350feee281c6be3aa59d86e84d945886293c0458e37466","abstract_canon_sha256":"7aac4354480b94b9e000a6f3c3aa0f3488b6cb67959fdd06bc9e23d67925dee9"},"schema_version":"1.0"},"canonical_sha256":"316238348356de2ca43cbb85e916e305093bf44c17387b8bc96ae58ed39001f5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:53.152201Z","signature_b64":"HvVL/KWNZjFRBRG2xQKzSqzVj0tDVUPTnpJpqtrWV3hOHTgAgjMjnRnp54ML0OiSUU6eTC+zfQSidnjC1hibCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"316238348356de2ca43cbb85e916e305093bf44c17387b8bc96ae58ed39001f5","last_reissued_at":"2026-05-18T00:24:53.151404Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:53.151404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.06864","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:24:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k8eTFhwt0xQX1cKS7Ae6ueRHgr4txDeopsCljfjyxzJB0ozxEe5xdmAppQ2ejuqmzW6ipHL9aa7hPGlVW7PvDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T21:10:45.725755Z"},"content_sha256":"d107eb0c8bff5a7edb86215e08929c3f467815681a5f36422caba0ad3bda7933","schema_version":"1.0","event_id":"sha256:d107eb0c8bff5a7edb86215e08929c3f467815681a5f36422caba0ad3bda7933"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:GFRDQNEDK3PCZJB4XOC6SFXDAU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on the acylindrical hyperbolicity of groups acting on CAT(0) cube complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alexandre Martin, Indira Chatterji","submitted_at":"2016-10-21T17:13:25Z","abstract_excerpt":"We study the acylindrical hyperbolicity of groups acting by isometries on CAT(0) cube complexes, and obtain simple criteria formulated in terms of stabilisers for the action. Namely, we show that a group acting essentially and non-elementarily on a finite dimensional irreducible CAT(0) cube complex is acylindrically hyperbolic if there exist two hyperplanes whose stabilisers intersect along a finite subgroup. We also give further conditions on the geometry of the complex so that the result holds if we only require the existence of a single pair of points whose stabilisers intersect along a fin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06864","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:24:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Iy86rDRtdgq9VVFxArbJ0mdddY6WwxpWWN8d1MzGSSKOtOqK9uSQatjT7JoJUJK4GBlAfBXLC6Pq6VheEnMjCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T21:10:45.726585Z"},"content_sha256":"3a5dd6aeb7e6e569d9c28640e20e8483da431004cfbeef37d4158542e0923b2c","schema_version":"1.0","event_id":"sha256:3a5dd6aeb7e6e569d9c28640e20e8483da431004cfbeef37d4158542e0923b2c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GFRDQNEDK3PCZJB4XOC6SFXDAU/bundle.json","state_url":"https://pith.science/pith/GFRDQNEDK3PCZJB4XOC6SFXDAU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GFRDQNEDK3PCZJB4XOC6SFXDAU/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-11T21:10:45Z","links":{"resolver":"https://pith.science/pith/GFRDQNEDK3PCZJB4XOC6SFXDAU","bundle":"https://pith.science/pith/GFRDQNEDK3PCZJB4XOC6SFXDAU/bundle.json","state":"https://pith.science/pith/GFRDQNEDK3PCZJB4XOC6SFXDAU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GFRDQNEDK3PCZJB4XOC6SFXDAU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GFRDQNEDK3PCZJB4XOC6SFXDAU","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":"7aac4354480b94b9e000a6f3c3aa0f3488b6cb67959fdd06bc9e23d67925dee9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-10-21T17:13:25Z","title_canon_sha256":"eb8f2bf5433bdb3f82350feee281c6be3aa59d86e84d945886293c0458e37466"},"schema_version":"1.0","source":{"id":"1610.06864","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.06864","created_at":"2026-05-18T00:24:53Z"},{"alias_kind":"arxiv_version","alias_value":"1610.06864v3","created_at":"2026-05-18T00:24:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06864","created_at":"2026-05-18T00:24:53Z"},{"alias_kind":"pith_short_12","alias_value":"GFRDQNEDK3PC","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GFRDQNEDK3PCZJB4","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GFRDQNED","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:3a5dd6aeb7e6e569d9c28640e20e8483da431004cfbeef37d4158542e0923b2c","target":"graph","created_at":"2026-05-18T00:24:53Z","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"},"paper":{"abstract_excerpt":"We study the acylindrical hyperbolicity of groups acting by isometries on CAT(0) cube complexes, and obtain simple criteria formulated in terms of stabilisers for the action. Namely, we show that a group acting essentially and non-elementarily on a finite dimensional irreducible CAT(0) cube complex is acylindrically hyperbolic if there exist two hyperplanes whose stabilisers intersect along a finite subgroup. We also give further conditions on the geometry of the complex so that the result holds if we only require the existence of a single pair of points whose stabilisers intersect along a fin","authors_text":"Alexandre Martin, Indira Chatterji","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-10-21T17:13:25Z","title":"A note on the acylindrical hyperbolicity of groups acting on CAT(0) cube complexes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06864","kind":"arxiv","version":3},"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:d107eb0c8bff5a7edb86215e08929c3f467815681a5f36422caba0ad3bda7933","target":"record","created_at":"2026-05-18T00:24:53Z","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":"7aac4354480b94b9e000a6f3c3aa0f3488b6cb67959fdd06bc9e23d67925dee9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-10-21T17:13:25Z","title_canon_sha256":"eb8f2bf5433bdb3f82350feee281c6be3aa59d86e84d945886293c0458e37466"},"schema_version":"1.0","source":{"id":"1610.06864","kind":"arxiv","version":3}},"canonical_sha256":"316238348356de2ca43cbb85e916e305093bf44c17387b8bc96ae58ed39001f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"316238348356de2ca43cbb85e916e305093bf44c17387b8bc96ae58ed39001f5","first_computed_at":"2026-05-18T00:24:53.151404Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:53.151404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HvVL/KWNZjFRBRG2xQKzSqzVj0tDVUPTnpJpqtrWV3hOHTgAgjMjnRnp54ML0OiSUU6eTC+zfQSidnjC1hibCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:53.152201Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.06864","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d107eb0c8bff5a7edb86215e08929c3f467815681a5f36422caba0ad3bda7933","sha256:3a5dd6aeb7e6e569d9c28640e20e8483da431004cfbeef37d4158542e0923b2c"],"state_sha256":"85f15d184ba3d0f376a83b3af7288586ddbdfc722e740000898a5f19c70b3ee9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VnORjN/G8oE3EbwLtidAaVGAeP9BbJdI4dnfH3/fEfXT8hlplZ5JluJXRNG0Xw4HTjQSdz9T62MaAZNSGfgMBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T21:10:45.731221Z","bundle_sha256":"0e2e40dc5cee9e70192ba9cc810f3a32c535dba254505a21caf3f251252e26a3"}}