{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:367CTRLHALYPZGL3R4JYWIRKYE","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":"d224d4fa87fe1a7166b40a96239c7205817bd8fd15c903249acf19448e5d3438","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2019-07-15T02:43:15Z","title_canon_sha256":"b95c2b43e04f650cc7c7ced7d359329488323f3a8fa5e1f6f36a2e56c68e5345"},"schema_version":"1.0","source":{"id":"1907.06316","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.06316","created_at":"2026-05-17T23:40:37Z"},{"alias_kind":"arxiv_version","alias_value":"1907.06316v1","created_at":"2026-05-17T23:40:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.06316","created_at":"2026-05-17T23:40:37Z"},{"alias_kind":"pith_short_12","alias_value":"367CTRLHALYP","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"367CTRLHALYPZGL3","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"367CTRLH","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:6152bca4195d92a780da55b3e9b868b7d6f26d03bcb6f5fc460c110b19cd744f","target":"graph","created_at":"2026-05-17T23:40:37Z","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":"In \\cite{E_2018}, Ern\\'e relaxed the concept of sobriety in order to extend the theory of sober spaces and locally hypercompact spaces to situations where directed joins were missing, and introduced three kinds of non-sober spaces: cut spaces, weakly sober spaces, and quasisober spaces. In this paper, their basic properties are investigated. It is shown that some properties which are similar to that of sober spaces hold and others do not hold.","authors_text":"Xiaoquan Xu, Xinpeng Wen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2019-07-15T02:43:15Z","title":"On some kinds of weakly sober spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.06316","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:ed26361f17d5f6cd5bbc38329a7120ad28605664b1f2f09adf25a312865c8d56","target":"record","created_at":"2026-05-17T23:40:37Z","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":"d224d4fa87fe1a7166b40a96239c7205817bd8fd15c903249acf19448e5d3438","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2019-07-15T02:43:15Z","title_canon_sha256":"b95c2b43e04f650cc7c7ced7d359329488323f3a8fa5e1f6f36a2e56c68e5345"},"schema_version":"1.0","source":{"id":"1907.06316","kind":"arxiv","version":1}},"canonical_sha256":"dfbe29c56702f0fc997b8f138b222ac1080d0156c67459395091ca7e63216383","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dfbe29c56702f0fc997b8f138b222ac1080d0156c67459395091ca7e63216383","first_computed_at":"2026-05-17T23:40:37.943427Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:37.943427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"br/XtLyiVnklO4V/DSHrqtb5LgEN9sX7rzGgPAkzqHTXU4P0cLbP6Kfbfp+2HRsy9bnHW990guQgcMzEJnNCBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:37.943832Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.06316","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed26361f17d5f6cd5bbc38329a7120ad28605664b1f2f09adf25a312865c8d56","sha256:6152bca4195d92a780da55b3e9b868b7d6f26d03bcb6f5fc460c110b19cd744f"],"state_sha256":"0e46d4254fc315d16180852d50ee72b85a0e67b52c5901e29b0d3a7636eda4f7"}