{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:Z4IHASIKJ3RQ5HUSHRCMTUN7B6","short_pith_number":"pith:Z4IHASIK","canonical_record":{"source":{"id":"1101.5191","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-01-27T01:23:07Z","cross_cats_sorted":[],"title_canon_sha256":"2b2170e36a37dfeccdb0b46fb4f6dfb23827c9425d2dd49ac9c399f643a0139a","abstract_canon_sha256":"bfffea85e4a20af37144be3afbe5c007fb60c6891a4301dee42f0ec8819cc947"},"schema_version":"1.0"},"canonical_sha256":"cf1070490a4ee30e9e923c44c9d1bf0fbb40970cbe4bc1d5e7725ce4a2f6a33d","source":{"kind":"arxiv","id":"1101.5191","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.5191","created_at":"2026-05-18T02:22:49Z"},{"alias_kind":"arxiv_version","alias_value":"1101.5191v6","created_at":"2026-05-18T02:22:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.5191","created_at":"2026-05-18T02:22:49Z"},{"alias_kind":"pith_short_12","alias_value":"Z4IHASIKJ3RQ","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"Z4IHASIKJ3RQ5HUS","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"Z4IHASIK","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:Z4IHASIKJ3RQ5HUSHRCMTUN7B6","target":"record","payload":{"canonical_record":{"source":{"id":"1101.5191","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-01-27T01:23:07Z","cross_cats_sorted":[],"title_canon_sha256":"2b2170e36a37dfeccdb0b46fb4f6dfb23827c9425d2dd49ac9c399f643a0139a","abstract_canon_sha256":"bfffea85e4a20af37144be3afbe5c007fb60c6891a4301dee42f0ec8819cc947"},"schema_version":"1.0"},"canonical_sha256":"cf1070490a4ee30e9e923c44c9d1bf0fbb40970cbe4bc1d5e7725ce4a2f6a33d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:22:49.318015Z","signature_b64":"YL7C8BcEe9AGp1LPMQnHJTINgtsgyfO1k4bROztgi5tw5Xtps4JD/iBi7KPIZ3Bd1HPxnP4YgVWrg9OIGZ5PDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf1070490a4ee30e9e923c44c9d1bf0fbb40970cbe4bc1d5e7725ce4a2f6a33d","last_reissued_at":"2026-05-18T02:22:49.317162Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:22:49.317162Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.5191","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:22:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z80zaXhUYSG8vC8dDAQUOz3snjjTH3uzqjYkDGmNyUZN49ef2ihUTd1gDKum9mRcs2GKyqpnmDNGBBVI3uixCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T23:49:40.175438Z"},"content_sha256":"26b95f19c22bef486b768f12b1244922a6135425162bdd51c65a161302b44c54","schema_version":"1.0","event_id":"sha256:26b95f19c22bef486b768f12b1244922a6135425162bdd51c65a161302b44c54"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:Z4IHASIKJ3RQ5HUSHRCMTUN7B6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weak hyperbolicity of cube complexes and quasi-arboreal groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Mark F. Hagen","submitted_at":"2011-01-27T01:23:07Z","abstract_excerpt":"We examine a graph $\\Gamma$ encoding the intersection of hyperplane carriers in a CAT(0) cube complex $\\widetilde X$. The main result is that $\\Gamma$ is quasi-isometric to a tree. This implies that a group $G$ acting properly and cocompactly on $\\widetilde X$ is weakly hyperbolic relative to the hyperplane stabilizers. Using disc diagram techniques and Wright's recent result on the aymptotic dimension of CAT(0) cube complexes, we give a generalization of a theorem of Bell and Dranishnikov on the finite asymptotic dimension of graphs of asymptotically finite-dimensional groups. More precisely,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.5191","kind":"arxiv","version":6},"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":"2026-05-18T02:22:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b7kZ0ZmjroGIjW5vsr9hnCT7fkHrkAR8XPaeuC8a4ahmM8FcJOirhGXA5Ih38GehG731TIfvAAQR97mGxV4DDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T23:49:40.175799Z"},"content_sha256":"eab7680f02abd94673b73e04a510316c22e95ced2cea88c6cf8d6f3f874bbb89","schema_version":"1.0","event_id":"sha256:eab7680f02abd94673b73e04a510316c22e95ced2cea88c6cf8d6f3f874bbb89"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z4IHASIKJ3RQ5HUSHRCMTUN7B6/bundle.json","state_url":"https://pith.science/pith/Z