{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:O6DVCK4KFVTDSL4VLSG36XT5BZ","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":"2356f3bc82d3f72e5caf4aa1a98a3699436d6243cbfafa5f6e82e8bb87338987","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-05-14T18:01:10Z","title_canon_sha256":"c0ccf3e7af5b3c4f95894f21384e3aa34c5eaf0fff4cd02da639138438eeb8f8"},"schema_version":"1.0","source":{"id":"1505.03817","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.03817","created_at":"2026-05-17T23:52:19Z"},{"alias_kind":"arxiv_version","alias_value":"1505.03817v1","created_at":"2026-05-17T23:52:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.03817","created_at":"2026-05-17T23:52:19Z"},{"alias_kind":"pith_short_12","alias_value":"O6DVCK4KFVTD","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"O6DVCK4KFVTDSL4V","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"O6DVCK4K","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:1bacf0e0a609415d5dfa9f70c9a810f258811e1e01f95a820316fa89d130044e","target":"graph","created_at":"2026-05-17T23:52:19Z","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":"For n>6, we show that if G is a torsion-free hyperbolic group whose visual boundary is an (n-2)-dimensional Sierpinski space, then G=\\pi_1(W) for some aspherical n-manifold W with nonempty boundary. Concerning the converse, we construct, for each n>3, examples of aspherical manifolds with boundary, whose fundamental group G is hyperbolic, but with visual boundary not homeomorphic to an (n-2)-dimensional Sierpinski space.","authors_text":"Bena Tshishiku, Jean-Fran\\c{c}ois Lafont","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-05-14T18:01:10Z","title":"Hyperbolic groups with boundary an n-dimensional Sierpinski space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03817","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":"sha256:634a1b477f0a3f8899bb073f1ea4892bc332a4549aa6c87160af42be24f1c5c3","target":"record","created_at":"2026-05-17T23:52:19Z","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":"2356f3bc82d3f72e5caf4aa1a98a3699436d6243cbfafa5f6e82e8bb87338987","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-05-14T18:01:10Z","title_canon_sha256":"c0ccf3e7af5b3c4f95894f21384e3aa34c5eaf0fff4cd02da639138438eeb8f8"},"schema_version":"1.0","source":{"id":"1505.03817","kind":"arxiv","version":1}},"canonical_sha256":"7787512b8a2d66392f955c8dbf5e7d0e4092eac639799416635d81ec32c36f4c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7787512b8a2d66392f955c8dbf5e7d0e4092eac639799416635d81ec32c36f4c","first_computed_at":"2026-05-17T23:52:19.334362Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:19.334362Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0f6utpL5uHnbzouCZikt+fUMAfeMuvBcaopqMXPVhQGFVbdDyfaZgDR18ICK53uRnn5Sig8FBT2bBvLzuEACBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:19.335052Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.03817","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:634a1b477f0a3f8899bb073f1ea4892bc332a4549aa6c87160af42be24f1c5c3","sha256:1bacf0e0a609415d5dfa9f70c9a810f258811e1e01f95a820316fa89d130044e"],"state_sha256":"0fced6153bd3ac5733571c282e954feb09baf171c15bb8968232c768d68b24be"}