{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:5UZCICJ3N5SUDK7X6EITHZJE4P","short_pith_number":"pith:5UZCICJ3","canonical_record":{"source":{"id":"1903.05471","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-03-13T13:10:44Z","cross_cats_sorted":[],"title_canon_sha256":"40187623d5ad6cbee147c8b9cc113e971d85bde2326d9311a76179c143abe8c8","abstract_canon_sha256":"595a78bf7b224be8a4dc0704dd67afddfc6474aa574e832a3083a50a750c4b2d"},"schema_version":"1.0"},"canonical_sha256":"ed3224093b6f6541abf7f11133e524e3f99d868b30cd43707a8f0ce49610abcd","source":{"kind":"arxiv","id":"1903.05471","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.05471","created_at":"2026-05-17T23:50:48Z"},{"alias_kind":"arxiv_version","alias_value":"1903.05471v2","created_at":"2026-05-17T23:50:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.05471","created_at":"2026-05-17T23:50:48Z"},{"alias_kind":"pith_short_12","alias_value":"5UZCICJ3N5SU","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"5UZCICJ3N5SUDK7X","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"5UZCICJ3","created_at":"2026-05-18T12:33:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:5UZCICJ3N5SUDK7X6EITHZJE4P","target":"record","payload":{"canonical_record":{"source":{"id":"1903.05471","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-03-13T13:10:44Z","cross_cats_sorted":[],"title_canon_sha256":"40187623d5ad6cbee147c8b9cc113e971d85bde2326d9311a76179c143abe8c8","abstract_canon_sha256":"595a78bf7b224be8a4dc0704dd67afddfc6474aa574e832a3083a50a750c4b2d"},"schema_version":"1.0"},"canonical_sha256":"ed3224093b6f6541abf7f11133e524e3f99d868b30cd43707a8f0ce49610abcd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:48.495989Z","signature_b64":"n0sD53QdYykQRnC0Td/YEiyMZ1c/RGNKlxMh0NFRg/Z/44jsKpCMWhAah/Tk3NRMsZzltptBn2qFYNB/9hUWAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed3224093b6f6541abf7f11133e524e3f99d868b30cd43707a8f0ce49610abcd","last_reissued_at":"2026-05-17T23:50:48.495395Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:48.495395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.05471","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:50:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QskS1CQCQP+zAVTpkgMj9qm0xv5RUGoMhP6ioXE2aVjwQ9uNCgIoZPnYTwoW2TBMVHmeg4WommLnaUD8hsXlCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T13:30:07.309021Z"},"content_sha256":"870347e306818a7156b8dbc5515e0da211b3a1d3bb1a40c9faa38d945f481796","schema_version":"1.0","event_id":"sha256:870347e306818a7156b8dbc5515e0da211b3a1d3bb1a40c9faa38d945f481796"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:5UZCICJ3N5SUDK7X6EITHZJE4P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On hyperbolicity and virtual freeness of automorphism groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Olga Varghese","submitted_at":"2019-03-13T13:10:44Z","abstract_excerpt":"We show that word hyperbolicity of automorphism groups of graph products $G_\\Gamma$ and of Coxeter groups $W_\\Gamma$ depends strongly on the shape of the defining graph $\\Gamma$. We also characterized those $Aut(G_\\Gamma)$ and $Aut(W_\\Gamma)$ in terms of $\\Gamma$ that are virtually free."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.05471","kind":"arxiv","version":2},"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":"2026-05-17T23:50:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"op6PnB+w3Nhvr40evlry8VC00tjW9G/kUrtaUtTLZZnniNsOiPu6XIzh0LXf+cpqi7Kj+orCJG5K+W/NHbJkAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T13:30:07.309372Z"},"content_sha256":"9b34e5c0f9590524e1a8f13a834f5bf6c9983171e77dd0bc795e131d8f84e1dc","schema_version":"1.0","event_id":"sha256:9b34e5c0f9590524e1a8f13a834f5bf6c9983171e77dd0bc795e131d8f84e1dc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5UZCICJ3N5SUDK7X6EITHZJE4P/bundle.json","state_url":"https://pith.science/pith/5UZCICJ3N5SUDK7X6EITHZJE4P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5UZCICJ3N5SUDK7X6EITHZJE4P/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":"2026-07-03T13:30:07Z","links":{"resolver":"https://pith.science/pith/5UZCICJ3N5SUDK7X6EITHZJE4P","bundle":"https://pith.science/pith/5UZCICJ3N5SUDK7X6EITHZJE4P/bundle.json","state":"https://pith.science/pith/5UZCICJ3N5SUDK7X6EITHZJE4P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5UZCICJ3N5SUDK7X6EITHZJE4P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:5UZCICJ3N5SUDK7X6EITHZJE4P","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":"595a78bf7b224be8a4dc0704dd67afddfc6474aa574e832a3083a50a750c4b2d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-03-13T13:10:44Z","title_canon_sha256":"40187623d5ad6cbee147c8b9cc113e971d85bde2326d9311a76179c143abe8c8"},"schema_version":"1.0","source":{"id":"1903.05471","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.05471","created_at":"2026-05-17T23:50:48Z"},{"alias_kind":"arxiv_version","alias_value":"1903.05471v2","created_at":"2026-05-17T23:50:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.05471","created_at":"2026-05-17T23:50:48Z"},{"alias_kind":"pith_short_12","alias_value":"5UZCICJ3N5SU","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"5UZCICJ3N5SUDK7X","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"5UZCICJ3","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:9b34e5c0f9590524e1a8f13a834f5bf6c9983171e77dd0bc795e131d8f84e1dc","target":"graph","created_at":"2026-05-17T23:50:48Z","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 show that word hyperbolicity of automorphism groups of graph products $G_\\Gamma$ and of Coxeter groups $W_\\Gamma$ depends strongly on the shape of the defining graph $\\Gamma$. We also characterized those $Aut(G_\\Gamma)$ and $Aut(W_\\Gamma)$ in terms of $\\Gamma$ that are virtually free.","authors_text":"Olga Varghese","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-03-13T13:10:44Z","title":"On hyperbolicity and virtual freeness of automorphism groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.05471","kind":"arxiv","version":2},"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":"sha256:870347e306818a7156b8dbc5515e0da211b3a1d3bb1a40c9faa38d945f481796","target":"record","created_at":"2026-05-17T23:50:48Z","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":"595a78bf7b224be8a4dc0704dd67afddfc6474aa574e832a3083a50a750c4b2d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-03-13T13:10:44Z","title_canon_sha256":"40187623d5ad6cbee147c8b9cc113e971d85bde2326d9311a76179c143abe8c8"},"schema_version":"1.0","source":{"id":"1903.05471","kind":"arxiv","version":2}},"canonical_sha256":"ed3224093b6f6541abf7f11133e524e3f99d868b30cd43707a8f0ce49610abcd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ed3224093b6f6541abf7f11133e524e3f99d868b30cd43707a8f0ce49610abcd","first_computed_at":"2026-05-17T23:50:48.495395Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:48.495395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n0sD53QdYykQRnC0Td/YEiyMZ1c/RGNKlxMh0NFRg/Z/44jsKpCMWhAah/Tk3NRMsZzltptBn2qFYNB/9hUWAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:48.495989Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.05471","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:870347e306818a7156b8dbc5515e0da211b3a1d3bb1a40c9faa38d945f481796","sha256:9b34e5c0f9590524e1a8f13a834f5bf6c9983171e77dd0bc795e131d8f84e1dc"],"state_sha256":"28b387519175df078b43238cc7ccd0e7dcab2ba62b7f51e0a3e5d7e3380e16a3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HTKIU6hgJrVLT/jztlZ5chrdbj5LVrAsXHDu1340nHsx9yIp5XA1yLwdgLdsfpQX0h+Db0VynSdPKXOABuRVCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T13:30:07.311292Z","bundle_sha256":"7f0b2c3881338574510cbf36493574d90a5e1cf5c65af362eee5b1f16c4a5fe4"}}