{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:BHWWMK7G3WK6ICR6YOWQN4FIOQ","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":"6529be627f975b9ae376a8e6d072a4bd265f44938d9971ed6ec45156d027d868","cross_cats_sorted":["math.GR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2023-09-15T19:52:52Z","title_canon_sha256":"01df82e73e3c4f10ef2b4066333f240243e589e458acecdc85d65bfa6570e6c5"},"schema_version":"1.0","source":{"id":"2309.08735","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.08735","created_at":"2026-05-20T00:02:45Z"},{"alias_kind":"arxiv_version","alias_value":"2309.08735v3","created_at":"2026-05-20T00:02:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.08735","created_at":"2026-05-20T00:02:45Z"},{"alias_kind":"pith_short_12","alias_value":"BHWWMK7G3WK6","created_at":"2026-05-20T00:02:45Z"},{"alias_kind":"pith_short_16","alias_value":"BHWWMK7G3WK6ICR6","created_at":"2026-05-20T00:02:45Z"},{"alias_kind":"pith_short_8","alias_value":"BHWWMK7G","created_at":"2026-05-20T00:02:45Z"}],"graph_snapshots":[{"event_id":"sha256:076d42fb91c8b59e1460f8e1cde3cd2aea1044947afbc94f9fe104c5bf1a8ea4","target":"graph","created_at":"2026-05-20T00:02:45Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2309.08735/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study relatively hyperbolic group pairs whose boundaries are Schottky sets. We characterize the groups that have boundaries where the Schottky sets have incidence graphs with 1 or 2 components.","authors_text":"Genevieve Walsh, Luisa Paoluzzi, Peter Ha\\\"issinsky","cross_cats":["math.GR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2023-09-15T19:52:52Z","title":"On groups with Schottky set boundary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.08735","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":"sha256:05fc4c57f5eed90d25600d94240521c0bd5723f8aa29c1e44f0174484ca9c30f","target":"record","created_at":"2026-05-20T00:02:45Z","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":"6529be627f975b9ae376a8e6d072a4bd265f44938d9971ed6ec45156d027d868","cross_cats_sorted":["math.GR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2023-09-15T19:52:52Z","title_canon_sha256":"01df82e73e3c4f10ef2b4066333f240243e589e458acecdc85d65bfa6570e6c5"},"schema_version":"1.0","source":{"id":"2309.08735","kind":"arxiv","version":3}},"canonical_sha256":"09ed662be6dd95e40a3ec3ad06f0a87428bc93eae9a81292d0e930a7089f69f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"09ed662be6dd95e40a3ec3ad06f0a87428bc93eae9a81292d0e930a7089f69f9","first_computed_at":"2026-05-20T00:02:45.262687Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:02:45.262687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YVYsS1ebmuS3DDM8V8154p8XPssJTGzxB5QTs1XL/YfyMDXqbTCcvQN+NDwV8At+fZuOe0JG8MCXt7EGrC3fBA==","signature_status":"signed_v1","signed_at":"2026-05-20T00:02:45.263398Z","signed_message":"canonical_sha256_bytes"},"source_id":"2309.08735","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05fc4c57f5eed90d25600d94240521c0bd5723f8aa29c1e44f0174484ca9c30f","sha256:076d42fb91c8b59e1460f8e1cde3cd2aea1044947afbc94f9fe104c5bf1a8ea4"],"state_sha256":"b6f5370ee6eacd9d3bce3103f127f823e67499f3b9373c268baa1163fd7287f6"}