{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:7MA7A3E5NZ4OWQMFAOZBEPBDRJ","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":"02b26660137bb71500f00915f9a7e372274d7d55562f2338301cd01b7c930906","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-12-03T15:25:47Z","title_canon_sha256":"37047ff9581725cac7555cd753bce9fa73fd6b78ffb68b094fe65e8455245891"},"schema_version":"1.0","source":{"id":"1712.00780","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.00780","created_at":"2026-05-18T00:29:00Z"},{"alias_kind":"arxiv_version","alias_value":"1712.00780v1","created_at":"2026-05-18T00:29:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.00780","created_at":"2026-05-18T00:29:00Z"},{"alias_kind":"pith_short_12","alias_value":"7MA7A3E5NZ4O","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7MA7A3E5NZ4OWQMF","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7MA7A3E5","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:4b7c809aae342d0137cdc7be9dfc1d49d8f8179cdaa8dc8424630628da5decc4","target":"graph","created_at":"2026-05-18T00:29:00Z","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":"A line pattern in a free group $F$ is defined by a malnormal collection of cyclic subgroups. Otal defined a decomposition space $\\mathcal{D}$ associated to a line pattern. We provide an algorithm that computes a presentation for the \\v{C}ech cohomology of $\\mathcal{D}$, thought of as a $F$-module. This answers a relative version of a question of Epstein about boundaries of hyperbolic groups.","authors_text":"Benjamin Barrett","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-12-03T15:25:47Z","title":"Computing the Cech cohomology of decomposition spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00780","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:fc05865a0211738cbc39df4241cc151dd3122adaf88c22a7d34c5d001df21eb1","target":"record","created_at":"2026-05-18T00:29:00Z","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":"02b26660137bb71500f00915f9a7e372274d7d55562f2338301cd01b7c930906","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-12-03T15:25:47Z","title_canon_sha256":"37047ff9581725cac7555cd753bce9fa73fd6b78ffb68b094fe65e8455245891"},"schema_version":"1.0","source":{"id":"1712.00780","kind":"arxiv","version":1}},"canonical_sha256":"fb01f06c9d6e78eb418503b2123c238a712721696f60957b4b555513114aa5c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb01f06c9d6e78eb418503b2123c238a712721696f60957b4b555513114aa5c7","first_computed_at":"2026-05-18T00:29:00.423671Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:00.423671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GCAXrBsbz/rVLjookagK/mLhGjL4vuEwCl1++MbwDeGcPmhAmopjiSKbVvJ68ubOhUhrhOHWU1ojfhy+MnvPBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:00.424198Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.00780","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc05865a0211738cbc39df4241cc151dd3122adaf88c22a7d34c5d001df21eb1","sha256:4b7c809aae342d0137cdc7be9dfc1d49d8f8179cdaa8dc8424630628da5decc4"],"state_sha256":"38fe955641228a82af870ba8c47593948524bcaba4fdbe78b7d8c315461bcde7"}