4IHASIKJ3RQ5HUSHRCMTUN7B6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z4IHASIKJ3RQ5HUSHRCMTUN7B6/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":"2026-07-04T23:49:40Z","links":{"resolver":"https://pith.science/pith/Z4IHASIKJ3RQ5HUSHRCMTUN7B6","bundle":"https://pith.science/pith/Z4IHASIKJ3RQ5HUSHRCMTUN7B6/bundle.json","state":"https://pith.science/pith/Z4IHASIKJ3RQ5HUSHRCMTUN7B6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z4IHASIKJ3RQ5HUSHRCMTUN7B6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:Z4IHASIKJ3RQ5HUSHRCMTUN7B6","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":"bfffea85e4a20af37144be3afbe5c007fb60c6891a4301dee42f0ec8819cc947","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-01-27T01:23:07Z","title_canon_sha256":"2b2170e36a37dfeccdb0b46fb4f6dfb23827c9425d2dd49ac9c399f643a0139a"},"schema_version":"1.0","source":{"id":"1101.5191","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.5191","created_at":"2026-05-18T02:22:49Z"},{"alias_kind":"arxiv_version","alias_value":"1101.5191v6","created_at":"2026-05-18T02:22:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.5191","created_at":"2026-05-18T02:22:49Z"},{"alias_kind":"pith_short_12","alias_value":"Z4IHASIKJ3RQ","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"Z4IHASIKJ3RQ5HUS","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"Z4IHASIK","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:eab7680f02abd94673b73e04a510316c22e95ced2cea88c6cf8d6f3f874bbb89","target":"graph","created_at":"2026-05-18T02:22:49Z","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 examine a graph $\\Gamma$ encoding the intersection of hyperplane carriers in a CAT(0) cube complex $\\widetilde X$. The main result is that $\\Gamma$ is quasi-isometric to a tree. This implies that a group $G$ acting properly and cocompactly on $\\widetilde X$ is weakly hyperbolic relative to the hyperplane stabilizers. Using disc diagram techniques and Wright's recent result on the aymptotic dimension of CAT(0) cube complexes, we give a generalization of a theorem of Bell and Dranishnikov on the finite asymptotic dimension of graphs of asymptotically finite-dimensional groups. More precisely,","authors_text":"Mark F. Hagen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-01-27T01:23:07Z","title":"Weak hyperbolicity of cube complexes and quasi-arboreal groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.5191","kind":"arxiv","version":6},"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":"sha256:26b95f19c22bef486b768f12b1244922a6135425162bdd51c65a161302b44c54","target":"record","created_at":"2026-05-18T02:22:49Z","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":"bfffea85e4a20af37144be3afbe5c007fb60c6891a4301dee42f0ec8819cc947","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-01-27T01:23:07Z","title_canon_sha256":"2b2170e36a37dfeccdb0b46fb4f6dfb23827c9425d2dd49ac9c399f643a0139a"},"schema_version":"1.0","source":{"id":"1101.5191","kind":"arxiv","version":6}},"canonical_sha256":"cf1070490a4ee30e9e923c44c9d1bf0fbb40970cbe4bc1d5e7725ce4a2f6a33d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf1070490a4ee30e9e923c44c9d1bf0fbb40970cbe4bc1d5e7725ce4a2f6a33d","first_computed_at":"2026-05-18T02:22:49.317162Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:22:49.317162Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YL7C8BcEe9AGp1LPMQnHJTINgtsgyfO1k4bROztgi5tw5Xtps4JD/iBi7KPIZ3Bd1HPxnP4YgVWrg9OIGZ5PDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:22:49.318015Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.5191","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:26b95f19c22bef486b768f12b1244922a6135425162bdd51c65a161302b44c54","sha256:eab7680f02abd94673b73e04a510316c22e95ced2cea88c6cf8d6f3f874bbb89"],"state_sha256":"14474f01633164cf64b7232945cdf40ff0e28f09498734ff15149bb05496c7b3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wykI8YLTCd33kNvc+f3rUk14BnNpvc/7G2FDMGp6meDRO+ev9TZT+k+L3+kYM8QUYC3c+EobDqAbg85ETfk0DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T23:49:40.177661Z","bundle_sha256":"17c90b45686f339e3ee1cd9a03d5def95025db182f333145459f0b90d9c3180b"}}